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Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
1
Control of an MR Tuned Vibration Absorber for Wind Turbine Application
Utilising the Refined Force Tracking Algorithm
Paweł Martynowicz
AGH University of Science and Technology Department of Process Control al Mickiewicza
30 30-059 Cracow Poland
e-mail pmartynaghedupl
ABSTRACT
This work covers selected control issues concerning the wind turbine tower-nacelle
laboratory model equipped with a magnetorheological (MR) damper based tuned vibration
absorber (TVA) The objective of the current research is a development and experimental
implementation of the control algorithm that couples a basic adaptive stiffness solution with
refined stock MR damper force tracking concept to obtain a quality tower vibration reduction
system The experiments were conducted assuming monoharmonic horizontal excitation
applied to the assembly modelling the nacelle The frequency range comprised the
neighbourhood of the first bending mode of the tower-nacelle system The results proved the
effectiveness of the adopted algorithm referring to the other high performance solutions
1 INTRODUCTION
The wind energy sector is rapidly growing nowadays Wind turbines are ecological solutions
yet their implementation cost is significant Structural vibrations and their consequences
imply relatively high investment into the construction process which is one of the greatest
contributors to the amount that wind farm implementation costs The aerodynamic load (and
the hydrodynamicice load for offshore structures) that varies in time including wind shear
Karman vortices blade passing effect differences in inflow conditions for each of the blades
as well as rotating turbine elements unbalance and generator operation these are the major
contributors to the structural vibrations of towers and blades [1] The cyclic stress that the
tower is subjected to may decrease reliable operation time due to structure fatigue wear [2]
or even a failure accident These vibrations are generally lightly damped especially
considering low aeroelastic damping for the first tower lateral mode [3456] The lateral
modes are excited due to Karman vortices generator operation sea wave variable load and
rotating machinery unbalance rather than due to direct wind load variations and the blade
passing effect as for longitudinal modes In the current project tower vibration only is being
analysed
The solutions utilised to reduce wind turbines towers vibrations include collective blade
pitch control generator electromagnetic torque control [789] and tuned vibration absorbers
(TVAs) [10111213] In the standard (passive) approach a TVA consists of an additional
moving mass spring and viscous damper which parameters are tuned to the selected (most
often the first) mode of vibration [1014] Passive TVAs work well at the load conditions
characterised with a single frequency to which they are tuned but cannot adapt to a wide
excitation spectrum [15] thus more advanced TVAs are required to changetune the TVA
operating frequency Among them magnetorheological (MR) TVAs are placed [15] as using
an MR damper instead of a viscous one guarantees a wide range of resistance force
millisecond response time high operational robustness including lower sensitivity to
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
2
temperature change and minor energy requirements as compared with active systems
[1617181920212223] Simulations and experiments show that implementation of an MR
damper in the TVA system may lead to further vibration reduction in relation to passive TVA
[24252627]
Within the scope of the current project a specially developed and built tower-nacelle
laboratory model (Fig 1) was made in which all turbine components (a nacelle blades a
hub a shaft a generator and possibly a gearbox) are represented by nacelle concentrated
mass The laboratory test rig of the wind turbine tower-nacelle system makes it possible to
model tower vibrations under various excitation sources as the horizontal concentrated force
generated by the dedicated shaker may model the load applied to the nacelle or to the tower
itself at the arbitrary height Both locations enable to force tower bending modes of vibration
The rig may also be laid down on the horizontally excited platform to model the vibrations of
buoy-floating wind turbine structures or vibrations due to seismic excitation
The problem of wind turbine tower vibration control with an MR TVA utilising an
adaptive stiffness concept with a newly developed force tracking algorithm is presented here
Both the adaptive stiffness and the MR damper force tracking solutions were investigated
previously separately however limited (numerical or hardware in the loop only continuous ndash
with no discontinuities or two-level force current pattern regarded) implementation
scenarios were presented only [2829303132] or the quality of the force follow-up left the
field for further improvements [242526] The MR damper real-time force tracking problem
along with the adaptive stiffness and damping friction was investigated extensively with fair
results in [33343536] Weber in [33] uses a series of BoucndashWen models computed in
parallel to estimate the required control current with no need of force sensor however
presented measured tracking of clipped viscous damping with negative stiffness exhibits slow
force rise after piston velocity sign change The interesting logics is adopted in [34] for a
system tailored MR damper dealing separately with the regions of rapid MR damper force
increase decrease and the transition between these two relations together with the negative
current spikes just before the desired force sign changes However measured real-time
tracking of force patterns exhibiting negative stiffness is again characterised with
insufficiently sharp force rise while tracking of force patterns exhibiting positive stiffness is
characterised with significant force error (overshoot) due to the remanent magnetization
These two problems occurring either if the actual MR damper force should be quickly
increased to a large value or if the force should be rapidly decreased to zero both at the
displacement extreme (and force sign change) are not removed by this approach utilising MR
damper inverse model feed forward and force sensor feedback even using negative current
applied each half cycle [35] Weber in [36] also uses MR damper inverse model combined
with force sensor Again measured real-time tracking of force patterns is characterised with
insufficiently rapid force rise or significant overshoot both after force sign change
The current work covers real-time realisation of the improved (over the previous solutions
[24252629313237]) stock MR damper continuous pattern tracking algorithm coping well
with the discontinuities (rapid value changes) of the force and the magnetic remanence
combining MR damper forward model with force sign change prediction (feed forward)
force sensor feedback and dedicated logics together with a basic adaptive stiffness
implementation resulting in a quality vibration reduction system As a reference passive
solutions with several MR damper constant input current values the adaptive stiffness
concept with previously tested MR damper hyperbolic tangent inverse model and PI-based
force tracking algorithms [24252629313237] along with a modified ground hook control
[2526] results are presented Only the first bending mode of vibration frequency
neighbourhood is analysed here
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
3
The paper is organised as follows In the forthcoming section the wind turbine tower-
nacelle laboratory model is introduced Then a vibration control algorithm is presented and
followed by the experimental analysis results The paper is finished with several conclusions
2 THE WIND TURBINE TOWER-NACELLE LABORATORY MODEL
The model to be analysed (Fig 1) consists of a titanium (Ti Gr5) rod 1 arranged vertically
representing the wind-turbine tower and a stiff body (system of steel plates) 2 fixed rigidly to
the top of the rod representing both nacelle and turbine assemblies The bottom end of the
rod is rigidly mounted to the ground via an adequately stiff steel foundation frame 3 As the
first tower bending mode has dominant modal mass participation (ca fivefold greater than the
next mode) a vibration reduction system (an MR TVA) is located at the top of the rod (at the
nacelle) The MR TVA is an additional stiff body 6 (an absorber) moving horizontally along
linear bearing guides connected with the system representing the nacelle via a spring and
Lord RD 1097-1 MR damper [38] in parallel 7 The absorber mass m2 and the spring stiffness
k2 parameters of the TVA were tuned to the first bending mode of the tower-nacelle system
vibrations on the basis of standard principles of the TVA tuning [10] The RD 1097-1 damper
(which force depends on the current fed to its coil) is an actuator of such vibration reduction
system The MR TVA operates along the same direction as the vibration excitation applied
(assuming small bending angles) Force excitation system comprises The Modal Shop
lightweight electrodynamic force exciter of 2060E series 4 [39] with the drive train assembly
5 of the changeable leverage [4041424344]
The horizontal displacement and velocity of the system modelling the nacelle are
designated by x1 and v1 (respectively) while the horizontal displacement and velocity of the
absorber (the TVA mass) are x2 and v2 Thus x1ndashx2 designates the MR damper relative
displacement (that is measured by LVDT transducer 8) while v1ndashv2 designates the MR
damper relative velocity The MR damper force PMR is measured by the tensometric
transducer 9
Figure 1 The laboratory test rig
1
2 6
3
4
5
6 7 9
8 2
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
4
3 THE CONTROL ALGORITHM
The underlying idea of the implemented control system is presented in Fig 2 Three
measurement input signals are regarded spring MR damper relative displacement x1ndashx2meas
MR damper current iMRmeas and MR damper force PMR
meas The MR Damper Required Force
subsystem corresponds to the real-time calculation of the demanded MR damper force PMRreq
ndash for the purpose of the current analysis the algorithm of the undamped dynamic vibration
absorber [10] that tracks excitation frequency [252628] is emulated using the MR damper
The MR damper should generate positive or negative stiffness force in such a way that the
TVA stiffness 2
reqk in equations (1) and (2) is tuned to the actual operationexcitation
frequency exc rather than to the tower-nacelle system first bending frequency Based on this
assumption the real-time determination of exc is followed by the real-time calculation of the
TVA required stiffness force 2 1 2
req req
stiffP k x x while the damping is assumed to be zero
(for the most efficient vibration mitigation at the frequency of tuning) leading to the MR
damper required force formula
2 2 1 2
req req
MRP k k x x (1)
with
2
2
2
req
exck m (2)
where γ is a correction factor that is present as the MR damper cannot deliver energy to the
system thus the force defined by equation (1) cannot be exactly mapped
Figure 2 The schematic diagram of the control system
When active forces are required zero force is assumed Thus arises a problem of a precise
MR damper force tracking in the case of pattern being discontinuous due to such a switching
A quick timeous (with possible prediction) and sharp force follow-up is needed whereas the
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
5
actuator dynamics exhibits the inertia due to the coil electrical resistance and inductance
magnetic remanence as well as the time lag hysteresis resulting from the MR effect
(particle chains formation) delay MR fluid preyield operation regime These effects cannot
be eliminated by a simple PIPID feedback controller with the sign adjustments
[242526313237] as it can shape the force-velocity relationship only into a linear or a
higher-order polynomial function with the inherent time lag even utilising the adequate
current controller Thus a dedicated MR damper force follow-up PID-based control
algorithm that was specially developed and refined during the current study based on
[252631] is represented by the PID Force Controller with Correction Demagnetisation amp
Sharpening subsystem (see Fig 2) Apart from the demanded MR damper force PMRreq input
the measured actual MR damper force PMRmeas and the modelled MR damper force PMR
modelled
signals are fed to the input of this subsystem PMRmodelled is the real-time calculated force with
the use of the MR damper forward hyperbolic tangent model (the MR Damper Model
subsystem) in the form of
1 2 1 1 2 0 1 2 2 1 2tanh p pmodelled
MR cP P v v x x c v v x x (3)
where Pc = C1iMR + C2 and c0 = C3iMR + C4 are the MR damper current (iMR) dependent
friction force and viscous damping coefficients (respectively) while p1 and p2 are the
scaling parameters The parameters initial values taken from Ref [45] were modified
accordingly for the current analysis frequency and piston travel ranges Additionally p1 and
p2 values were lowered down to be negative to obtain the earlier MR damper response sign
changes serving as PMRmeas sign change prediction The resultant MR damper model
parameters are gathered in the Tab 1 The Kalman Filter subsystem as introduced in [27] is
used for the real-time reproduction of the unmeasured state namely the MR damper relative
velocity v1ndashv2 in a presence of measurement noise that otherwise would be amplified by the
simple differentiating of x1ndashx2
Table 1 The adopted parameters of the MR damper model
Parameter Value
ν 130
p1 -250
p2 -100
C1 202
C2 225
C3 312
C4 467
The PID Force Controller with Correction Demagnetisation amp Sharpening subsystem
representation in Simulink is depicted in Fig 3 Its three main elements are the PID
Controller with Correction the Demagnetisation and the Response Sharpening subsystems
The primary version (V1) of the PID Controller with Correction subsystem is depicted in
Fig 4 It consists of the Abs blocks the Gain block Alpha1 as the scaling factor (Alpha1gt1 is
necessary as |PMRreq|=|PMR
meas| case should not result in zero control) the PID Controller
with Alpha2 Constrained Integration block (Alpha2lt1 multiplier constraints the integral
action when Alpha1|PMRreq|le|PMR
meas|) the multiplying blocks sign relations of
PMRreqampPMR
meas PMRreqampPMR
modelled PMRmeasampPMR
modelled determination conditional (rhombus)
blocks with logical (marked in grey) outputs and the Switch blocks with grey logical inputs
and black switched signals inputs Standard automatic control PID tuning techniques were
used for selection of proportional P integral I and derivative D path gains Additionally the
Saturation block is used with constants idemag=1510ndash2 A (the MR damper magnetic path amp
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
6
MR fluid particles demagnetisation current value) and imax=15 A while the Gain ndash1 is for
negation and the Max block with ndash02imax (ndash03 A) constant input are used to sharpen the
system response when PMRmeas changes sign (while PMR
req sign is maintained) what is
predicted by PMRmodelled signal to set the instantaneous current adequately early to ndash03 A and
moreover obtain minimum MR damper residual force modulus (that is greater due to the
remanent magnetisation) after PMRmeas sign change (see time range of (0315 0350) s in Figs
18 19 and 21 (b) vs Figs 16 and 17) Such constructed MR damper force tracking idea is
insensitive to MR damper dynamics changes due to eg temperature or stroke amplitude
variation during its operation as PMRmodelled sign is considered here instead of PMR
modelled value
Figure 3 Simulink diagram of the PID Force Controller with Correction
Demagnetisation amp Sharpening subsystem
Figure 4 Simulink diagram of the PID Controller with Correction subsystem V1
The second version (V2) of the PID Controller with Correction concept is depicted in
Fig 5 It differs from V1 by an idea of the integrator resetting when PMRmeas and PMR
modelled
have the opposite signs while the integrator initial condition (after the reset) is Alpha3
(Alpha3lt1) times the most recent nonzero integrator state This solution is implemented to
cope with the integrator wind-up problem that may be observed for the V1 concept (see Fig
18 vs Fig 19 starting eg at 005 s) and comes along with possibly enlarged I path gain and
higher integration constraint Alpha2 (Alpha2lt1) in relation to V1 concept
The Demagnetisation subsystem (see Fig 3) is depicted in Fig 6 It produces the
exponentially decaying current pattern (due to the presence of derivative element with first
order inertia and T=0067tperiod where tperiod= 2 exc ) that is switched between positive and
negative values using Rectangle Pulse Generator multiplier block (with two levels ndashidemag
and idemag) when the force should be zero due to the MR damper inability to produce active
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
7
forces (see Fig 21 (b)) The Running Mean subsystem (Fig 7) calculates the difference of the
outputs of two integrator blocks with the level-type reset (integration runs only when the
required value of the control current is ndashidemag ie PMRreq and PMR
meas have opposite signs ndash
see Figs 4 and 5) with the delay time tdelay=0067tperiod between them assuming that the
vibration patterns are characterised by single dominant frequency which is the case in the
most real world wind turbine structures operation scenarios
Figure 5 Simulink diagram of the PID Controller with Correction subsystem V2
Figure 6 Simulink diagram of the Demagnetisation subsystem
Figure 7 Simulink diagram of the Running Mean subsystem
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
8
The Response sharpening subsystem (see Fig 3) is presented in Fig 8 Its aim is to
sharpen the MR damper response at the moment of PMRmeas signal sign change while PMR
req
sign has changed earlier however the MR damper (as a dissipative device) was unable to
produce the active force (see Figs 13 and 14) To fulfil this task the control current is
enlarged by the value of 05 A when PMRmeas modulus is decreasing and is lower than 10 of
PMRmeas running amplitude and PMR
meas sign is consistent within last two sampling periods t0
(see Figs 13 14 and 21 (a) t0=110ndash3 s was assumed) Thanks to such logics the required
value of the control current iMRreq precedes the sign change of PMR
meas thus the control current
that actually flows through the MR damper coil iMRmeas is set at the moment of the PMR
meas
sign change with no delay The Running Amplitude subsystem (Fig 9) calculates the
difference of the outputs of the two integrator blocks with delay of five oscillation periods
between them The input to both integrators is the quantity (PMRmeas) squared (Sqr block) The
resultant difference is multiplied by two and divided by a time of five periods to obtain the
amplitude squared thus finally the Sqrt (square root) block is needed only to obtain
amplitude A(bull) of the input signal (assuming that vibration pattern is characterised by single
dominant frequency)
The parameters imax idemag tdelay Alpha1 Alpha2 Alpha3 values were selected on the
basis of numerical simulations supported by MR damper dynamics experimental testing
Figure 8 Simulink diagram of the Response sharpening subsystem
Figure 9 Simulink diagram of the Running Amplitude subsystem
The system in Fig 2 also includes standard analogue PID Current Controller subsystem
aimed to control MR damper with the use of an electronic board that enforces the MR damper
current via a control voltage uMR based on iMRmeas and iMR
req signals (see Figs 22 (a)(b))
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
9
4 THE EXPERIMENTAL ANALYSIS
For the purpose of the current experimental analysis that is oriented to the development of the
refined MR damper force tracking algorithm the value of γ = 1 was assumed while the
selection of γ was not a scope of the present research The theoretical study of γ determination
for the idealised semiactive device case of negligible response time zero residual force and
zero inherent system damping is presented in [28]
The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic
horizontal excitation applied to the nacelle The frequency range comprised the
neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz
Several system configurations were regarded passive system with the constant control
current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the
newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2
respectively) or with the simple previously tested MR damper hyperbolic tangent inverse
model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm
(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)
that was previously proved to be the best approach [242526] was selected The obtained
output frequency response functions of the tower tip horizontal displacement x1 amplitude are
presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1
the MR damper force PMRreq PMR
meas and the MR damper current iMRreq iMR
meas (adequately
scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-
displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT
PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and
435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most
crucial concerning preferable control solutions (see Fig 10 open loop systems are not of
interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR
meas
and the MR damper current iMRreq iMR
meas (adequately scaled and zoomed) obtained for the
system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current
Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)
25 3 35 4 45 505
1
15
2
25
3
35
4
45
5
55x 10
-3
Frequency [Hz]
Dis
pla
cem
ent A
mplit
ude A
(x1)
[m]
P0 = 61 N
00 A
01 A
02 A
03 A
04 A
05 A
ADPT V1
ADPT V2
ADPT INV
ADPT PI
ModGND
Figure 10 Tower tip displacement amplitude output frequency response functions
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
10
0 01 02 03 04 05 06 07-3
-2
-1
0
1
2
3
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
11
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
12
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops
Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
005 006
-1
0
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
13
0 005 01 015 02 025 03 035 04 045-2
-15
-1
-05
0
05
1
15
2
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops
021 0215 022 0225 023
-14
-12
-1
-08
-06
-04
-02
0
02
04
06
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
0315 032 0325 033 0335 034 0345 035
-03
-02
-01
0
01
02
03
04
05
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
001 x
PMR
req
001 x
PMR
meas
i MR
req
i MR
meas
Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
14
0 001 002 003 004 005-01
0
01
02
03
04
05
06
07
08
09
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
0 001 002 003 004 005-04
-03
-02
-01
0
01
02
03
04
05
06
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
Figure 22 PID current controller operation at
(a) positive (b) negative step change of iMRreq
Table 2 presents values of the quality index Q (best values in bold) being a root-mean-
square of the PMRreqndashPMR
meas difference
2
1
Nreq meas
MR MR
j
Q P j P j
(4)
where j is the time sample number and N is the number of the regarded samples ModGND
solution is omitted here as it is not based on required MR damper force tracking idea
Table 2 Values of the quality index Q (4)
System 295 [Hz] 435 [Hz]
ADPT INV 3002 6531
ADPT PI 2679 6274
ADPT V1 2366 4955
ADPT V2 2273 5374
In Fig 10 two maxima that are typical for TVA operation are apparent for all the
solutions but 02 03 04 and 05 A for which the damping is relatively too high
Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most
favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood
(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)
however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or
some positive damping added may improve the system response (as higher amplitude of
PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR
req ADPT V2
may become a preferred choice as it copes better with the integrator wind-up (by changing
the value of γ either the first maxima is lowered while the second maxima is elevated or the
second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to
the previously introduced [242526313237] ADPT PI and especially to ADPT INV within
the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper
required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz
for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially
considering the time instants immediately following PMRmeas sign changes (all presented time
patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the
difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
15
MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI
and especially for ADPT INV are incomparable to the respective patterns registered for
ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The
same may be concluded concerning PMRreq force tracking quality just before PMR
meas sign
changes although ADPT INV characteristics (Fig 16) could not be even described as
acceptable Concerning the MR damper residual force minimisation both ADPT V1 and
ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted
for the demagnetisation and response sharpening do the job properly The MR damper force-
displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along
with the friction (due to the MR damper residual force) phenomena at 295 Hz and the
positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper
measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not
differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2
however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash
as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated
according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of
nonlinear damping
As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one
may observe iMRreq signal rise at a time instant of 005 s while PMR
meas response modulus rise
is at ca 006 s what makes a real challenge for the follow-up-type-controller operational
quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations
present in Figs 13 and 14
5 CONCLUSION
The conducted experimental analysis proved the effectiveness of the proposed refined MR
damper force tracking algorithm in two versions The obtained output frequency response
function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels
former solutions (designated by ADPT PI and ADPT INV) and is comparable to the
frequency response of the ModGND system that previously demonstrated the best
performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range
while ModGND excels for frequencies higher than 435 Hz and marginally in the (300
320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope
best with the problem of the residual MR damper force magnetic remanence when zero
force is assumed due to the MR damper inability to generate active forces The
implementation of these logics for the ModGND algorithm along with the analysis of the
demanded value of γ for the real-world system with response time residual force and
inherent damping all of which are nonzero shall be a subject of the future research The
minimisation of the residual force negative effects and the quality of positive stiffness
tracking will also be investigated Based on these analyses results and laboratory model
measurements and considering the dynamic similarity study that includes determined time
and length scale factors [41] in combination with force scale factor [44] direct calculation of
the demanded control signal for a real-world full scale vibration reduction system MR TVA
will be possible
Acknowledgment
This work is supported by AGH University of Science and Technology under research
program No 1111130958
References
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL
[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech
Struct amp Mach (1996) 24 (2) 155-187
[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering
low structural damping and soil structure interaction European Wind Energy Association
Annual Event (2012) Copenhagen 16-19042012
[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic
damping of operational wind turbine modes from experiments European Wind Energy
Association Annual Event (2012) Copenhagen 16-19042012
[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z
wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)
209-216
[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M
Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European
Wind Energy Association Annual Event (2012) Copenhagen 16-19042012
[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p
harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen
16-19042012
[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor
speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)
Monaco
[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind
turbines on two floating platforms Mechatronics (2011) 21 691-703
[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY
[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation
test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013
[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu
M Wind turbine tower load reduction using passive and semiactive dampers European Wind
Energy Association Annual Event (2011) Brussels
[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace
Exposition (2010) Orlando
[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej
z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198
[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR
damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds
Lisse CRC Press
[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and
experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State
Phenomena (2011) 177 (Control engineering in materials processing) 102-115
[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR
shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)
[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical
and Applied Mechanics (2007) 45 (1) 133-146
[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension
system with MR shock absorbers Computers and Structures (2008) 86 379-385
[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the
Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32
(1+2) 67-80
[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based
vibration reduction system Bulletin Of The Polish Academy Of
Sciences-Technical Sciences (2011) 59 (1) 75-80
[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes
Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
2
temperature change and minor energy requirements as compared with active systems
[1617181920212223] Simulations and experiments show that implementation of an MR
damper in the TVA system may lead to further vibration reduction in relation to passive TVA
[24252627]
Within the scope of the current project a specially developed and built tower-nacelle
laboratory model (Fig 1) was made in which all turbine components (a nacelle blades a
hub a shaft a generator and possibly a gearbox) are represented by nacelle concentrated
mass The laboratory test rig of the wind turbine tower-nacelle system makes it possible to
model tower vibrations under various excitation sources as the horizontal concentrated force
generated by the dedicated shaker may model the load applied to the nacelle or to the tower
itself at the arbitrary height Both locations enable to force tower bending modes of vibration
The rig may also be laid down on the horizontally excited platform to model the vibrations of
buoy-floating wind turbine structures or vibrations due to seismic excitation
The problem of wind turbine tower vibration control with an MR TVA utilising an
adaptive stiffness concept with a newly developed force tracking algorithm is presented here
Both the adaptive stiffness and the MR damper force tracking solutions were investigated
previously separately however limited (numerical or hardware in the loop only continuous ndash
with no discontinuities or two-level force current pattern regarded) implementation
scenarios were presented only [2829303132] or the quality of the force follow-up left the
field for further improvements [242526] The MR damper real-time force tracking problem
along with the adaptive stiffness and damping friction was investigated extensively with fair
results in [33343536] Weber in [33] uses a series of BoucndashWen models computed in
parallel to estimate the required control current with no need of force sensor however
presented measured tracking of clipped viscous damping with negative stiffness exhibits slow
force rise after piston velocity sign change The interesting logics is adopted in [34] for a
system tailored MR damper dealing separately with the regions of rapid MR damper force
increase decrease and the transition between these two relations together with the negative
current spikes just before the desired force sign changes However measured real-time
tracking of force patterns exhibiting negative stiffness is again characterised with
insufficiently sharp force rise while tracking of force patterns exhibiting positive stiffness is
characterised with significant force error (overshoot) due to the remanent magnetization
These two problems occurring either if the actual MR damper force should be quickly
increased to a large value or if the force should be rapidly decreased to zero both at the
displacement extreme (and force sign change) are not removed by this approach utilising MR
damper inverse model feed forward and force sensor feedback even using negative current
applied each half cycle [35] Weber in [36] also uses MR damper inverse model combined
with force sensor Again measured real-time tracking of force patterns is characterised with
insufficiently rapid force rise or significant overshoot both after force sign change
The current work covers real-time realisation of the improved (over the previous solutions
[24252629313237]) stock MR damper continuous pattern tracking algorithm coping well
with the discontinuities (rapid value changes) of the force and the magnetic remanence
combining MR damper forward model with force sign change prediction (feed forward)
force sensor feedback and dedicated logics together with a basic adaptive stiffness
implementation resulting in a quality vibration reduction system As a reference passive
solutions with several MR damper constant input current values the adaptive stiffness
concept with previously tested MR damper hyperbolic tangent inverse model and PI-based
force tracking algorithms [24252629313237] along with a modified ground hook control
[2526] results are presented Only the first bending mode of vibration frequency
neighbourhood is analysed here
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
3
The paper is organised as follows In the forthcoming section the wind turbine tower-
nacelle laboratory model is introduced Then a vibration control algorithm is presented and
followed by the experimental analysis results The paper is finished with several conclusions
2 THE WIND TURBINE TOWER-NACELLE LABORATORY MODEL
The model to be analysed (Fig 1) consists of a titanium (Ti Gr5) rod 1 arranged vertically
representing the wind-turbine tower and a stiff body (system of steel plates) 2 fixed rigidly to
the top of the rod representing both nacelle and turbine assemblies The bottom end of the
rod is rigidly mounted to the ground via an adequately stiff steel foundation frame 3 As the
first tower bending mode has dominant modal mass participation (ca fivefold greater than the
next mode) a vibration reduction system (an MR TVA) is located at the top of the rod (at the
nacelle) The MR TVA is an additional stiff body 6 (an absorber) moving horizontally along
linear bearing guides connected with the system representing the nacelle via a spring and
Lord RD 1097-1 MR damper [38] in parallel 7 The absorber mass m2 and the spring stiffness
k2 parameters of the TVA were tuned to the first bending mode of the tower-nacelle system
vibrations on the basis of standard principles of the TVA tuning [10] The RD 1097-1 damper
(which force depends on the current fed to its coil) is an actuator of such vibration reduction
system The MR TVA operates along the same direction as the vibration excitation applied
(assuming small bending angles) Force excitation system comprises The Modal Shop
lightweight electrodynamic force exciter of 2060E series 4 [39] with the drive train assembly
5 of the changeable leverage [4041424344]
The horizontal displacement and velocity of the system modelling the nacelle are
designated by x1 and v1 (respectively) while the horizontal displacement and velocity of the
absorber (the TVA mass) are x2 and v2 Thus x1ndashx2 designates the MR damper relative
displacement (that is measured by LVDT transducer 8) while v1ndashv2 designates the MR
damper relative velocity The MR damper force PMR is measured by the tensometric
transducer 9
Figure 1 The laboratory test rig
1
2 6
3
4
5
6 7 9
8 2
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
4
3 THE CONTROL ALGORITHM
The underlying idea of the implemented control system is presented in Fig 2 Three
measurement input signals are regarded spring MR damper relative displacement x1ndashx2meas
MR damper current iMRmeas and MR damper force PMR
meas The MR Damper Required Force
subsystem corresponds to the real-time calculation of the demanded MR damper force PMRreq
ndash for the purpose of the current analysis the algorithm of the undamped dynamic vibration
absorber [10] that tracks excitation frequency [252628] is emulated using the MR damper
The MR damper should generate positive or negative stiffness force in such a way that the
TVA stiffness 2
reqk in equations (1) and (2) is tuned to the actual operationexcitation
frequency exc rather than to the tower-nacelle system first bending frequency Based on this
assumption the real-time determination of exc is followed by the real-time calculation of the
TVA required stiffness force 2 1 2
req req
stiffP k x x while the damping is assumed to be zero
(for the most efficient vibration mitigation at the frequency of tuning) leading to the MR
damper required force formula
2 2 1 2
req req
MRP k k x x (1)
with
2
2
2
req
exck m (2)
where γ is a correction factor that is present as the MR damper cannot deliver energy to the
system thus the force defined by equation (1) cannot be exactly mapped
Figure 2 The schematic diagram of the control system
When active forces are required zero force is assumed Thus arises a problem of a precise
MR damper force tracking in the case of pattern being discontinuous due to such a switching
A quick timeous (with possible prediction) and sharp force follow-up is needed whereas the
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
5
actuator dynamics exhibits the inertia due to the coil electrical resistance and inductance
magnetic remanence as well as the time lag hysteresis resulting from the MR effect
(particle chains formation) delay MR fluid preyield operation regime These effects cannot
be eliminated by a simple PIPID feedback controller with the sign adjustments
[242526313237] as it can shape the force-velocity relationship only into a linear or a
higher-order polynomial function with the inherent time lag even utilising the adequate
current controller Thus a dedicated MR damper force follow-up PID-based control
algorithm that was specially developed and refined during the current study based on
[252631] is represented by the PID Force Controller with Correction Demagnetisation amp
Sharpening subsystem (see Fig 2) Apart from the demanded MR damper force PMRreq input
the measured actual MR damper force PMRmeas and the modelled MR damper force PMR
modelled
signals are fed to the input of this subsystem PMRmodelled is the real-time calculated force with
the use of the MR damper forward hyperbolic tangent model (the MR Damper Model
subsystem) in the form of
1 2 1 1 2 0 1 2 2 1 2tanh p pmodelled
MR cP P v v x x c v v x x (3)
where Pc = C1iMR + C2 and c0 = C3iMR + C4 are the MR damper current (iMR) dependent
friction force and viscous damping coefficients (respectively) while p1 and p2 are the
scaling parameters The parameters initial values taken from Ref [45] were modified
accordingly for the current analysis frequency and piston travel ranges Additionally p1 and
p2 values were lowered down to be negative to obtain the earlier MR damper response sign
changes serving as PMRmeas sign change prediction The resultant MR damper model
parameters are gathered in the Tab 1 The Kalman Filter subsystem as introduced in [27] is
used for the real-time reproduction of the unmeasured state namely the MR damper relative
velocity v1ndashv2 in a presence of measurement noise that otherwise would be amplified by the
simple differentiating of x1ndashx2
Table 1 The adopted parameters of the MR damper model
Parameter Value
ν 130
p1 -250
p2 -100
C1 202
C2 225
C3 312
C4 467
The PID Force Controller with Correction Demagnetisation amp Sharpening subsystem
representation in Simulink is depicted in Fig 3 Its three main elements are the PID
Controller with Correction the Demagnetisation and the Response Sharpening subsystems
The primary version (V1) of the PID Controller with Correction subsystem is depicted in
Fig 4 It consists of the Abs blocks the Gain block Alpha1 as the scaling factor (Alpha1gt1 is
necessary as |PMRreq|=|PMR
meas| case should not result in zero control) the PID Controller
with Alpha2 Constrained Integration block (Alpha2lt1 multiplier constraints the integral
action when Alpha1|PMRreq|le|PMR
meas|) the multiplying blocks sign relations of
PMRreqampPMR
meas PMRreqampPMR
modelled PMRmeasampPMR
modelled determination conditional (rhombus)
blocks with logical (marked in grey) outputs and the Switch blocks with grey logical inputs
and black switched signals inputs Standard automatic control PID tuning techniques were
used for selection of proportional P integral I and derivative D path gains Additionally the
Saturation block is used with constants idemag=1510ndash2 A (the MR damper magnetic path amp
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
6
MR fluid particles demagnetisation current value) and imax=15 A while the Gain ndash1 is for
negation and the Max block with ndash02imax (ndash03 A) constant input are used to sharpen the
system response when PMRmeas changes sign (while PMR
req sign is maintained) what is
predicted by PMRmodelled signal to set the instantaneous current adequately early to ndash03 A and
moreover obtain minimum MR damper residual force modulus (that is greater due to the
remanent magnetisation) after PMRmeas sign change (see time range of (0315 0350) s in Figs
18 19 and 21 (b) vs Figs 16 and 17) Such constructed MR damper force tracking idea is
insensitive to MR damper dynamics changes due to eg temperature or stroke amplitude
variation during its operation as PMRmodelled sign is considered here instead of PMR
modelled value
Figure 3 Simulink diagram of the PID Force Controller with Correction
Demagnetisation amp Sharpening subsystem
Figure 4 Simulink diagram of the PID Controller with Correction subsystem V1
The second version (V2) of the PID Controller with Correction concept is depicted in
Fig 5 It differs from V1 by an idea of the integrator resetting when PMRmeas and PMR
modelled
have the opposite signs while the integrator initial condition (after the reset) is Alpha3
(Alpha3lt1) times the most recent nonzero integrator state This solution is implemented to
cope with the integrator wind-up problem that may be observed for the V1 concept (see Fig
18 vs Fig 19 starting eg at 005 s) and comes along with possibly enlarged I path gain and
higher integration constraint Alpha2 (Alpha2lt1) in relation to V1 concept
The Demagnetisation subsystem (see Fig 3) is depicted in Fig 6 It produces the
exponentially decaying current pattern (due to the presence of derivative element with first
order inertia and T=0067tperiod where tperiod= 2 exc ) that is switched between positive and
negative values using Rectangle Pulse Generator multiplier block (with two levels ndashidemag
and idemag) when the force should be zero due to the MR damper inability to produce active
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
7
forces (see Fig 21 (b)) The Running Mean subsystem (Fig 7) calculates the difference of the
outputs of two integrator blocks with the level-type reset (integration runs only when the
required value of the control current is ndashidemag ie PMRreq and PMR
meas have opposite signs ndash
see Figs 4 and 5) with the delay time tdelay=0067tperiod between them assuming that the
vibration patterns are characterised by single dominant frequency which is the case in the
most real world wind turbine structures operation scenarios
Figure 5 Simulink diagram of the PID Controller with Correction subsystem V2
Figure 6 Simulink diagram of the Demagnetisation subsystem
Figure 7 Simulink diagram of the Running Mean subsystem
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
8
The Response sharpening subsystem (see Fig 3) is presented in Fig 8 Its aim is to
sharpen the MR damper response at the moment of PMRmeas signal sign change while PMR
req
sign has changed earlier however the MR damper (as a dissipative device) was unable to
produce the active force (see Figs 13 and 14) To fulfil this task the control current is
enlarged by the value of 05 A when PMRmeas modulus is decreasing and is lower than 10 of
PMRmeas running amplitude and PMR
meas sign is consistent within last two sampling periods t0
(see Figs 13 14 and 21 (a) t0=110ndash3 s was assumed) Thanks to such logics the required
value of the control current iMRreq precedes the sign change of PMR
meas thus the control current
that actually flows through the MR damper coil iMRmeas is set at the moment of the PMR
meas
sign change with no delay The Running Amplitude subsystem (Fig 9) calculates the
difference of the outputs of the two integrator blocks with delay of five oscillation periods
between them The input to both integrators is the quantity (PMRmeas) squared (Sqr block) The
resultant difference is multiplied by two and divided by a time of five periods to obtain the
amplitude squared thus finally the Sqrt (square root) block is needed only to obtain
amplitude A(bull) of the input signal (assuming that vibration pattern is characterised by single
dominant frequency)
The parameters imax idemag tdelay Alpha1 Alpha2 Alpha3 values were selected on the
basis of numerical simulations supported by MR damper dynamics experimental testing
Figure 8 Simulink diagram of the Response sharpening subsystem
Figure 9 Simulink diagram of the Running Amplitude subsystem
The system in Fig 2 also includes standard analogue PID Current Controller subsystem
aimed to control MR damper with the use of an electronic board that enforces the MR damper
current via a control voltage uMR based on iMRmeas and iMR
req signals (see Figs 22 (a)(b))
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
9
4 THE EXPERIMENTAL ANALYSIS
For the purpose of the current experimental analysis that is oriented to the development of the
refined MR damper force tracking algorithm the value of γ = 1 was assumed while the
selection of γ was not a scope of the present research The theoretical study of γ determination
for the idealised semiactive device case of negligible response time zero residual force and
zero inherent system damping is presented in [28]
The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic
horizontal excitation applied to the nacelle The frequency range comprised the
neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz
Several system configurations were regarded passive system with the constant control
current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the
newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2
respectively) or with the simple previously tested MR damper hyperbolic tangent inverse
model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm
(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)
that was previously proved to be the best approach [242526] was selected The obtained
output frequency response functions of the tower tip horizontal displacement x1 amplitude are
presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1
the MR damper force PMRreq PMR
meas and the MR damper current iMRreq iMR
meas (adequately
scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-
displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT
PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and
435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most
crucial concerning preferable control solutions (see Fig 10 open loop systems are not of
interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR
meas
and the MR damper current iMRreq iMR
meas (adequately scaled and zoomed) obtained for the
system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current
Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)
25 3 35 4 45 505
1
15
2
25
3
35
4
45
5
55x 10
-3
Frequency [Hz]
Dis
pla
cem
ent A
mplit
ude A
(x1)
[m]
P0 = 61 N
00 A
01 A
02 A
03 A
04 A
05 A
ADPT V1
ADPT V2
ADPT INV
ADPT PI
ModGND
Figure 10 Tower tip displacement amplitude output frequency response functions
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
10
0 01 02 03 04 05 06 07-3
-2
-1
0
1
2
3
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
11
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
12
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops
Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
005 006
-1
0
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
13
0 005 01 015 02 025 03 035 04 045-2
-15
-1
-05
0
05
1
15
2
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops
021 0215 022 0225 023
-14
-12
-1
-08
-06
-04
-02
0
02
04
06
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
0315 032 0325 033 0335 034 0345 035
-03
-02
-01
0
01
02
03
04
05
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
001 x
PMR
req
001 x
PMR
meas
i MR
req
i MR
meas
Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
14
0 001 002 003 004 005-01
0
01
02
03
04
05
06
07
08
09
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
0 001 002 003 004 005-04
-03
-02
-01
0
01
02
03
04
05
06
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
Figure 22 PID current controller operation at
(a) positive (b) negative step change of iMRreq
Table 2 presents values of the quality index Q (best values in bold) being a root-mean-
square of the PMRreqndashPMR
meas difference
2
1
Nreq meas
MR MR
j
Q P j P j
(4)
where j is the time sample number and N is the number of the regarded samples ModGND
solution is omitted here as it is not based on required MR damper force tracking idea
Table 2 Values of the quality index Q (4)
System 295 [Hz] 435 [Hz]
ADPT INV 3002 6531
ADPT PI 2679 6274
ADPT V1 2366 4955
ADPT V2 2273 5374
In Fig 10 two maxima that are typical for TVA operation are apparent for all the
solutions but 02 03 04 and 05 A for which the damping is relatively too high
Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most
favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood
(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)
however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or
some positive damping added may improve the system response (as higher amplitude of
PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR
req ADPT V2
may become a preferred choice as it copes better with the integrator wind-up (by changing
the value of γ either the first maxima is lowered while the second maxima is elevated or the
second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to
the previously introduced [242526313237] ADPT PI and especially to ADPT INV within
the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper
required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz
for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially
considering the time instants immediately following PMRmeas sign changes (all presented time
patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the
difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
15
MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI
and especially for ADPT INV are incomparable to the respective patterns registered for
ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The
same may be concluded concerning PMRreq force tracking quality just before PMR
meas sign
changes although ADPT INV characteristics (Fig 16) could not be even described as
acceptable Concerning the MR damper residual force minimisation both ADPT V1 and
ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted
for the demagnetisation and response sharpening do the job properly The MR damper force-
displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along
with the friction (due to the MR damper residual force) phenomena at 295 Hz and the
positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper
measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not
differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2
however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash
as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated
according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of
nonlinear damping
As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one
may observe iMRreq signal rise at a time instant of 005 s while PMR
meas response modulus rise
is at ca 006 s what makes a real challenge for the follow-up-type-controller operational
quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations
present in Figs 13 and 14
5 CONCLUSION
The conducted experimental analysis proved the effectiveness of the proposed refined MR
damper force tracking algorithm in two versions The obtained output frequency response
function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels
former solutions (designated by ADPT PI and ADPT INV) and is comparable to the
frequency response of the ModGND system that previously demonstrated the best
performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range
while ModGND excels for frequencies higher than 435 Hz and marginally in the (300
320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope
best with the problem of the residual MR damper force magnetic remanence when zero
force is assumed due to the MR damper inability to generate active forces The
implementation of these logics for the ModGND algorithm along with the analysis of the
demanded value of γ for the real-world system with response time residual force and
inherent damping all of which are nonzero shall be a subject of the future research The
minimisation of the residual force negative effects and the quality of positive stiffness
tracking will also be investigated Based on these analyses results and laboratory model
measurements and considering the dynamic similarity study that includes determined time
and length scale factors [41] in combination with force scale factor [44] direct calculation of
the demanded control signal for a real-world full scale vibration reduction system MR TVA
will be possible
Acknowledgment
This work is supported by AGH University of Science and Technology under research
program No 1111130958
References
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL
[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech
Struct amp Mach (1996) 24 (2) 155-187
[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering
low structural damping and soil structure interaction European Wind Energy Association
Annual Event (2012) Copenhagen 16-19042012
[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic
damping of operational wind turbine modes from experiments European Wind Energy
Association Annual Event (2012) Copenhagen 16-19042012
[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z
wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)
209-216
[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M
Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European
Wind Energy Association Annual Event (2012) Copenhagen 16-19042012
[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p
harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen
16-19042012
[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor
speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)
Monaco
[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind
turbines on two floating platforms Mechatronics (2011) 21 691-703
[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY
[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation
test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013
[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu
M Wind turbine tower load reduction using passive and semiactive dampers European Wind
Energy Association Annual Event (2011) Brussels
[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace
Exposition (2010) Orlando
[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej
z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198
[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR
damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds
Lisse CRC Press
[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and
experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State
Phenomena (2011) 177 (Control engineering in materials processing) 102-115
[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR
shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)
[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical
and Applied Mechanics (2007) 45 (1) 133-146
[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension
system with MR shock absorbers Computers and Structures (2008) 86 379-385
[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the
Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32
(1+2) 67-80
[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based
vibration reduction system Bulletin Of The Polish Academy Of
Sciences-Technical Sciences (2011) 59 (1) 75-80
[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes
Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
3
The paper is organised as follows In the forthcoming section the wind turbine tower-
nacelle laboratory model is introduced Then a vibration control algorithm is presented and
followed by the experimental analysis results The paper is finished with several conclusions
2 THE WIND TURBINE TOWER-NACELLE LABORATORY MODEL
The model to be analysed (Fig 1) consists of a titanium (Ti Gr5) rod 1 arranged vertically
representing the wind-turbine tower and a stiff body (system of steel plates) 2 fixed rigidly to
the top of the rod representing both nacelle and turbine assemblies The bottom end of the
rod is rigidly mounted to the ground via an adequately stiff steel foundation frame 3 As the
first tower bending mode has dominant modal mass participation (ca fivefold greater than the
next mode) a vibration reduction system (an MR TVA) is located at the top of the rod (at the
nacelle) The MR TVA is an additional stiff body 6 (an absorber) moving horizontally along
linear bearing guides connected with the system representing the nacelle via a spring and
Lord RD 1097-1 MR damper [38] in parallel 7 The absorber mass m2 and the spring stiffness
k2 parameters of the TVA were tuned to the first bending mode of the tower-nacelle system
vibrations on the basis of standard principles of the TVA tuning [10] The RD 1097-1 damper
(which force depends on the current fed to its coil) is an actuator of such vibration reduction
system The MR TVA operates along the same direction as the vibration excitation applied
(assuming small bending angles) Force excitation system comprises The Modal Shop
lightweight electrodynamic force exciter of 2060E series 4 [39] with the drive train assembly
5 of the changeable leverage [4041424344]
The horizontal displacement and velocity of the system modelling the nacelle are
designated by x1 and v1 (respectively) while the horizontal displacement and velocity of the
absorber (the TVA mass) are x2 and v2 Thus x1ndashx2 designates the MR damper relative
displacement (that is measured by LVDT transducer 8) while v1ndashv2 designates the MR
damper relative velocity The MR damper force PMR is measured by the tensometric
transducer 9
Figure 1 The laboratory test rig
1
2 6
3
4
5
6 7 9
8 2
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
4
3 THE CONTROL ALGORITHM
The underlying idea of the implemented control system is presented in Fig 2 Three
measurement input signals are regarded spring MR damper relative displacement x1ndashx2meas
MR damper current iMRmeas and MR damper force PMR
meas The MR Damper Required Force
subsystem corresponds to the real-time calculation of the demanded MR damper force PMRreq
ndash for the purpose of the current analysis the algorithm of the undamped dynamic vibration
absorber [10] that tracks excitation frequency [252628] is emulated using the MR damper
The MR damper should generate positive or negative stiffness force in such a way that the
TVA stiffness 2
reqk in equations (1) and (2) is tuned to the actual operationexcitation
frequency exc rather than to the tower-nacelle system first bending frequency Based on this
assumption the real-time determination of exc is followed by the real-time calculation of the
TVA required stiffness force 2 1 2
req req
stiffP k x x while the damping is assumed to be zero
(for the most efficient vibration mitigation at the frequency of tuning) leading to the MR
damper required force formula
2 2 1 2
req req
MRP k k x x (1)
with
2
2
2
req
exck m (2)
where γ is a correction factor that is present as the MR damper cannot deliver energy to the
system thus the force defined by equation (1) cannot be exactly mapped
Figure 2 The schematic diagram of the control system
When active forces are required zero force is assumed Thus arises a problem of a precise
MR damper force tracking in the case of pattern being discontinuous due to such a switching
A quick timeous (with possible prediction) and sharp force follow-up is needed whereas the
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
5
actuator dynamics exhibits the inertia due to the coil electrical resistance and inductance
magnetic remanence as well as the time lag hysteresis resulting from the MR effect
(particle chains formation) delay MR fluid preyield operation regime These effects cannot
be eliminated by a simple PIPID feedback controller with the sign adjustments
[242526313237] as it can shape the force-velocity relationship only into a linear or a
higher-order polynomial function with the inherent time lag even utilising the adequate
current controller Thus a dedicated MR damper force follow-up PID-based control
algorithm that was specially developed and refined during the current study based on
[252631] is represented by the PID Force Controller with Correction Demagnetisation amp
Sharpening subsystem (see Fig 2) Apart from the demanded MR damper force PMRreq input
the measured actual MR damper force PMRmeas and the modelled MR damper force PMR
modelled
signals are fed to the input of this subsystem PMRmodelled is the real-time calculated force with
the use of the MR damper forward hyperbolic tangent model (the MR Damper Model
subsystem) in the form of
1 2 1 1 2 0 1 2 2 1 2tanh p pmodelled
MR cP P v v x x c v v x x (3)
where Pc = C1iMR + C2 and c0 = C3iMR + C4 are the MR damper current (iMR) dependent
friction force and viscous damping coefficients (respectively) while p1 and p2 are the
scaling parameters The parameters initial values taken from Ref [45] were modified
accordingly for the current analysis frequency and piston travel ranges Additionally p1 and
p2 values were lowered down to be negative to obtain the earlier MR damper response sign
changes serving as PMRmeas sign change prediction The resultant MR damper model
parameters are gathered in the Tab 1 The Kalman Filter subsystem as introduced in [27] is
used for the real-time reproduction of the unmeasured state namely the MR damper relative
velocity v1ndashv2 in a presence of measurement noise that otherwise would be amplified by the
simple differentiating of x1ndashx2
Table 1 The adopted parameters of the MR damper model
Parameter Value
ν 130
p1 -250
p2 -100
C1 202
C2 225
C3 312
C4 467
The PID Force Controller with Correction Demagnetisation amp Sharpening subsystem
representation in Simulink is depicted in Fig 3 Its three main elements are the PID
Controller with Correction the Demagnetisation and the Response Sharpening subsystems
The primary version (V1) of the PID Controller with Correction subsystem is depicted in
Fig 4 It consists of the Abs blocks the Gain block Alpha1 as the scaling factor (Alpha1gt1 is
necessary as |PMRreq|=|PMR
meas| case should not result in zero control) the PID Controller
with Alpha2 Constrained Integration block (Alpha2lt1 multiplier constraints the integral
action when Alpha1|PMRreq|le|PMR
meas|) the multiplying blocks sign relations of
PMRreqampPMR
meas PMRreqampPMR
modelled PMRmeasampPMR
modelled determination conditional (rhombus)
blocks with logical (marked in grey) outputs and the Switch blocks with grey logical inputs
and black switched signals inputs Standard automatic control PID tuning techniques were
used for selection of proportional P integral I and derivative D path gains Additionally the
Saturation block is used with constants idemag=1510ndash2 A (the MR damper magnetic path amp
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
6
MR fluid particles demagnetisation current value) and imax=15 A while the Gain ndash1 is for
negation and the Max block with ndash02imax (ndash03 A) constant input are used to sharpen the
system response when PMRmeas changes sign (while PMR
req sign is maintained) what is
predicted by PMRmodelled signal to set the instantaneous current adequately early to ndash03 A and
moreover obtain minimum MR damper residual force modulus (that is greater due to the
remanent magnetisation) after PMRmeas sign change (see time range of (0315 0350) s in Figs
18 19 and 21 (b) vs Figs 16 and 17) Such constructed MR damper force tracking idea is
insensitive to MR damper dynamics changes due to eg temperature or stroke amplitude
variation during its operation as PMRmodelled sign is considered here instead of PMR
modelled value
Figure 3 Simulink diagram of the PID Force Controller with Correction
Demagnetisation amp Sharpening subsystem
Figure 4 Simulink diagram of the PID Controller with Correction subsystem V1
The second version (V2) of the PID Controller with Correction concept is depicted in
Fig 5 It differs from V1 by an idea of the integrator resetting when PMRmeas and PMR
modelled
have the opposite signs while the integrator initial condition (after the reset) is Alpha3
(Alpha3lt1) times the most recent nonzero integrator state This solution is implemented to
cope with the integrator wind-up problem that may be observed for the V1 concept (see Fig
18 vs Fig 19 starting eg at 005 s) and comes along with possibly enlarged I path gain and
higher integration constraint Alpha2 (Alpha2lt1) in relation to V1 concept
The Demagnetisation subsystem (see Fig 3) is depicted in Fig 6 It produces the
exponentially decaying current pattern (due to the presence of derivative element with first
order inertia and T=0067tperiod where tperiod= 2 exc ) that is switched between positive and
negative values using Rectangle Pulse Generator multiplier block (with two levels ndashidemag
and idemag) when the force should be zero due to the MR damper inability to produce active
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
7
forces (see Fig 21 (b)) The Running Mean subsystem (Fig 7) calculates the difference of the
outputs of two integrator blocks with the level-type reset (integration runs only when the
required value of the control current is ndashidemag ie PMRreq and PMR
meas have opposite signs ndash
see Figs 4 and 5) with the delay time tdelay=0067tperiod between them assuming that the
vibration patterns are characterised by single dominant frequency which is the case in the
most real world wind turbine structures operation scenarios
Figure 5 Simulink diagram of the PID Controller with Correction subsystem V2
Figure 6 Simulink diagram of the Demagnetisation subsystem
Figure 7 Simulink diagram of the Running Mean subsystem
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
8
The Response sharpening subsystem (see Fig 3) is presented in Fig 8 Its aim is to
sharpen the MR damper response at the moment of PMRmeas signal sign change while PMR
req
sign has changed earlier however the MR damper (as a dissipative device) was unable to
produce the active force (see Figs 13 and 14) To fulfil this task the control current is
enlarged by the value of 05 A when PMRmeas modulus is decreasing and is lower than 10 of
PMRmeas running amplitude and PMR
meas sign is consistent within last two sampling periods t0
(see Figs 13 14 and 21 (a) t0=110ndash3 s was assumed) Thanks to such logics the required
value of the control current iMRreq precedes the sign change of PMR
meas thus the control current
that actually flows through the MR damper coil iMRmeas is set at the moment of the PMR
meas
sign change with no delay The Running Amplitude subsystem (Fig 9) calculates the
difference of the outputs of the two integrator blocks with delay of five oscillation periods
between them The input to both integrators is the quantity (PMRmeas) squared (Sqr block) The
resultant difference is multiplied by two and divided by a time of five periods to obtain the
amplitude squared thus finally the Sqrt (square root) block is needed only to obtain
amplitude A(bull) of the input signal (assuming that vibration pattern is characterised by single
dominant frequency)
The parameters imax idemag tdelay Alpha1 Alpha2 Alpha3 values were selected on the
basis of numerical simulations supported by MR damper dynamics experimental testing
Figure 8 Simulink diagram of the Response sharpening subsystem
Figure 9 Simulink diagram of the Running Amplitude subsystem
The system in Fig 2 also includes standard analogue PID Current Controller subsystem
aimed to control MR damper with the use of an electronic board that enforces the MR damper
current via a control voltage uMR based on iMRmeas and iMR
req signals (see Figs 22 (a)(b))
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
9
4 THE EXPERIMENTAL ANALYSIS
For the purpose of the current experimental analysis that is oriented to the development of the
refined MR damper force tracking algorithm the value of γ = 1 was assumed while the
selection of γ was not a scope of the present research The theoretical study of γ determination
for the idealised semiactive device case of negligible response time zero residual force and
zero inherent system damping is presented in [28]
The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic
horizontal excitation applied to the nacelle The frequency range comprised the
neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz
Several system configurations were regarded passive system with the constant control
current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the
newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2
respectively) or with the simple previously tested MR damper hyperbolic tangent inverse
model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm
(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)
that was previously proved to be the best approach [242526] was selected The obtained
output frequency response functions of the tower tip horizontal displacement x1 amplitude are
presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1
the MR damper force PMRreq PMR
meas and the MR damper current iMRreq iMR
meas (adequately
scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-
displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT
PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and
435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most
crucial concerning preferable control solutions (see Fig 10 open loop systems are not of
interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR
meas
and the MR damper current iMRreq iMR
meas (adequately scaled and zoomed) obtained for the
system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current
Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)
25 3 35 4 45 505
1
15
2
25
3
35
4
45
5
55x 10
-3
Frequency [Hz]
Dis
pla
cem
ent A
mplit
ude A
(x1)
[m]
P0 = 61 N
00 A
01 A
02 A
03 A
04 A
05 A
ADPT V1
ADPT V2
ADPT INV
ADPT PI
ModGND
Figure 10 Tower tip displacement amplitude output frequency response functions
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
10
0 01 02 03 04 05 06 07-3
-2
-1
0
1
2
3
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
11
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
12
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops
Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
005 006
-1
0
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
13
0 005 01 015 02 025 03 035 04 045-2
-15
-1
-05
0
05
1
15
2
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops
021 0215 022 0225 023
-14
-12
-1
-08
-06
-04
-02
0
02
04
06
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
0315 032 0325 033 0335 034 0345 035
-03
-02
-01
0
01
02
03
04
05
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
001 x
PMR
req
001 x
PMR
meas
i MR
req
i MR
meas
Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
14
0 001 002 003 004 005-01
0
01
02
03
04
05
06
07
08
09
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
0 001 002 003 004 005-04
-03
-02
-01
0
01
02
03
04
05
06
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
Figure 22 PID current controller operation at
(a) positive (b) negative step change of iMRreq
Table 2 presents values of the quality index Q (best values in bold) being a root-mean-
square of the PMRreqndashPMR
meas difference
2
1
Nreq meas
MR MR
j
Q P j P j
(4)
where j is the time sample number and N is the number of the regarded samples ModGND
solution is omitted here as it is not based on required MR damper force tracking idea
Table 2 Values of the quality index Q (4)
System 295 [Hz] 435 [Hz]
ADPT INV 3002 6531
ADPT PI 2679 6274
ADPT V1 2366 4955
ADPT V2 2273 5374
In Fig 10 two maxima that are typical for TVA operation are apparent for all the
solutions but 02 03 04 and 05 A for which the damping is relatively too high
Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most
favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood
(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)
however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or
some positive damping added may improve the system response (as higher amplitude of
PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR
req ADPT V2
may become a preferred choice as it copes better with the integrator wind-up (by changing
the value of γ either the first maxima is lowered while the second maxima is elevated or the
second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to
the previously introduced [242526313237] ADPT PI and especially to ADPT INV within
the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper
required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz
for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially
considering the time instants immediately following PMRmeas sign changes (all presented time
patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the
difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
15
MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI
and especially for ADPT INV are incomparable to the respective patterns registered for
ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The
same may be concluded concerning PMRreq force tracking quality just before PMR
meas sign
changes although ADPT INV characteristics (Fig 16) could not be even described as
acceptable Concerning the MR damper residual force minimisation both ADPT V1 and
ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted
for the demagnetisation and response sharpening do the job properly The MR damper force-
displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along
with the friction (due to the MR damper residual force) phenomena at 295 Hz and the
positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper
measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not
differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2
however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash
as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated
according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of
nonlinear damping
As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one
may observe iMRreq signal rise at a time instant of 005 s while PMR
meas response modulus rise
is at ca 006 s what makes a real challenge for the follow-up-type-controller operational
quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations
present in Figs 13 and 14
5 CONCLUSION
The conducted experimental analysis proved the effectiveness of the proposed refined MR
damper force tracking algorithm in two versions The obtained output frequency response
function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels
former solutions (designated by ADPT PI and ADPT INV) and is comparable to the
frequency response of the ModGND system that previously demonstrated the best
performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range
while ModGND excels for frequencies higher than 435 Hz and marginally in the (300
320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope
best with the problem of the residual MR damper force magnetic remanence when zero
force is assumed due to the MR damper inability to generate active forces The
implementation of these logics for the ModGND algorithm along with the analysis of the
demanded value of γ for the real-world system with response time residual force and
inherent damping all of which are nonzero shall be a subject of the future research The
minimisation of the residual force negative effects and the quality of positive stiffness
tracking will also be investigated Based on these analyses results and laboratory model
measurements and considering the dynamic similarity study that includes determined time
and length scale factors [41] in combination with force scale factor [44] direct calculation of
the demanded control signal for a real-world full scale vibration reduction system MR TVA
will be possible
Acknowledgment
This work is supported by AGH University of Science and Technology under research
program No 1111130958
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Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
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[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
4
3 THE CONTROL ALGORITHM
The underlying idea of the implemented control system is presented in Fig 2 Three
measurement input signals are regarded spring MR damper relative displacement x1ndashx2meas
MR damper current iMRmeas and MR damper force PMR
meas The MR Damper Required Force
subsystem corresponds to the real-time calculation of the demanded MR damper force PMRreq
ndash for the purpose of the current analysis the algorithm of the undamped dynamic vibration
absorber [10] that tracks excitation frequency [252628] is emulated using the MR damper
The MR damper should generate positive or negative stiffness force in such a way that the
TVA stiffness 2
reqk in equations (1) and (2) is tuned to the actual operationexcitation
frequency exc rather than to the tower-nacelle system first bending frequency Based on this
assumption the real-time determination of exc is followed by the real-time calculation of the
TVA required stiffness force 2 1 2
req req
stiffP k x x while the damping is assumed to be zero
(for the most efficient vibration mitigation at the frequency of tuning) leading to the MR
damper required force formula
2 2 1 2
req req
MRP k k x x (1)
with
2
2
2
req
exck m (2)
where γ is a correction factor that is present as the MR damper cannot deliver energy to the
system thus the force defined by equation (1) cannot be exactly mapped
Figure 2 The schematic diagram of the control system
When active forces are required zero force is assumed Thus arises a problem of a precise
MR damper force tracking in the case of pattern being discontinuous due to such a switching
A quick timeous (with possible prediction) and sharp force follow-up is needed whereas the
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
5
actuator dynamics exhibits the inertia due to the coil electrical resistance and inductance
magnetic remanence as well as the time lag hysteresis resulting from the MR effect
(particle chains formation) delay MR fluid preyield operation regime These effects cannot
be eliminated by a simple PIPID feedback controller with the sign adjustments
[242526313237] as it can shape the force-velocity relationship only into a linear or a
higher-order polynomial function with the inherent time lag even utilising the adequate
current controller Thus a dedicated MR damper force follow-up PID-based control
algorithm that was specially developed and refined during the current study based on
[252631] is represented by the PID Force Controller with Correction Demagnetisation amp
Sharpening subsystem (see Fig 2) Apart from the demanded MR damper force PMRreq input
the measured actual MR damper force PMRmeas and the modelled MR damper force PMR
modelled
signals are fed to the input of this subsystem PMRmodelled is the real-time calculated force with
the use of the MR damper forward hyperbolic tangent model (the MR Damper Model
subsystem) in the form of
1 2 1 1 2 0 1 2 2 1 2tanh p pmodelled
MR cP P v v x x c v v x x (3)
where Pc = C1iMR + C2 and c0 = C3iMR + C4 are the MR damper current (iMR) dependent
friction force and viscous damping coefficients (respectively) while p1 and p2 are the
scaling parameters The parameters initial values taken from Ref [45] were modified
accordingly for the current analysis frequency and piston travel ranges Additionally p1 and
p2 values were lowered down to be negative to obtain the earlier MR damper response sign
changes serving as PMRmeas sign change prediction The resultant MR damper model
parameters are gathered in the Tab 1 The Kalman Filter subsystem as introduced in [27] is
used for the real-time reproduction of the unmeasured state namely the MR damper relative
velocity v1ndashv2 in a presence of measurement noise that otherwise would be amplified by the
simple differentiating of x1ndashx2
Table 1 The adopted parameters of the MR damper model
Parameter Value
ν 130
p1 -250
p2 -100
C1 202
C2 225
C3 312
C4 467
The PID Force Controller with Correction Demagnetisation amp Sharpening subsystem
representation in Simulink is depicted in Fig 3 Its three main elements are the PID
Controller with Correction the Demagnetisation and the Response Sharpening subsystems
The primary version (V1) of the PID Controller with Correction subsystem is depicted in
Fig 4 It consists of the Abs blocks the Gain block Alpha1 as the scaling factor (Alpha1gt1 is
necessary as |PMRreq|=|PMR
meas| case should not result in zero control) the PID Controller
with Alpha2 Constrained Integration block (Alpha2lt1 multiplier constraints the integral
action when Alpha1|PMRreq|le|PMR
meas|) the multiplying blocks sign relations of
PMRreqampPMR
meas PMRreqampPMR
modelled PMRmeasampPMR
modelled determination conditional (rhombus)
blocks with logical (marked in grey) outputs and the Switch blocks with grey logical inputs
and black switched signals inputs Standard automatic control PID tuning techniques were
used for selection of proportional P integral I and derivative D path gains Additionally the
Saturation block is used with constants idemag=1510ndash2 A (the MR damper magnetic path amp
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
6
MR fluid particles demagnetisation current value) and imax=15 A while the Gain ndash1 is for
negation and the Max block with ndash02imax (ndash03 A) constant input are used to sharpen the
system response when PMRmeas changes sign (while PMR
req sign is maintained) what is
predicted by PMRmodelled signal to set the instantaneous current adequately early to ndash03 A and
moreover obtain minimum MR damper residual force modulus (that is greater due to the
remanent magnetisation) after PMRmeas sign change (see time range of (0315 0350) s in Figs
18 19 and 21 (b) vs Figs 16 and 17) Such constructed MR damper force tracking idea is
insensitive to MR damper dynamics changes due to eg temperature or stroke amplitude
variation during its operation as PMRmodelled sign is considered here instead of PMR
modelled value
Figure 3 Simulink diagram of the PID Force Controller with Correction
Demagnetisation amp Sharpening subsystem
Figure 4 Simulink diagram of the PID Controller with Correction subsystem V1
The second version (V2) of the PID Controller with Correction concept is depicted in
Fig 5 It differs from V1 by an idea of the integrator resetting when PMRmeas and PMR
modelled
have the opposite signs while the integrator initial condition (after the reset) is Alpha3
(Alpha3lt1) times the most recent nonzero integrator state This solution is implemented to
cope with the integrator wind-up problem that may be observed for the V1 concept (see Fig
18 vs Fig 19 starting eg at 005 s) and comes along with possibly enlarged I path gain and
higher integration constraint Alpha2 (Alpha2lt1) in relation to V1 concept
The Demagnetisation subsystem (see Fig 3) is depicted in Fig 6 It produces the
exponentially decaying current pattern (due to the presence of derivative element with first
order inertia and T=0067tperiod where tperiod= 2 exc ) that is switched between positive and
negative values using Rectangle Pulse Generator multiplier block (with two levels ndashidemag
and idemag) when the force should be zero due to the MR damper inability to produce active
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
7
forces (see Fig 21 (b)) The Running Mean subsystem (Fig 7) calculates the difference of the
outputs of two integrator blocks with the level-type reset (integration runs only when the
required value of the control current is ndashidemag ie PMRreq and PMR
meas have opposite signs ndash
see Figs 4 and 5) with the delay time tdelay=0067tperiod between them assuming that the
vibration patterns are characterised by single dominant frequency which is the case in the
most real world wind turbine structures operation scenarios
Figure 5 Simulink diagram of the PID Controller with Correction subsystem V2
Figure 6 Simulink diagram of the Demagnetisation subsystem
Figure 7 Simulink diagram of the Running Mean subsystem
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
8
The Response sharpening subsystem (see Fig 3) is presented in Fig 8 Its aim is to
sharpen the MR damper response at the moment of PMRmeas signal sign change while PMR
req
sign has changed earlier however the MR damper (as a dissipative device) was unable to
produce the active force (see Figs 13 and 14) To fulfil this task the control current is
enlarged by the value of 05 A when PMRmeas modulus is decreasing and is lower than 10 of
PMRmeas running amplitude and PMR
meas sign is consistent within last two sampling periods t0
(see Figs 13 14 and 21 (a) t0=110ndash3 s was assumed) Thanks to such logics the required
value of the control current iMRreq precedes the sign change of PMR
meas thus the control current
that actually flows through the MR damper coil iMRmeas is set at the moment of the PMR
meas
sign change with no delay The Running Amplitude subsystem (Fig 9) calculates the
difference of the outputs of the two integrator blocks with delay of five oscillation periods
between them The input to both integrators is the quantity (PMRmeas) squared (Sqr block) The
resultant difference is multiplied by two and divided by a time of five periods to obtain the
amplitude squared thus finally the Sqrt (square root) block is needed only to obtain
amplitude A(bull) of the input signal (assuming that vibration pattern is characterised by single
dominant frequency)
The parameters imax idemag tdelay Alpha1 Alpha2 Alpha3 values were selected on the
basis of numerical simulations supported by MR damper dynamics experimental testing
Figure 8 Simulink diagram of the Response sharpening subsystem
Figure 9 Simulink diagram of the Running Amplitude subsystem
The system in Fig 2 also includes standard analogue PID Current Controller subsystem
aimed to control MR damper with the use of an electronic board that enforces the MR damper
current via a control voltage uMR based on iMRmeas and iMR
req signals (see Figs 22 (a)(b))
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
9
4 THE EXPERIMENTAL ANALYSIS
For the purpose of the current experimental analysis that is oriented to the development of the
refined MR damper force tracking algorithm the value of γ = 1 was assumed while the
selection of γ was not a scope of the present research The theoretical study of γ determination
for the idealised semiactive device case of negligible response time zero residual force and
zero inherent system damping is presented in [28]
The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic
horizontal excitation applied to the nacelle The frequency range comprised the
neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz
Several system configurations were regarded passive system with the constant control
current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the
newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2
respectively) or with the simple previously tested MR damper hyperbolic tangent inverse
model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm
(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)
that was previously proved to be the best approach [242526] was selected The obtained
output frequency response functions of the tower tip horizontal displacement x1 amplitude are
presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1
the MR damper force PMRreq PMR
meas and the MR damper current iMRreq iMR
meas (adequately
scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-
displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT
PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and
435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most
crucial concerning preferable control solutions (see Fig 10 open loop systems are not of
interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR
meas
and the MR damper current iMRreq iMR
meas (adequately scaled and zoomed) obtained for the
system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current
Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)
25 3 35 4 45 505
1
15
2
25
3
35
4
45
5
55x 10
-3
Frequency [Hz]
Dis
pla
cem
ent A
mplit
ude A
(x1)
[m]
P0 = 61 N
00 A
01 A
02 A
03 A
04 A
05 A
ADPT V1
ADPT V2
ADPT INV
ADPT PI
ModGND
Figure 10 Tower tip displacement amplitude output frequency response functions
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
10
0 01 02 03 04 05 06 07-3
-2
-1
0
1
2
3
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
11
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
12
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops
Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
005 006
-1
0
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
13
0 005 01 015 02 025 03 035 04 045-2
-15
-1
-05
0
05
1
15
2
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops
021 0215 022 0225 023
-14
-12
-1
-08
-06
-04
-02
0
02
04
06
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
0315 032 0325 033 0335 034 0345 035
-03
-02
-01
0
01
02
03
04
05
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
001 x
PMR
req
001 x
PMR
meas
i MR
req
i MR
meas
Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
14
0 001 002 003 004 005-01
0
01
02
03
04
05
06
07
08
09
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
0 001 002 003 004 005-04
-03
-02
-01
0
01
02
03
04
05
06
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
Figure 22 PID current controller operation at
(a) positive (b) negative step change of iMRreq
Table 2 presents values of the quality index Q (best values in bold) being a root-mean-
square of the PMRreqndashPMR
meas difference
2
1
Nreq meas
MR MR
j
Q P j P j
(4)
where j is the time sample number and N is the number of the regarded samples ModGND
solution is omitted here as it is not based on required MR damper force tracking idea
Table 2 Values of the quality index Q (4)
System 295 [Hz] 435 [Hz]
ADPT INV 3002 6531
ADPT PI 2679 6274
ADPT V1 2366 4955
ADPT V2 2273 5374
In Fig 10 two maxima that are typical for TVA operation are apparent for all the
solutions but 02 03 04 and 05 A for which the damping is relatively too high
Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most
favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood
(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)
however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or
some positive damping added may improve the system response (as higher amplitude of
PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR
req ADPT V2
may become a preferred choice as it copes better with the integrator wind-up (by changing
the value of γ either the first maxima is lowered while the second maxima is elevated or the
second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to
the previously introduced [242526313237] ADPT PI and especially to ADPT INV within
the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper
required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz
for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially
considering the time instants immediately following PMRmeas sign changes (all presented time
patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the
difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
15
MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI
and especially for ADPT INV are incomparable to the respective patterns registered for
ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The
same may be concluded concerning PMRreq force tracking quality just before PMR
meas sign
changes although ADPT INV characteristics (Fig 16) could not be even described as
acceptable Concerning the MR damper residual force minimisation both ADPT V1 and
ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted
for the demagnetisation and response sharpening do the job properly The MR damper force-
displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along
with the friction (due to the MR damper residual force) phenomena at 295 Hz and the
positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper
measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not
differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2
however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash
as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated
according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of
nonlinear damping
As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one
may observe iMRreq signal rise at a time instant of 005 s while PMR
meas response modulus rise
is at ca 006 s what makes a real challenge for the follow-up-type-controller operational
quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations
present in Figs 13 and 14
5 CONCLUSION
The conducted experimental analysis proved the effectiveness of the proposed refined MR
damper force tracking algorithm in two versions The obtained output frequency response
function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels
former solutions (designated by ADPT PI and ADPT INV) and is comparable to the
frequency response of the ModGND system that previously demonstrated the best
performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range
while ModGND excels for frequencies higher than 435 Hz and marginally in the (300
320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope
best with the problem of the residual MR damper force magnetic remanence when zero
force is assumed due to the MR damper inability to generate active forces The
implementation of these logics for the ModGND algorithm along with the analysis of the
demanded value of γ for the real-world system with response time residual force and
inherent damping all of which are nonzero shall be a subject of the future research The
minimisation of the residual force negative effects and the quality of positive stiffness
tracking will also be investigated Based on these analyses results and laboratory model
measurements and considering the dynamic similarity study that includes determined time
and length scale factors [41] in combination with force scale factor [44] direct calculation of
the demanded control signal for a real-world full scale vibration reduction system MR TVA
will be possible
Acknowledgment
This work is supported by AGH University of Science and Technology under research
program No 1111130958
References
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL
[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech
Struct amp Mach (1996) 24 (2) 155-187
[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering
low structural damping and soil structure interaction European Wind Energy Association
Annual Event (2012) Copenhagen 16-19042012
[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic
damping of operational wind turbine modes from experiments European Wind Energy
Association Annual Event (2012) Copenhagen 16-19042012
[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z
wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)
209-216
[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M
Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European
Wind Energy Association Annual Event (2012) Copenhagen 16-19042012
[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p
harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen
16-19042012
[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor
speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)
Monaco
[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind
turbines on two floating platforms Mechatronics (2011) 21 691-703
[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY
[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation
test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013
[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu
M Wind turbine tower load reduction using passive and semiactive dampers European Wind
Energy Association Annual Event (2011) Brussels
[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace
Exposition (2010) Orlando
[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej
z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198
[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR
damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds
Lisse CRC Press
[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and
experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State
Phenomena (2011) 177 (Control engineering in materials processing) 102-115
[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR
shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)
[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical
and Applied Mechanics (2007) 45 (1) 133-146
[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension
system with MR shock absorbers Computers and Structures (2008) 86 379-385
[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the
Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32
(1+2) 67-80
[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based
vibration reduction system Bulletin Of The Polish Academy Of
Sciences-Technical Sciences (2011) 59 (1) 75-80
[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes
Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
5
actuator dynamics exhibits the inertia due to the coil electrical resistance and inductance
magnetic remanence as well as the time lag hysteresis resulting from the MR effect
(particle chains formation) delay MR fluid preyield operation regime These effects cannot
be eliminated by a simple PIPID feedback controller with the sign adjustments
[242526313237] as it can shape the force-velocity relationship only into a linear or a
higher-order polynomial function with the inherent time lag even utilising the adequate
current controller Thus a dedicated MR damper force follow-up PID-based control
algorithm that was specially developed and refined during the current study based on
[252631] is represented by the PID Force Controller with Correction Demagnetisation amp
Sharpening subsystem (see Fig 2) Apart from the demanded MR damper force PMRreq input
the measured actual MR damper force PMRmeas and the modelled MR damper force PMR
modelled
signals are fed to the input of this subsystem PMRmodelled is the real-time calculated force with
the use of the MR damper forward hyperbolic tangent model (the MR Damper Model
subsystem) in the form of
1 2 1 1 2 0 1 2 2 1 2tanh p pmodelled
MR cP P v v x x c v v x x (3)
where Pc = C1iMR + C2 and c0 = C3iMR + C4 are the MR damper current (iMR) dependent
friction force and viscous damping coefficients (respectively) while p1 and p2 are the
scaling parameters The parameters initial values taken from Ref [45] were modified
accordingly for the current analysis frequency and piston travel ranges Additionally p1 and
p2 values were lowered down to be negative to obtain the earlier MR damper response sign
changes serving as PMRmeas sign change prediction The resultant MR damper model
parameters are gathered in the Tab 1 The Kalman Filter subsystem as introduced in [27] is
used for the real-time reproduction of the unmeasured state namely the MR damper relative
velocity v1ndashv2 in a presence of measurement noise that otherwise would be amplified by the
simple differentiating of x1ndashx2
Table 1 The adopted parameters of the MR damper model
Parameter Value
ν 130
p1 -250
p2 -100
C1 202
C2 225
C3 312
C4 467
The PID Force Controller with Correction Demagnetisation amp Sharpening subsystem
representation in Simulink is depicted in Fig 3 Its three main elements are the PID
Controller with Correction the Demagnetisation and the Response Sharpening subsystems
The primary version (V1) of the PID Controller with Correction subsystem is depicted in
Fig 4 It consists of the Abs blocks the Gain block Alpha1 as the scaling factor (Alpha1gt1 is
necessary as |PMRreq|=|PMR
meas| case should not result in zero control) the PID Controller
with Alpha2 Constrained Integration block (Alpha2lt1 multiplier constraints the integral
action when Alpha1|PMRreq|le|PMR
meas|) the multiplying blocks sign relations of
PMRreqampPMR
meas PMRreqampPMR
modelled PMRmeasampPMR
modelled determination conditional (rhombus)
blocks with logical (marked in grey) outputs and the Switch blocks with grey logical inputs
and black switched signals inputs Standard automatic control PID tuning techniques were
used for selection of proportional P integral I and derivative D path gains Additionally the
Saturation block is used with constants idemag=1510ndash2 A (the MR damper magnetic path amp
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
6
MR fluid particles demagnetisation current value) and imax=15 A while the Gain ndash1 is for
negation and the Max block with ndash02imax (ndash03 A) constant input are used to sharpen the
system response when PMRmeas changes sign (while PMR
req sign is maintained) what is
predicted by PMRmodelled signal to set the instantaneous current adequately early to ndash03 A and
moreover obtain minimum MR damper residual force modulus (that is greater due to the
remanent magnetisation) after PMRmeas sign change (see time range of (0315 0350) s in Figs
18 19 and 21 (b) vs Figs 16 and 17) Such constructed MR damper force tracking idea is
insensitive to MR damper dynamics changes due to eg temperature or stroke amplitude
variation during its operation as PMRmodelled sign is considered here instead of PMR
modelled value
Figure 3 Simulink diagram of the PID Force Controller with Correction
Demagnetisation amp Sharpening subsystem
Figure 4 Simulink diagram of the PID Controller with Correction subsystem V1
The second version (V2) of the PID Controller with Correction concept is depicted in
Fig 5 It differs from V1 by an idea of the integrator resetting when PMRmeas and PMR
modelled
have the opposite signs while the integrator initial condition (after the reset) is Alpha3
(Alpha3lt1) times the most recent nonzero integrator state This solution is implemented to
cope with the integrator wind-up problem that may be observed for the V1 concept (see Fig
18 vs Fig 19 starting eg at 005 s) and comes along with possibly enlarged I path gain and
higher integration constraint Alpha2 (Alpha2lt1) in relation to V1 concept
The Demagnetisation subsystem (see Fig 3) is depicted in Fig 6 It produces the
exponentially decaying current pattern (due to the presence of derivative element with first
order inertia and T=0067tperiod where tperiod= 2 exc ) that is switched between positive and
negative values using Rectangle Pulse Generator multiplier block (with two levels ndashidemag
and idemag) when the force should be zero due to the MR damper inability to produce active
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
7
forces (see Fig 21 (b)) The Running Mean subsystem (Fig 7) calculates the difference of the
outputs of two integrator blocks with the level-type reset (integration runs only when the
required value of the control current is ndashidemag ie PMRreq and PMR
meas have opposite signs ndash
see Figs 4 and 5) with the delay time tdelay=0067tperiod between them assuming that the
vibration patterns are characterised by single dominant frequency which is the case in the
most real world wind turbine structures operation scenarios
Figure 5 Simulink diagram of the PID Controller with Correction subsystem V2
Figure 6 Simulink diagram of the Demagnetisation subsystem
Figure 7 Simulink diagram of the Running Mean subsystem
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
8
The Response sharpening subsystem (see Fig 3) is presented in Fig 8 Its aim is to
sharpen the MR damper response at the moment of PMRmeas signal sign change while PMR
req
sign has changed earlier however the MR damper (as a dissipative device) was unable to
produce the active force (see Figs 13 and 14) To fulfil this task the control current is
enlarged by the value of 05 A when PMRmeas modulus is decreasing and is lower than 10 of
PMRmeas running amplitude and PMR
meas sign is consistent within last two sampling periods t0
(see Figs 13 14 and 21 (a) t0=110ndash3 s was assumed) Thanks to such logics the required
value of the control current iMRreq precedes the sign change of PMR
meas thus the control current
that actually flows through the MR damper coil iMRmeas is set at the moment of the PMR
meas
sign change with no delay The Running Amplitude subsystem (Fig 9) calculates the
difference of the outputs of the two integrator blocks with delay of five oscillation periods
between them The input to both integrators is the quantity (PMRmeas) squared (Sqr block) The
resultant difference is multiplied by two and divided by a time of five periods to obtain the
amplitude squared thus finally the Sqrt (square root) block is needed only to obtain
amplitude A(bull) of the input signal (assuming that vibration pattern is characterised by single
dominant frequency)
The parameters imax idemag tdelay Alpha1 Alpha2 Alpha3 values were selected on the
basis of numerical simulations supported by MR damper dynamics experimental testing
Figure 8 Simulink diagram of the Response sharpening subsystem
Figure 9 Simulink diagram of the Running Amplitude subsystem
The system in Fig 2 also includes standard analogue PID Current Controller subsystem
aimed to control MR damper with the use of an electronic board that enforces the MR damper
current via a control voltage uMR based on iMRmeas and iMR
req signals (see Figs 22 (a)(b))
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
9
4 THE EXPERIMENTAL ANALYSIS
For the purpose of the current experimental analysis that is oriented to the development of the
refined MR damper force tracking algorithm the value of γ = 1 was assumed while the
selection of γ was not a scope of the present research The theoretical study of γ determination
for the idealised semiactive device case of negligible response time zero residual force and
zero inherent system damping is presented in [28]
The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic
horizontal excitation applied to the nacelle The frequency range comprised the
neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz
Several system configurations were regarded passive system with the constant control
current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the
newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2
respectively) or with the simple previously tested MR damper hyperbolic tangent inverse
model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm
(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)
that was previously proved to be the best approach [242526] was selected The obtained
output frequency response functions of the tower tip horizontal displacement x1 amplitude are
presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1
the MR damper force PMRreq PMR
meas and the MR damper current iMRreq iMR
meas (adequately
scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-
displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT
PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and
435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most
crucial concerning preferable control solutions (see Fig 10 open loop systems are not of
interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR
meas
and the MR damper current iMRreq iMR
meas (adequately scaled and zoomed) obtained for the
system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current
Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)
25 3 35 4 45 505
1
15
2
25
3
35
4
45
5
55x 10
-3
Frequency [Hz]
Dis
pla
cem
ent A
mplit
ude A
(x1)
[m]
P0 = 61 N
00 A
01 A
02 A
03 A
04 A
05 A
ADPT V1
ADPT V2
ADPT INV
ADPT PI
ModGND
Figure 10 Tower tip displacement amplitude output frequency response functions
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
10
0 01 02 03 04 05 06 07-3
-2
-1
0
1
2
3
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
11
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
12
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops
Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
005 006
-1
0
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
13
0 005 01 015 02 025 03 035 04 045-2
-15
-1
-05
0
05
1
15
2
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops
021 0215 022 0225 023
-14
-12
-1
-08
-06
-04
-02
0
02
04
06
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
0315 032 0325 033 0335 034 0345 035
-03
-02
-01
0
01
02
03
04
05
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
001 x
PMR
req
001 x
PMR
meas
i MR
req
i MR
meas
Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
14
0 001 002 003 004 005-01
0
01
02
03
04
05
06
07
08
09
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
0 001 002 003 004 005-04
-03
-02
-01
0
01
02
03
04
05
06
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
Figure 22 PID current controller operation at
(a) positive (b) negative step change of iMRreq
Table 2 presents values of the quality index Q (best values in bold) being a root-mean-
square of the PMRreqndashPMR
meas difference
2
1
Nreq meas
MR MR
j
Q P j P j
(4)
where j is the time sample number and N is the number of the regarded samples ModGND
solution is omitted here as it is not based on required MR damper force tracking idea
Table 2 Values of the quality index Q (4)
System 295 [Hz] 435 [Hz]
ADPT INV 3002 6531
ADPT PI 2679 6274
ADPT V1 2366 4955
ADPT V2 2273 5374
In Fig 10 two maxima that are typical for TVA operation are apparent for all the
solutions but 02 03 04 and 05 A for which the damping is relatively too high
Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most
favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood
(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)
however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or
some positive damping added may improve the system response (as higher amplitude of
PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR
req ADPT V2
may become a preferred choice as it copes better with the integrator wind-up (by changing
the value of γ either the first maxima is lowered while the second maxima is elevated or the
second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to
the previously introduced [242526313237] ADPT PI and especially to ADPT INV within
the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper
required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz
for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially
considering the time instants immediately following PMRmeas sign changes (all presented time
patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the
difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
15
MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI
and especially for ADPT INV are incomparable to the respective patterns registered for
ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The
same may be concluded concerning PMRreq force tracking quality just before PMR
meas sign
changes although ADPT INV characteristics (Fig 16) could not be even described as
acceptable Concerning the MR damper residual force minimisation both ADPT V1 and
ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted
for the demagnetisation and response sharpening do the job properly The MR damper force-
displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along
with the friction (due to the MR damper residual force) phenomena at 295 Hz and the
positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper
measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not
differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2
however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash
as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated
according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of
nonlinear damping
As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one
may observe iMRreq signal rise at a time instant of 005 s while PMR
meas response modulus rise
is at ca 006 s what makes a real challenge for the follow-up-type-controller operational
quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations
present in Figs 13 and 14
5 CONCLUSION
The conducted experimental analysis proved the effectiveness of the proposed refined MR
damper force tracking algorithm in two versions The obtained output frequency response
function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels
former solutions (designated by ADPT PI and ADPT INV) and is comparable to the
frequency response of the ModGND system that previously demonstrated the best
performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range
while ModGND excels for frequencies higher than 435 Hz and marginally in the (300
320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope
best with the problem of the residual MR damper force magnetic remanence when zero
force is assumed due to the MR damper inability to generate active forces The
implementation of these logics for the ModGND algorithm along with the analysis of the
demanded value of γ for the real-world system with response time residual force and
inherent damping all of which are nonzero shall be a subject of the future research The
minimisation of the residual force negative effects and the quality of positive stiffness
tracking will also be investigated Based on these analyses results and laboratory model
measurements and considering the dynamic similarity study that includes determined time
and length scale factors [41] in combination with force scale factor [44] direct calculation of
the demanded control signal for a real-world full scale vibration reduction system MR TVA
will be possible
Acknowledgment
This work is supported by AGH University of Science and Technology under research
program No 1111130958
References
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL
[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech
Struct amp Mach (1996) 24 (2) 155-187
[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering
low structural damping and soil structure interaction European Wind Energy Association
Annual Event (2012) Copenhagen 16-19042012
[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic
damping of operational wind turbine modes from experiments European Wind Energy
Association Annual Event (2012) Copenhagen 16-19042012
[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z
wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)
209-216
[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M
Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European
Wind Energy Association Annual Event (2012) Copenhagen 16-19042012
[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p
harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen
16-19042012
[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor
speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)
Monaco
[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind
turbines on two floating platforms Mechatronics (2011) 21 691-703
[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY
[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation
test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013
[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu
M Wind turbine tower load reduction using passive and semiactive dampers European Wind
Energy Association Annual Event (2011) Brussels
[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace
Exposition (2010) Orlando
[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej
z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198
[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR
damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds
Lisse CRC Press
[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and
experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State
Phenomena (2011) 177 (Control engineering in materials processing) 102-115
[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR
shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)
[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical
and Applied Mechanics (2007) 45 (1) 133-146
[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension
system with MR shock absorbers Computers and Structures (2008) 86 379-385
[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the
Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32
(1+2) 67-80
[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based
vibration reduction system Bulletin Of The Polish Academy Of
Sciences-Technical Sciences (2011) 59 (1) 75-80
[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes
Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
6
MR fluid particles demagnetisation current value) and imax=15 A while the Gain ndash1 is for
negation and the Max block with ndash02imax (ndash03 A) constant input are used to sharpen the
system response when PMRmeas changes sign (while PMR
req sign is maintained) what is
predicted by PMRmodelled signal to set the instantaneous current adequately early to ndash03 A and
moreover obtain minimum MR damper residual force modulus (that is greater due to the
remanent magnetisation) after PMRmeas sign change (see time range of (0315 0350) s in Figs
18 19 and 21 (b) vs Figs 16 and 17) Such constructed MR damper force tracking idea is
insensitive to MR damper dynamics changes due to eg temperature or stroke amplitude
variation during its operation as PMRmodelled sign is considered here instead of PMR
modelled value
Figure 3 Simulink diagram of the PID Force Controller with Correction
Demagnetisation amp Sharpening subsystem
Figure 4 Simulink diagram of the PID Controller with Correction subsystem V1
The second version (V2) of the PID Controller with Correction concept is depicted in
Fig 5 It differs from V1 by an idea of the integrator resetting when PMRmeas and PMR
modelled
have the opposite signs while the integrator initial condition (after the reset) is Alpha3
(Alpha3lt1) times the most recent nonzero integrator state This solution is implemented to
cope with the integrator wind-up problem that may be observed for the V1 concept (see Fig
18 vs Fig 19 starting eg at 005 s) and comes along with possibly enlarged I path gain and
higher integration constraint Alpha2 (Alpha2lt1) in relation to V1 concept
The Demagnetisation subsystem (see Fig 3) is depicted in Fig 6 It produces the
exponentially decaying current pattern (due to the presence of derivative element with first
order inertia and T=0067tperiod where tperiod= 2 exc ) that is switched between positive and
negative values using Rectangle Pulse Generator multiplier block (with two levels ndashidemag
and idemag) when the force should be zero due to the MR damper inability to produce active
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
7
forces (see Fig 21 (b)) The Running Mean subsystem (Fig 7) calculates the difference of the
outputs of two integrator blocks with the level-type reset (integration runs only when the
required value of the control current is ndashidemag ie PMRreq and PMR
meas have opposite signs ndash
see Figs 4 and 5) with the delay time tdelay=0067tperiod between them assuming that the
vibration patterns are characterised by single dominant frequency which is the case in the
most real world wind turbine structures operation scenarios
Figure 5 Simulink diagram of the PID Controller with Correction subsystem V2
Figure 6 Simulink diagram of the Demagnetisation subsystem
Figure 7 Simulink diagram of the Running Mean subsystem
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
8
The Response sharpening subsystem (see Fig 3) is presented in Fig 8 Its aim is to
sharpen the MR damper response at the moment of PMRmeas signal sign change while PMR
req
sign has changed earlier however the MR damper (as a dissipative device) was unable to
produce the active force (see Figs 13 and 14) To fulfil this task the control current is
enlarged by the value of 05 A when PMRmeas modulus is decreasing and is lower than 10 of
PMRmeas running amplitude and PMR
meas sign is consistent within last two sampling periods t0
(see Figs 13 14 and 21 (a) t0=110ndash3 s was assumed) Thanks to such logics the required
value of the control current iMRreq precedes the sign change of PMR
meas thus the control current
that actually flows through the MR damper coil iMRmeas is set at the moment of the PMR
meas
sign change with no delay The Running Amplitude subsystem (Fig 9) calculates the
difference of the outputs of the two integrator blocks with delay of five oscillation periods
between them The input to both integrators is the quantity (PMRmeas) squared (Sqr block) The
resultant difference is multiplied by two and divided by a time of five periods to obtain the
amplitude squared thus finally the Sqrt (square root) block is needed only to obtain
amplitude A(bull) of the input signal (assuming that vibration pattern is characterised by single
dominant frequency)
The parameters imax idemag tdelay Alpha1 Alpha2 Alpha3 values were selected on the
basis of numerical simulations supported by MR damper dynamics experimental testing
Figure 8 Simulink diagram of the Response sharpening subsystem
Figure 9 Simulink diagram of the Running Amplitude subsystem
The system in Fig 2 also includes standard analogue PID Current Controller subsystem
aimed to control MR damper with the use of an electronic board that enforces the MR damper
current via a control voltage uMR based on iMRmeas and iMR
req signals (see Figs 22 (a)(b))
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
9
4 THE EXPERIMENTAL ANALYSIS
For the purpose of the current experimental analysis that is oriented to the development of the
refined MR damper force tracking algorithm the value of γ = 1 was assumed while the
selection of γ was not a scope of the present research The theoretical study of γ determination
for the idealised semiactive device case of negligible response time zero residual force and
zero inherent system damping is presented in [28]
The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic
horizontal excitation applied to the nacelle The frequency range comprised the
neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz
Several system configurations were regarded passive system with the constant control
current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the
newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2
respectively) or with the simple previously tested MR damper hyperbolic tangent inverse
model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm
(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)
that was previously proved to be the best approach [242526] was selected The obtained
output frequency response functions of the tower tip horizontal displacement x1 amplitude are
presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1
the MR damper force PMRreq PMR
meas and the MR damper current iMRreq iMR
meas (adequately
scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-
displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT
PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and
435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most
crucial concerning preferable control solutions (see Fig 10 open loop systems are not of
interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR
meas
and the MR damper current iMRreq iMR
meas (adequately scaled and zoomed) obtained for the
system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current
Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)
25 3 35 4 45 505
1
15
2
25
3
35
4
45
5
55x 10
-3
Frequency [Hz]
Dis
pla
cem
ent A
mplit
ude A
(x1)
[m]
P0 = 61 N
00 A
01 A
02 A
03 A
04 A
05 A
ADPT V1
ADPT V2
ADPT INV
ADPT PI
ModGND
Figure 10 Tower tip displacement amplitude output frequency response functions
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
10
0 01 02 03 04 05 06 07-3
-2
-1
0
1
2
3
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
11
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
12
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops
Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
005 006
-1
0
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
13
0 005 01 015 02 025 03 035 04 045-2
-15
-1
-05
0
05
1
15
2
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops
021 0215 022 0225 023
-14
-12
-1
-08
-06
-04
-02
0
02
04
06
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
0315 032 0325 033 0335 034 0345 035
-03
-02
-01
0
01
02
03
04
05
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
001 x
PMR
req
001 x
PMR
meas
i MR
req
i MR
meas
Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
14
0 001 002 003 004 005-01
0
01
02
03
04
05
06
07
08
09
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
0 001 002 003 004 005-04
-03
-02
-01
0
01
02
03
04
05
06
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
Figure 22 PID current controller operation at
(a) positive (b) negative step change of iMRreq
Table 2 presents values of the quality index Q (best values in bold) being a root-mean-
square of the PMRreqndashPMR
meas difference
2
1
Nreq meas
MR MR
j
Q P j P j
(4)
where j is the time sample number and N is the number of the regarded samples ModGND
solution is omitted here as it is not based on required MR damper force tracking idea
Table 2 Values of the quality index Q (4)
System 295 [Hz] 435 [Hz]
ADPT INV 3002 6531
ADPT PI 2679 6274
ADPT V1 2366 4955
ADPT V2 2273 5374
In Fig 10 two maxima that are typical for TVA operation are apparent for all the
solutions but 02 03 04 and 05 A for which the damping is relatively too high
Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most
favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood
(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)
however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or
some positive damping added may improve the system response (as higher amplitude of
PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR
req ADPT V2
may become a preferred choice as it copes better with the integrator wind-up (by changing
the value of γ either the first maxima is lowered while the second maxima is elevated or the
second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to
the previously introduced [242526313237] ADPT PI and especially to ADPT INV within
the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper
required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz
for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially
considering the time instants immediately following PMRmeas sign changes (all presented time
patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the
difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
15
MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI
and especially for ADPT INV are incomparable to the respective patterns registered for
ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The
same may be concluded concerning PMRreq force tracking quality just before PMR
meas sign
changes although ADPT INV characteristics (Fig 16) could not be even described as
acceptable Concerning the MR damper residual force minimisation both ADPT V1 and
ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted
for the demagnetisation and response sharpening do the job properly The MR damper force-
displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along
with the friction (due to the MR damper residual force) phenomena at 295 Hz and the
positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper
measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not
differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2
however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash
as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated
according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of
nonlinear damping
As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one
may observe iMRreq signal rise at a time instant of 005 s while PMR
meas response modulus rise
is at ca 006 s what makes a real challenge for the follow-up-type-controller operational
quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations
present in Figs 13 and 14
5 CONCLUSION
The conducted experimental analysis proved the effectiveness of the proposed refined MR
damper force tracking algorithm in two versions The obtained output frequency response
function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels
former solutions (designated by ADPT PI and ADPT INV) and is comparable to the
frequency response of the ModGND system that previously demonstrated the best
performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range
while ModGND excels for frequencies higher than 435 Hz and marginally in the (300
320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope
best with the problem of the residual MR damper force magnetic remanence when zero
force is assumed due to the MR damper inability to generate active forces The
implementation of these logics for the ModGND algorithm along with the analysis of the
demanded value of γ for the real-world system with response time residual force and
inherent damping all of which are nonzero shall be a subject of the future research The
minimisation of the residual force negative effects and the quality of positive stiffness
tracking will also be investigated Based on these analyses results and laboratory model
measurements and considering the dynamic similarity study that includes determined time
and length scale factors [41] in combination with force scale factor [44] direct calculation of
the demanded control signal for a real-world full scale vibration reduction system MR TVA
will be possible
Acknowledgment
This work is supported by AGH University of Science and Technology under research
program No 1111130958
References
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL
[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech
Struct amp Mach (1996) 24 (2) 155-187
[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering
low structural damping and soil structure interaction European Wind Energy Association
Annual Event (2012) Copenhagen 16-19042012
[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic
damping of operational wind turbine modes from experiments European Wind Energy
Association Annual Event (2012) Copenhagen 16-19042012
[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z
wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)
209-216
[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M
Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European
Wind Energy Association Annual Event (2012) Copenhagen 16-19042012
[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p
harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen
16-19042012
[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor
speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)
Monaco
[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind
turbines on two floating platforms Mechatronics (2011) 21 691-703
[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY
[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation
test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013
[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu
M Wind turbine tower load reduction using passive and semiactive dampers European Wind
Energy Association Annual Event (2011) Brussels
[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace
Exposition (2010) Orlando
[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej
z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198
[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR
damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds
Lisse CRC Press
[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and
experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State
Phenomena (2011) 177 (Control engineering in materials processing) 102-115
[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR
shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)
[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical
and Applied Mechanics (2007) 45 (1) 133-146
[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension
system with MR shock absorbers Computers and Structures (2008) 86 379-385
[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the
Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32
(1+2) 67-80
[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based
vibration reduction system Bulletin Of The Polish Academy Of
Sciences-Technical Sciences (2011) 59 (1) 75-80
[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes
Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
7
forces (see Fig 21 (b)) The Running Mean subsystem (Fig 7) calculates the difference of the
outputs of two integrator blocks with the level-type reset (integration runs only when the
required value of the control current is ndashidemag ie PMRreq and PMR
meas have opposite signs ndash
see Figs 4 and 5) with the delay time tdelay=0067tperiod between them assuming that the
vibration patterns are characterised by single dominant frequency which is the case in the
most real world wind turbine structures operation scenarios
Figure 5 Simulink diagram of the PID Controller with Correction subsystem V2
Figure 6 Simulink diagram of the Demagnetisation subsystem
Figure 7 Simulink diagram of the Running Mean subsystem
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
8
The Response sharpening subsystem (see Fig 3) is presented in Fig 8 Its aim is to
sharpen the MR damper response at the moment of PMRmeas signal sign change while PMR
req
sign has changed earlier however the MR damper (as a dissipative device) was unable to
produce the active force (see Figs 13 and 14) To fulfil this task the control current is
enlarged by the value of 05 A when PMRmeas modulus is decreasing and is lower than 10 of
PMRmeas running amplitude and PMR
meas sign is consistent within last two sampling periods t0
(see Figs 13 14 and 21 (a) t0=110ndash3 s was assumed) Thanks to such logics the required
value of the control current iMRreq precedes the sign change of PMR
meas thus the control current
that actually flows through the MR damper coil iMRmeas is set at the moment of the PMR
meas
sign change with no delay The Running Amplitude subsystem (Fig 9) calculates the
difference of the outputs of the two integrator blocks with delay of five oscillation periods
between them The input to both integrators is the quantity (PMRmeas) squared (Sqr block) The
resultant difference is multiplied by two and divided by a time of five periods to obtain the
amplitude squared thus finally the Sqrt (square root) block is needed only to obtain
amplitude A(bull) of the input signal (assuming that vibration pattern is characterised by single
dominant frequency)
The parameters imax idemag tdelay Alpha1 Alpha2 Alpha3 values were selected on the
basis of numerical simulations supported by MR damper dynamics experimental testing
Figure 8 Simulink diagram of the Response sharpening subsystem
Figure 9 Simulink diagram of the Running Amplitude subsystem
The system in Fig 2 also includes standard analogue PID Current Controller subsystem
aimed to control MR damper with the use of an electronic board that enforces the MR damper
current via a control voltage uMR based on iMRmeas and iMR
req signals (see Figs 22 (a)(b))
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
9
4 THE EXPERIMENTAL ANALYSIS
For the purpose of the current experimental analysis that is oriented to the development of the
refined MR damper force tracking algorithm the value of γ = 1 was assumed while the
selection of γ was not a scope of the present research The theoretical study of γ determination
for the idealised semiactive device case of negligible response time zero residual force and
zero inherent system damping is presented in [28]
The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic
horizontal excitation applied to the nacelle The frequency range comprised the
neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz
Several system configurations were regarded passive system with the constant control
current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the
newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2
respectively) or with the simple previously tested MR damper hyperbolic tangent inverse
model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm
(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)
that was previously proved to be the best approach [242526] was selected The obtained
output frequency response functions of the tower tip horizontal displacement x1 amplitude are
presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1
the MR damper force PMRreq PMR
meas and the MR damper current iMRreq iMR
meas (adequately
scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-
displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT
PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and
435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most
crucial concerning preferable control solutions (see Fig 10 open loop systems are not of
interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR
meas
and the MR damper current iMRreq iMR
meas (adequately scaled and zoomed) obtained for the
system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current
Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)
25 3 35 4 45 505
1
15
2
25
3
35
4
45
5
55x 10
-3
Frequency [Hz]
Dis
pla
cem
ent A
mplit
ude A
(x1)
[m]
P0 = 61 N
00 A
01 A
02 A
03 A
04 A
05 A
ADPT V1
ADPT V2
ADPT INV
ADPT PI
ModGND
Figure 10 Tower tip displacement amplitude output frequency response functions
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
10
0 01 02 03 04 05 06 07-3
-2
-1
0
1
2
3
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
11
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
12
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops
Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
005 006
-1
0
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
13
0 005 01 015 02 025 03 035 04 045-2
-15
-1
-05
0
05
1
15
2
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops
021 0215 022 0225 023
-14
-12
-1
-08
-06
-04
-02
0
02
04
06
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
0315 032 0325 033 0335 034 0345 035
-03
-02
-01
0
01
02
03
04
05
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
001 x
PMR
req
001 x
PMR
meas
i MR
req
i MR
meas
Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
14
0 001 002 003 004 005-01
0
01
02
03
04
05
06
07
08
09
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
0 001 002 003 004 005-04
-03
-02
-01
0
01
02
03
04
05
06
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
Figure 22 PID current controller operation at
(a) positive (b) negative step change of iMRreq
Table 2 presents values of the quality index Q (best values in bold) being a root-mean-
square of the PMRreqndashPMR
meas difference
2
1
Nreq meas
MR MR
j
Q P j P j
(4)
where j is the time sample number and N is the number of the regarded samples ModGND
solution is omitted here as it is not based on required MR damper force tracking idea
Table 2 Values of the quality index Q (4)
System 295 [Hz] 435 [Hz]
ADPT INV 3002 6531
ADPT PI 2679 6274
ADPT V1 2366 4955
ADPT V2 2273 5374
In Fig 10 two maxima that are typical for TVA operation are apparent for all the
solutions but 02 03 04 and 05 A for which the damping is relatively too high
Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most
favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood
(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)
however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or
some positive damping added may improve the system response (as higher amplitude of
PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR
req ADPT V2
may become a preferred choice as it copes better with the integrator wind-up (by changing
the value of γ either the first maxima is lowered while the second maxima is elevated or the
second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to
the previously introduced [242526313237] ADPT PI and especially to ADPT INV within
the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper
required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz
for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially
considering the time instants immediately following PMRmeas sign changes (all presented time
patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the
difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
15
MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI
and especially for ADPT INV are incomparable to the respective patterns registered for
ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The
same may be concluded concerning PMRreq force tracking quality just before PMR
meas sign
changes although ADPT INV characteristics (Fig 16) could not be even described as
acceptable Concerning the MR damper residual force minimisation both ADPT V1 and
ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted
for the demagnetisation and response sharpening do the job properly The MR damper force-
displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along
with the friction (due to the MR damper residual force) phenomena at 295 Hz and the
positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper
measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not
differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2
however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash
as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated
according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of
nonlinear damping
As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one
may observe iMRreq signal rise at a time instant of 005 s while PMR
meas response modulus rise
is at ca 006 s what makes a real challenge for the follow-up-type-controller operational
quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations
present in Figs 13 and 14
5 CONCLUSION
The conducted experimental analysis proved the effectiveness of the proposed refined MR
damper force tracking algorithm in two versions The obtained output frequency response
function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels
former solutions (designated by ADPT PI and ADPT INV) and is comparable to the
frequency response of the ModGND system that previously demonstrated the best
performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range
while ModGND excels for frequencies higher than 435 Hz and marginally in the (300
320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope
best with the problem of the residual MR damper force magnetic remanence when zero
force is assumed due to the MR damper inability to generate active forces The
implementation of these logics for the ModGND algorithm along with the analysis of the
demanded value of γ for the real-world system with response time residual force and
inherent damping all of which are nonzero shall be a subject of the future research The
minimisation of the residual force negative effects and the quality of positive stiffness
tracking will also be investigated Based on these analyses results and laboratory model
measurements and considering the dynamic similarity study that includes determined time
and length scale factors [41] in combination with force scale factor [44] direct calculation of
the demanded control signal for a real-world full scale vibration reduction system MR TVA
will be possible
Acknowledgment
This work is supported by AGH University of Science and Technology under research
program No 1111130958
References
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL
[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech
Struct amp Mach (1996) 24 (2) 155-187
[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering
low structural damping and soil structure interaction European Wind Energy Association
Annual Event (2012) Copenhagen 16-19042012
[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic
damping of operational wind turbine modes from experiments European Wind Energy
Association Annual Event (2012) Copenhagen 16-19042012
[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z
wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)
209-216
[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M
Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European
Wind Energy Association Annual Event (2012) Copenhagen 16-19042012
[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p
harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen
16-19042012
[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor
speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)
Monaco
[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind
turbines on two floating platforms Mechatronics (2011) 21 691-703
[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY
[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation
test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013
[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu
M Wind turbine tower load reduction using passive and semiactive dampers European Wind
Energy Association Annual Event (2011) Brussels
[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace
Exposition (2010) Orlando
[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej
z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198
[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR
damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds
Lisse CRC Press
[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and
experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State
Phenomena (2011) 177 (Control engineering in materials processing) 102-115
[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR
shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)
[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical
and Applied Mechanics (2007) 45 (1) 133-146
[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension
system with MR shock absorbers Computers and Structures (2008) 86 379-385
[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the
Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32
(1+2) 67-80
[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based
vibration reduction system Bulletin Of The Polish Academy Of
Sciences-Technical Sciences (2011) 59 (1) 75-80
[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes
Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
8
The Response sharpening subsystem (see Fig 3) is presented in Fig 8 Its aim is to
sharpen the MR damper response at the moment of PMRmeas signal sign change while PMR
req
sign has changed earlier however the MR damper (as a dissipative device) was unable to
produce the active force (see Figs 13 and 14) To fulfil this task the control current is
enlarged by the value of 05 A when PMRmeas modulus is decreasing and is lower than 10 of
PMRmeas running amplitude and PMR
meas sign is consistent within last two sampling periods t0
(see Figs 13 14 and 21 (a) t0=110ndash3 s was assumed) Thanks to such logics the required
value of the control current iMRreq precedes the sign change of PMR
meas thus the control current
that actually flows through the MR damper coil iMRmeas is set at the moment of the PMR
meas
sign change with no delay The Running Amplitude subsystem (Fig 9) calculates the
difference of the outputs of the two integrator blocks with delay of five oscillation periods
between them The input to both integrators is the quantity (PMRmeas) squared (Sqr block) The
resultant difference is multiplied by two and divided by a time of five periods to obtain the
amplitude squared thus finally the Sqrt (square root) block is needed only to obtain
amplitude A(bull) of the input signal (assuming that vibration pattern is characterised by single
dominant frequency)
The parameters imax idemag tdelay Alpha1 Alpha2 Alpha3 values were selected on the
basis of numerical simulations supported by MR damper dynamics experimental testing
Figure 8 Simulink diagram of the Response sharpening subsystem
Figure 9 Simulink diagram of the Running Amplitude subsystem
The system in Fig 2 also includes standard analogue PID Current Controller subsystem
aimed to control MR damper with the use of an electronic board that enforces the MR damper
current via a control voltage uMR based on iMRmeas and iMR
req signals (see Figs 22 (a)(b))
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
9
4 THE EXPERIMENTAL ANALYSIS
For the purpose of the current experimental analysis that is oriented to the development of the
refined MR damper force tracking algorithm the value of γ = 1 was assumed while the
selection of γ was not a scope of the present research The theoretical study of γ determination
for the idealised semiactive device case of negligible response time zero residual force and
zero inherent system damping is presented in [28]
The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic
horizontal excitation applied to the nacelle The frequency range comprised the
neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz
Several system configurations were regarded passive system with the constant control
current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the
newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2
respectively) or with the simple previously tested MR damper hyperbolic tangent inverse
model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm
(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)
that was previously proved to be the best approach [242526] was selected The obtained
output frequency response functions of the tower tip horizontal displacement x1 amplitude are
presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1
the MR damper force PMRreq PMR
meas and the MR damper current iMRreq iMR
meas (adequately
scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-
displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT
PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and
435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most
crucial concerning preferable control solutions (see Fig 10 open loop systems are not of
interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR
meas
and the MR damper current iMRreq iMR
meas (adequately scaled and zoomed) obtained for the
system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current
Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)
25 3 35 4 45 505
1
15
2
25
3
35
4
45
5
55x 10
-3
Frequency [Hz]
Dis
pla
cem
ent A
mplit
ude A
(x1)
[m]
P0 = 61 N
00 A
01 A
02 A
03 A
04 A
05 A
ADPT V1
ADPT V2
ADPT INV
ADPT PI
ModGND
Figure 10 Tower tip displacement amplitude output frequency response functions
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
10
0 01 02 03 04 05 06 07-3
-2
-1
0
1
2
3
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
11
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
12
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops
Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
005 006
-1
0
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
13
0 005 01 015 02 025 03 035 04 045-2
-15
-1
-05
0
05
1
15
2
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops
021 0215 022 0225 023
-14
-12
-1
-08
-06
-04
-02
0
02
04
06
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
0315 032 0325 033 0335 034 0345 035
-03
-02
-01
0
01
02
03
04
05
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
001 x
PMR
req
001 x
PMR
meas
i MR
req
i MR
meas
Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
14
0 001 002 003 004 005-01
0
01
02
03
04
05
06
07
08
09
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
0 001 002 003 004 005-04
-03
-02
-01
0
01
02
03
04
05
06
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
Figure 22 PID current controller operation at
(a) positive (b) negative step change of iMRreq
Table 2 presents values of the quality index Q (best values in bold) being a root-mean-
square of the PMRreqndashPMR
meas difference
2
1
Nreq meas
MR MR
j
Q P j P j
(4)
where j is the time sample number and N is the number of the regarded samples ModGND
solution is omitted here as it is not based on required MR damper force tracking idea
Table 2 Values of the quality index Q (4)
System 295 [Hz] 435 [Hz]
ADPT INV 3002 6531
ADPT PI 2679 6274
ADPT V1 2366 4955
ADPT V2 2273 5374
In Fig 10 two maxima that are typical for TVA operation are apparent for all the
solutions but 02 03 04 and 05 A for which the damping is relatively too high
Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most
favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood
(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)
however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or
some positive damping added may improve the system response (as higher amplitude of
PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR
req ADPT V2
may become a preferred choice as it copes better with the integrator wind-up (by changing
the value of γ either the first maxima is lowered while the second maxima is elevated or the
second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to
the previously introduced [242526313237] ADPT PI and especially to ADPT INV within
the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper
required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz
for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially
considering the time instants immediately following PMRmeas sign changes (all presented time
patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the
difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
15
MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI
and especially for ADPT INV are incomparable to the respective patterns registered for
ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The
same may be concluded concerning PMRreq force tracking quality just before PMR
meas sign
changes although ADPT INV characteristics (Fig 16) could not be even described as
acceptable Concerning the MR damper residual force minimisation both ADPT V1 and
ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted
for the demagnetisation and response sharpening do the job properly The MR damper force-
displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along
with the friction (due to the MR damper residual force) phenomena at 295 Hz and the
positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper
measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not
differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2
however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash
as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated
according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of
nonlinear damping
As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one
may observe iMRreq signal rise at a time instant of 005 s while PMR
meas response modulus rise
is at ca 006 s what makes a real challenge for the follow-up-type-controller operational
quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations
present in Figs 13 and 14
5 CONCLUSION
The conducted experimental analysis proved the effectiveness of the proposed refined MR
damper force tracking algorithm in two versions The obtained output frequency response
function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels
former solutions (designated by ADPT PI and ADPT INV) and is comparable to the
frequency response of the ModGND system that previously demonstrated the best
performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range
while ModGND excels for frequencies higher than 435 Hz and marginally in the (300
320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope
best with the problem of the residual MR damper force magnetic remanence when zero
force is assumed due to the MR damper inability to generate active forces The
implementation of these logics for the ModGND algorithm along with the analysis of the
demanded value of γ for the real-world system with response time residual force and
inherent damping all of which are nonzero shall be a subject of the future research The
minimisation of the residual force negative effects and the quality of positive stiffness
tracking will also be investigated Based on these analyses results and laboratory model
measurements and considering the dynamic similarity study that includes determined time
and length scale factors [41] in combination with force scale factor [44] direct calculation of
the demanded control signal for a real-world full scale vibration reduction system MR TVA
will be possible
Acknowledgment
This work is supported by AGH University of Science and Technology under research
program No 1111130958
References
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL
[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech
Struct amp Mach (1996) 24 (2) 155-187
[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering
low structural damping and soil structure interaction European Wind Energy Association
Annual Event (2012) Copenhagen 16-19042012
[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic
damping of operational wind turbine modes from experiments European Wind Energy
Association Annual Event (2012) Copenhagen 16-19042012
[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z
wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)
209-216
[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M
Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European
Wind Energy Association Annual Event (2012) Copenhagen 16-19042012
[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p
harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen
16-19042012
[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor
speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)
Monaco
[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind
turbines on two floating platforms Mechatronics (2011) 21 691-703
[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY
[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation
test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013
[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu
M Wind turbine tower load reduction using passive and semiactive dampers European Wind
Energy Association Annual Event (2011) Brussels
[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace
Exposition (2010) Orlando
[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej
z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198
[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR
damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds
Lisse CRC Press
[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and
experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State
Phenomena (2011) 177 (Control engineering in materials processing) 102-115
[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR
shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)
[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical
and Applied Mechanics (2007) 45 (1) 133-146
[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension
system with MR shock absorbers Computers and Structures (2008) 86 379-385
[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the
Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32
(1+2) 67-80
[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based
vibration reduction system Bulletin Of The Polish Academy Of
Sciences-Technical Sciences (2011) 59 (1) 75-80
[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes
Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
9
4 THE EXPERIMENTAL ANALYSIS
For the purpose of the current experimental analysis that is oriented to the development of the
refined MR damper force tracking algorithm the value of γ = 1 was assumed while the
selection of γ was not a scope of the present research The theoretical study of γ determination
for the idealised semiactive device case of negligible response time zero residual force and
zero inherent system damping is presented in [28]
The experiments were conducted assuming P0 = 61 N amplitude of the monoharmonic
horizontal excitation applied to the nacelle The frequency range comprised the
neighbourhood of the tower-nacelle system first bending frequency ie (250 500) Hz
Several system configurations were regarded passive system with the constant control
current of 00 01 02 03 04 and 05 A and the adaptive solutions (see eqn (1)) with the
newly developed V1 and V2 force tracking algorithms (ADPT V1 and ADPT V2
respectively) or with the simple previously tested MR damper hyperbolic tangent inverse
model (ADPT INV derived directly from eqn(3)) and PI-based force tracking algorithm
(ADPT PI) [2526] As a reference solution the modified ground hook algorithm (ModGND)
that was previously proved to be the best approach [242526] was selected The obtained
output frequency response functions of the tower tip horizontal displacement x1 amplitude are
presented all in Fig 10 Figs 11-20 contain time responses of the tower tip displacement x1
the MR damper force PMRreq PMR
meas and the MR damper current iMRreq iMR
meas (adequately
scaled to fit the same coordinate axes indicated by (a)) alongside the MR damper force-
displacement loops (indicated by (b)) obtained for the respective systems (ADPT INV ADPT
PI ADPT V1 ADPT V2 and ModGND) at the frequency of 295 Hz (Figs 11-15) and
435 Hz (Figs 16-20) Frequency neighbourhoods of 295 Hz and 435 Hz are the most
crucial concerning preferable control solutions (see Fig 10 open loop systems are not of
interest here) Figs 21 (a)(b) contain time responses of the MR damper force PMRreq PMR
meas
and the MR damper current iMRreq iMR
meas (adequately scaled and zoomed) obtained for the
system ADPT V2 at 295 Hz and 435 Hz Time patterns illustrating the PID Current
Controller operation at positive negative step change of iMRreq are given in Figs 22 (a)(b)
25 3 35 4 45 505
1
15
2
25
3
35
4
45
5
55x 10
-3
Frequency [Hz]
Dis
pla
cem
ent A
mplit
ude A
(x1)
[m]
P0 = 61 N
00 A
01 A
02 A
03 A
04 A
05 A
ADPT V1
ADPT V2
ADPT INV
ADPT PI
ModGND
Figure 10 Tower tip displacement amplitude output frequency response functions
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
10
0 01 02 03 04 05 06 07-3
-2
-1
0
1
2
3
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
11
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
12
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops
Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
005 006
-1
0
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
13
0 005 01 015 02 025 03 035 04 045-2
-15
-1
-05
0
05
1
15
2
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops
021 0215 022 0225 023
-14
-12
-1
-08
-06
-04
-02
0
02
04
06
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
0315 032 0325 033 0335 034 0345 035
-03
-02
-01
0
01
02
03
04
05
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
001 x
PMR
req
001 x
PMR
meas
i MR
req
i MR
meas
Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
14
0 001 002 003 004 005-01
0
01
02
03
04
05
06
07
08
09
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
0 001 002 003 004 005-04
-03
-02
-01
0
01
02
03
04
05
06
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
Figure 22 PID current controller operation at
(a) positive (b) negative step change of iMRreq
Table 2 presents values of the quality index Q (best values in bold) being a root-mean-
square of the PMRreqndashPMR
meas difference
2
1
Nreq meas
MR MR
j
Q P j P j
(4)
where j is the time sample number and N is the number of the regarded samples ModGND
solution is omitted here as it is not based on required MR damper force tracking idea
Table 2 Values of the quality index Q (4)
System 295 [Hz] 435 [Hz]
ADPT INV 3002 6531
ADPT PI 2679 6274
ADPT V1 2366 4955
ADPT V2 2273 5374
In Fig 10 two maxima that are typical for TVA operation are apparent for all the
solutions but 02 03 04 and 05 A for which the damping is relatively too high
Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most
favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood
(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)
however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or
some positive damping added may improve the system response (as higher amplitude of
PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR
req ADPT V2
may become a preferred choice as it copes better with the integrator wind-up (by changing
the value of γ either the first maxima is lowered while the second maxima is elevated or the
second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to
the previously introduced [242526313237] ADPT PI and especially to ADPT INV within
the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper
required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz
for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially
considering the time instants immediately following PMRmeas sign changes (all presented time
patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the
difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
15
MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI
and especially for ADPT INV are incomparable to the respective patterns registered for
ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The
same may be concluded concerning PMRreq force tracking quality just before PMR
meas sign
changes although ADPT INV characteristics (Fig 16) could not be even described as
acceptable Concerning the MR damper residual force minimisation both ADPT V1 and
ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted
for the demagnetisation and response sharpening do the job properly The MR damper force-
displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along
with the friction (due to the MR damper residual force) phenomena at 295 Hz and the
positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper
measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not
differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2
however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash
as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated
according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of
nonlinear damping
As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one
may observe iMRreq signal rise at a time instant of 005 s while PMR
meas response modulus rise
is at ca 006 s what makes a real challenge for the follow-up-type-controller operational
quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations
present in Figs 13 and 14
5 CONCLUSION
The conducted experimental analysis proved the effectiveness of the proposed refined MR
damper force tracking algorithm in two versions The obtained output frequency response
function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels
former solutions (designated by ADPT PI and ADPT INV) and is comparable to the
frequency response of the ModGND system that previously demonstrated the best
performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range
while ModGND excels for frequencies higher than 435 Hz and marginally in the (300
320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope
best with the problem of the residual MR damper force magnetic remanence when zero
force is assumed due to the MR damper inability to generate active forces The
implementation of these logics for the ModGND algorithm along with the analysis of the
demanded value of γ for the real-world system with response time residual force and
inherent damping all of which are nonzero shall be a subject of the future research The
minimisation of the residual force negative effects and the quality of positive stiffness
tracking will also be investigated Based on these analyses results and laboratory model
measurements and considering the dynamic similarity study that includes determined time
and length scale factors [41] in combination with force scale factor [44] direct calculation of
the demanded control signal for a real-world full scale vibration reduction system MR TVA
will be possible
Acknowledgment
This work is supported by AGH University of Science and Technology under research
program No 1111130958
References
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL
[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech
Struct amp Mach (1996) 24 (2) 155-187
[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering
low structural damping and soil structure interaction European Wind Energy Association
Annual Event (2012) Copenhagen 16-19042012
[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic
damping of operational wind turbine modes from experiments European Wind Energy
Association Annual Event (2012) Copenhagen 16-19042012
[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z
wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)
209-216
[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M
Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European
Wind Energy Association Annual Event (2012) Copenhagen 16-19042012
[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p
harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen
16-19042012
[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor
speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)
Monaco
[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind
turbines on two floating platforms Mechatronics (2011) 21 691-703
[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY
[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation
test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013
[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu
M Wind turbine tower load reduction using passive and semiactive dampers European Wind
Energy Association Annual Event (2011) Brussels
[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace
Exposition (2010) Orlando
[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej
z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198
[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR
damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds
Lisse CRC Press
[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and
experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State
Phenomena (2011) 177 (Control engineering in materials processing) 102-115
[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR
shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)
[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical
and Applied Mechanics (2007) 45 (1) 133-146
[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension
system with MR shock absorbers Computers and Structures (2008) 86 379-385
[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the
Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32
(1+2) 67-80
[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based
vibration reduction system Bulletin Of The Polish Academy Of
Sciences-Technical Sciences (2011) 59 (1) 75-80
[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes
Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
10
0 01 02 03 04 05 06 07-3
-2
-1
0
1
2
3
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 11 ADPT INV system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 12 ADPT PI system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 13 ADPT V1 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
11
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
12
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops
Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
005 006
-1
0
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
13
0 005 01 015 02 025 03 035 04 045-2
-15
-1
-05
0
05
1
15
2
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops
021 0215 022 0225 023
-14
-12
-1
-08
-06
-04
-02
0
02
04
06
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
0315 032 0325 033 0335 034 0345 035
-03
-02
-01
0
01
02
03
04
05
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
001 x
PMR
req
001 x
PMR
meas
i MR
req
i MR
meas
Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
14
0 001 002 003 004 005-01
0
01
02
03
04
05
06
07
08
09
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
0 001 002 003 004 005-04
-03
-02
-01
0
01
02
03
04
05
06
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
Figure 22 PID current controller operation at
(a) positive (b) negative step change of iMRreq
Table 2 presents values of the quality index Q (best values in bold) being a root-mean-
square of the PMRreqndashPMR
meas difference
2
1
Nreq meas
MR MR
j
Q P j P j
(4)
where j is the time sample number and N is the number of the regarded samples ModGND
solution is omitted here as it is not based on required MR damper force tracking idea
Table 2 Values of the quality index Q (4)
System 295 [Hz] 435 [Hz]
ADPT INV 3002 6531
ADPT PI 2679 6274
ADPT V1 2366 4955
ADPT V2 2273 5374
In Fig 10 two maxima that are typical for TVA operation are apparent for all the
solutions but 02 03 04 and 05 A for which the damping is relatively too high
Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most
favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood
(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)
however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or
some positive damping added may improve the system response (as higher amplitude of
PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR
req ADPT V2
may become a preferred choice as it copes better with the integrator wind-up (by changing
the value of γ either the first maxima is lowered while the second maxima is elevated or the
second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to
the previously introduced [242526313237] ADPT PI and especially to ADPT INV within
the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper
required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz
for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially
considering the time instants immediately following PMRmeas sign changes (all presented time
patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the
difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
15
MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI
and especially for ADPT INV are incomparable to the respective patterns registered for
ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The
same may be concluded concerning PMRreq force tracking quality just before PMR
meas sign
changes although ADPT INV characteristics (Fig 16) could not be even described as
acceptable Concerning the MR damper residual force minimisation both ADPT V1 and
ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted
for the demagnetisation and response sharpening do the job properly The MR damper force-
displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along
with the friction (due to the MR damper residual force) phenomena at 295 Hz and the
positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper
measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not
differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2
however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash
as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated
according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of
nonlinear damping
As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one
may observe iMRreq signal rise at a time instant of 005 s while PMR
meas response modulus rise
is at ca 006 s what makes a real challenge for the follow-up-type-controller operational
quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations
present in Figs 13 and 14
5 CONCLUSION
The conducted experimental analysis proved the effectiveness of the proposed refined MR
damper force tracking algorithm in two versions The obtained output frequency response
function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels
former solutions (designated by ADPT PI and ADPT INV) and is comparable to the
frequency response of the ModGND system that previously demonstrated the best
performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range
while ModGND excels for frequencies higher than 435 Hz and marginally in the (300
320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope
best with the problem of the residual MR damper force magnetic remanence when zero
force is assumed due to the MR damper inability to generate active forces The
implementation of these logics for the ModGND algorithm along with the analysis of the
demanded value of γ for the real-world system with response time residual force and
inherent damping all of which are nonzero shall be a subject of the future research The
minimisation of the residual force negative effects and the quality of positive stiffness
tracking will also be investigated Based on these analyses results and laboratory model
measurements and considering the dynamic similarity study that includes determined time
and length scale factors [41] in combination with force scale factor [44] direct calculation of
the demanded control signal for a real-world full scale vibration reduction system MR TVA
will be possible
Acknowledgment
This work is supported by AGH University of Science and Technology under research
program No 1111130958
References
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL
[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech
Struct amp Mach (1996) 24 (2) 155-187
[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering
low structural damping and soil structure interaction European Wind Energy Association
Annual Event (2012) Copenhagen 16-19042012
[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic
damping of operational wind turbine modes from experiments European Wind Energy
Association Annual Event (2012) Copenhagen 16-19042012
[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z
wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)
209-216
[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M
Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European
Wind Energy Association Annual Event (2012) Copenhagen 16-19042012
[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p
harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen
16-19042012
[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor
speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)
Monaco
[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind
turbines on two floating platforms Mechatronics (2011) 21 691-703
[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY
[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation
test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013
[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu
M Wind turbine tower load reduction using passive and semiactive dampers European Wind
Energy Association Annual Event (2011) Brussels
[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace
Exposition (2010) Orlando
[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej
z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198
[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR
damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds
Lisse CRC Press
[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and
experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State
Phenomena (2011) 177 (Control engineering in materials processing) 102-115
[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR
shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)
[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical
and Applied Mechanics (2007) 45 (1) 133-146
[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension
system with MR shock absorbers Computers and Structures (2008) 86 379-385
[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the
Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32
(1+2) 67-80
[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based
vibration reduction system Bulletin Of The Polish Academy Of
Sciences-Technical Sciences (2011) 59 (1) 75-80
[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes
Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
11
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 14 ADPT V2 system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 01 02 03 04 05 06 07-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 15 ModGND system at 295 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 16 ADPT INV system at 435 Hz (a) time responses (b) MR damper force-displacement loops
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
12
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops
Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
005 006
-1
0
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
13
0 005 01 015 02 025 03 035 04 045-2
-15
-1
-05
0
05
1
15
2
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops
021 0215 022 0225 023
-14
-12
-1
-08
-06
-04
-02
0
02
04
06
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
0315 032 0325 033 0335 034 0345 035
-03
-02
-01
0
01
02
03
04
05
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
001 x
PMR
req
001 x
PMR
meas
i MR
req
i MR
meas
Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
14
0 001 002 003 004 005-01
0
01
02
03
04
05
06
07
08
09
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
0 001 002 003 004 005-04
-03
-02
-01
0
01
02
03
04
05
06
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
Figure 22 PID current controller operation at
(a) positive (b) negative step change of iMRreq
Table 2 presents values of the quality index Q (best values in bold) being a root-mean-
square of the PMRreqndashPMR
meas difference
2
1
Nreq meas
MR MR
j
Q P j P j
(4)
where j is the time sample number and N is the number of the regarded samples ModGND
solution is omitted here as it is not based on required MR damper force tracking idea
Table 2 Values of the quality index Q (4)
System 295 [Hz] 435 [Hz]
ADPT INV 3002 6531
ADPT PI 2679 6274
ADPT V1 2366 4955
ADPT V2 2273 5374
In Fig 10 two maxima that are typical for TVA operation are apparent for all the
solutions but 02 03 04 and 05 A for which the damping is relatively too high
Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most
favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood
(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)
however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or
some positive damping added may improve the system response (as higher amplitude of
PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR
req ADPT V2
may become a preferred choice as it copes better with the integrator wind-up (by changing
the value of γ either the first maxima is lowered while the second maxima is elevated or the
second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to
the previously introduced [242526313237] ADPT PI and especially to ADPT INV within
the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper
required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz
for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially
considering the time instants immediately following PMRmeas sign changes (all presented time
patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the
difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
15
MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI
and especially for ADPT INV are incomparable to the respective patterns registered for
ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The
same may be concluded concerning PMRreq force tracking quality just before PMR
meas sign
changes although ADPT INV characteristics (Fig 16) could not be even described as
acceptable Concerning the MR damper residual force minimisation both ADPT V1 and
ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted
for the demagnetisation and response sharpening do the job properly The MR damper force-
displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along
with the friction (due to the MR damper residual force) phenomena at 295 Hz and the
positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper
measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not
differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2
however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash
as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated
according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of
nonlinear damping
As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one
may observe iMRreq signal rise at a time instant of 005 s while PMR
meas response modulus rise
is at ca 006 s what makes a real challenge for the follow-up-type-controller operational
quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations
present in Figs 13 and 14
5 CONCLUSION
The conducted experimental analysis proved the effectiveness of the proposed refined MR
damper force tracking algorithm in two versions The obtained output frequency response
function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels
former solutions (designated by ADPT PI and ADPT INV) and is comparable to the
frequency response of the ModGND system that previously demonstrated the best
performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range
while ModGND excels for frequencies higher than 435 Hz and marginally in the (300
320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope
best with the problem of the residual MR damper force magnetic remanence when zero
force is assumed due to the MR damper inability to generate active forces The
implementation of these logics for the ModGND algorithm along with the analysis of the
demanded value of γ for the real-world system with response time residual force and
inherent damping all of which are nonzero shall be a subject of the future research The
minimisation of the residual force negative effects and the quality of positive stiffness
tracking will also be investigated Based on these analyses results and laboratory model
measurements and considering the dynamic similarity study that includes determined time
and length scale factors [41] in combination with force scale factor [44] direct calculation of
the demanded control signal for a real-world full scale vibration reduction system MR TVA
will be possible
Acknowledgment
This work is supported by AGH University of Science and Technology under research
program No 1111130958
References
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL
[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech
Struct amp Mach (1996) 24 (2) 155-187
[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering
low structural damping and soil structure interaction European Wind Energy Association
Annual Event (2012) Copenhagen 16-19042012
[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic
damping of operational wind turbine modes from experiments European Wind Energy
Association Annual Event (2012) Copenhagen 16-19042012
[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z
wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)
209-216
[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M
Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European
Wind Energy Association Annual Event (2012) Copenhagen 16-19042012
[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p
harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen
16-19042012
[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor
speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)
Monaco
[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind
turbines on two floating platforms Mechatronics (2011) 21 691-703
[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY
[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation
test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013
[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu
M Wind turbine tower load reduction using passive and semiactive dampers European Wind
Energy Association Annual Event (2011) Brussels
[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace
Exposition (2010) Orlando
[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej
z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198
[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR
damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds
Lisse CRC Press
[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and
experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State
Phenomena (2011) 177 (Control engineering in materials processing) 102-115
[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR
shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)
[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical
and Applied Mechanics (2007) 45 (1) 133-146
[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension
system with MR shock absorbers Computers and Structures (2008) 86 379-385
[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the
Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32
(1+2) 67-80
[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based
vibration reduction system Bulletin Of The Polish Academy Of
Sciences-Technical Sciences (2011) 59 (1) 75-80
[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes
Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
12
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 17 ADPT PI system at 435 Hz (a) time responses (b) MR damper force-displacement loops
Figure 18 ADPT V1 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
Figure 19 ADPT V2 system at 435 Hz (a) time responses (b) MR damper force-displacement loops
0 005 01 015 02 025 03 035 04 045-25
-2
-15
-1
-05
0
05
1
15
2
25
Time[s]
x1 [
mm
] P
MR
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
005 006
-1
0
(a) (b)
(a) (b)
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
13
0 005 01 015 02 025 03 035 04 045-2
-15
-1
-05
0
05
1
15
2
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops
021 0215 022 0225 023
-14
-12
-1
-08
-06
-04
-02
0
02
04
06
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
0315 032 0325 033 0335 034 0345 035
-03
-02
-01
0
01
02
03
04
05
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
001 x
PMR
req
001 x
PMR
meas
i MR
req
i MR
meas
Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
14
0 001 002 003 004 005-01
0
01
02
03
04
05
06
07
08
09
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
0 001 002 003 004 005-04
-03
-02
-01
0
01
02
03
04
05
06
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
Figure 22 PID current controller operation at
(a) positive (b) negative step change of iMRreq
Table 2 presents values of the quality index Q (best values in bold) being a root-mean-
square of the PMRreqndashPMR
meas difference
2
1
Nreq meas
MR MR
j
Q P j P j
(4)
where j is the time sample number and N is the number of the regarded samples ModGND
solution is omitted here as it is not based on required MR damper force tracking idea
Table 2 Values of the quality index Q (4)
System 295 [Hz] 435 [Hz]
ADPT INV 3002 6531
ADPT PI 2679 6274
ADPT V1 2366 4955
ADPT V2 2273 5374
In Fig 10 two maxima that are typical for TVA operation are apparent for all the
solutions but 02 03 04 and 05 A for which the damping is relatively too high
Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most
favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood
(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)
however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or
some positive damping added may improve the system response (as higher amplitude of
PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR
req ADPT V2
may become a preferred choice as it copes better with the integrator wind-up (by changing
the value of γ either the first maxima is lowered while the second maxima is elevated or the
second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to
the previously introduced [242526313237] ADPT PI and especially to ADPT INV within
the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper
required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz
for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially
considering the time instants immediately following PMRmeas sign changes (all presented time
patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the
difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
15
MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI
and especially for ADPT INV are incomparable to the respective patterns registered for
ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The
same may be concluded concerning PMRreq force tracking quality just before PMR
meas sign
changes although ADPT INV characteristics (Fig 16) could not be even described as
acceptable Concerning the MR damper residual force minimisation both ADPT V1 and
ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted
for the demagnetisation and response sharpening do the job properly The MR damper force-
displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along
with the friction (due to the MR damper residual force) phenomena at 295 Hz and the
positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper
measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not
differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2
however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash
as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated
according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of
nonlinear damping
As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one
may observe iMRreq signal rise at a time instant of 005 s while PMR
meas response modulus rise
is at ca 006 s what makes a real challenge for the follow-up-type-controller operational
quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations
present in Figs 13 and 14
5 CONCLUSION
The conducted experimental analysis proved the effectiveness of the proposed refined MR
damper force tracking algorithm in two versions The obtained output frequency response
function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels
former solutions (designated by ADPT PI and ADPT INV) and is comparable to the
frequency response of the ModGND system that previously demonstrated the best
performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range
while ModGND excels for frequencies higher than 435 Hz and marginally in the (300
320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope
best with the problem of the residual MR damper force magnetic remanence when zero
force is assumed due to the MR damper inability to generate active forces The
implementation of these logics for the ModGND algorithm along with the analysis of the
demanded value of γ for the real-world system with response time residual force and
inherent damping all of which are nonzero shall be a subject of the future research The
minimisation of the residual force negative effects and the quality of positive stiffness
tracking will also be investigated Based on these analyses results and laboratory model
measurements and considering the dynamic similarity study that includes determined time
and length scale factors [41] in combination with force scale factor [44] direct calculation of
the demanded control signal for a real-world full scale vibration reduction system MR TVA
will be possible
Acknowledgment
This work is supported by AGH University of Science and Technology under research
program No 1111130958
References
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL
[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech
Struct amp Mach (1996) 24 (2) 155-187
[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering
low structural damping and soil structure interaction European Wind Energy Association
Annual Event (2012) Copenhagen 16-19042012
[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic
damping of operational wind turbine modes from experiments European Wind Energy
Association Annual Event (2012) Copenhagen 16-19042012
[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z
wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)
209-216
[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M
Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European
Wind Energy Association Annual Event (2012) Copenhagen 16-19042012
[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p
harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen
16-19042012
[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor
speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)
Monaco
[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind
turbines on two floating platforms Mechatronics (2011) 21 691-703
[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY
[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation
test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013
[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu
M Wind turbine tower load reduction using passive and semiactive dampers European Wind
Energy Association Annual Event (2011) Brussels
[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace
Exposition (2010) Orlando
[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej
z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198
[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR
damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds
Lisse CRC Press
[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and
experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State
Phenomena (2011) 177 (Control engineering in materials processing) 102-115
[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR
shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)
[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical
and Applied Mechanics (2007) 45 (1) 133-146
[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension
system with MR shock absorbers Computers and Structures (2008) 86 379-385
[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the
Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32
(1+2) 67-80
[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based
vibration reduction system Bulletin Of The Polish Academy Of
Sciences-Technical Sciences (2011) 59 (1) 75-80
[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes
Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
13
0 005 01 015 02 025 03 035 04 045-2
-15
-1
-05
0
05
1
15
2
Time[s]
x1 [
mm
] P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
x1
01 x
PMR
meas
i MR
req
i MR
meas
Figure 20 ModGND system at 435 Hz (a) time responses (b) MR damper force-displacement loops
021 0215 022 0225 023
-14
-12
-1
-08
-06
-04
-02
0
02
04
06
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
01 x
PMR
req
01 x
PMR
meas
i MR
req
i MR
meas
0315 032 0325 033 0335 034 0345 035
-03
-02
-01
0
01
02
03
04
05
Time[s]
PM
R
req
P
MR
meas [
N]
i M
R
req
i
MR
meas [
A]
001 x
PMR
req
001 x
PMR
meas
i MR
req
i MR
meas
Figure 21 Selected time responses of the system ADPT V2 at (a) 295 Hz (b) 435 Hz
(a) (b)
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
14
0 001 002 003 004 005-01
0
01
02
03
04
05
06
07
08
09
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
0 001 002 003 004 005-04
-03
-02
-01
0
01
02
03
04
05
06
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
Figure 22 PID current controller operation at
(a) positive (b) negative step change of iMRreq
Table 2 presents values of the quality index Q (best values in bold) being a root-mean-
square of the PMRreqndashPMR
meas difference
2
1
Nreq meas
MR MR
j
Q P j P j
(4)
where j is the time sample number and N is the number of the regarded samples ModGND
solution is omitted here as it is not based on required MR damper force tracking idea
Table 2 Values of the quality index Q (4)
System 295 [Hz] 435 [Hz]
ADPT INV 3002 6531
ADPT PI 2679 6274
ADPT V1 2366 4955
ADPT V2 2273 5374
In Fig 10 two maxima that are typical for TVA operation are apparent for all the
solutions but 02 03 04 and 05 A for which the damping is relatively too high
Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most
favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood
(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)
however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or
some positive damping added may improve the system response (as higher amplitude of
PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR
req ADPT V2
may become a preferred choice as it copes better with the integrator wind-up (by changing
the value of γ either the first maxima is lowered while the second maxima is elevated or the
second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to
the previously introduced [242526313237] ADPT PI and especially to ADPT INV within
the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper
required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz
for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially
considering the time instants immediately following PMRmeas sign changes (all presented time
patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the
difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
15
MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI
and especially for ADPT INV are incomparable to the respective patterns registered for
ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The
same may be concluded concerning PMRreq force tracking quality just before PMR
meas sign
changes although ADPT INV characteristics (Fig 16) could not be even described as
acceptable Concerning the MR damper residual force minimisation both ADPT V1 and
ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted
for the demagnetisation and response sharpening do the job properly The MR damper force-
displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along
with the friction (due to the MR damper residual force) phenomena at 295 Hz and the
positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper
measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not
differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2
however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash
as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated
according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of
nonlinear damping
As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one
may observe iMRreq signal rise at a time instant of 005 s while PMR
meas response modulus rise
is at ca 006 s what makes a real challenge for the follow-up-type-controller operational
quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations
present in Figs 13 and 14
5 CONCLUSION
The conducted experimental analysis proved the effectiveness of the proposed refined MR
damper force tracking algorithm in two versions The obtained output frequency response
function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels
former solutions (designated by ADPT PI and ADPT INV) and is comparable to the
frequency response of the ModGND system that previously demonstrated the best
performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range
while ModGND excels for frequencies higher than 435 Hz and marginally in the (300
320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope
best with the problem of the residual MR damper force magnetic remanence when zero
force is assumed due to the MR damper inability to generate active forces The
implementation of these logics for the ModGND algorithm along with the analysis of the
demanded value of γ for the real-world system with response time residual force and
inherent damping all of which are nonzero shall be a subject of the future research The
minimisation of the residual force negative effects and the quality of positive stiffness
tracking will also be investigated Based on these analyses results and laboratory model
measurements and considering the dynamic similarity study that includes determined time
and length scale factors [41] in combination with force scale factor [44] direct calculation of
the demanded control signal for a real-world full scale vibration reduction system MR TVA
will be possible
Acknowledgment
This work is supported by AGH University of Science and Technology under research
program No 1111130958
References
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL
[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech
Struct amp Mach (1996) 24 (2) 155-187
[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering
low structural damping and soil structure interaction European Wind Energy Association
Annual Event (2012) Copenhagen 16-19042012
[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic
damping of operational wind turbine modes from experiments European Wind Energy
Association Annual Event (2012) Copenhagen 16-19042012
[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z
wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)
209-216
[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M
Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European
Wind Energy Association Annual Event (2012) Copenhagen 16-19042012
[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p
harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen
16-19042012
[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor
speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)
Monaco
[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind
turbines on two floating platforms Mechatronics (2011) 21 691-703
[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY
[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation
test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013
[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu
M Wind turbine tower load reduction using passive and semiactive dampers European Wind
Energy Association Annual Event (2011) Brussels
[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace
Exposition (2010) Orlando
[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej
z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198
[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR
damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds
Lisse CRC Press
[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and
experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State
Phenomena (2011) 177 (Control engineering in materials processing) 102-115
[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR
shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)
[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical
and Applied Mechanics (2007) 45 (1) 133-146
[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension
system with MR shock absorbers Computers and Structures (2008) 86 379-385
[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the
Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32
(1+2) 67-80
[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based
vibration reduction system Bulletin Of The Polish Academy Of
Sciences-Technical Sciences (2011) 59 (1) 75-80
[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes
Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
14
0 001 002 003 004 005-01
0
01
02
03
04
05
06
07
08
09
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
0 001 002 003 004 005-04
-03
-02
-01
0
01
02
03
04
05
06
Time[s]
i M
R
req
i M
R
meas [
A]
uM
R [
V]
i MR
req
01 x
uMR
i MR
meas
Figure 22 PID current controller operation at
(a) positive (b) negative step change of iMRreq
Table 2 presents values of the quality index Q (best values in bold) being a root-mean-
square of the PMRreqndashPMR
meas difference
2
1
Nreq meas
MR MR
j
Q P j P j
(4)
where j is the time sample number and N is the number of the regarded samples ModGND
solution is omitted here as it is not based on required MR damper force tracking idea
Table 2 Values of the quality index Q (4)
System 295 [Hz] 435 [Hz]
ADPT INV 3002 6531
ADPT PI 2679 6274
ADPT V1 2366 4955
ADPT V2 2273 5374
In Fig 10 two maxima that are typical for TVA operation are apparent for all the
solutions but 02 03 04 and 05 A for which the damping is relatively too high
Throughout all the semiactive solutions ADPT V1 and ModGND prove to be the most
favourable ADPT V2 seems inferior to ADPT V1 in the second maxima neighbourhood
(while ADPT V1 is marginally worse in the first maxima neighbourhood than ADPT V2)
however comparison of Figs 18-20 may result in the conclusion that assumption of γ gt 1 or
some positive damping added may improve the system response (as higher amplitude of
PMRmeas seems more appropriate at 435 Hz) along with the increase of PMR
req ADPT V2
may become a preferred choice as it copes better with the integrator wind-up (by changing
the value of γ either the first maxima is lowered while the second maxima is elevated or the
second is lowered while the first ndash elevated) Both ADPT V1 and ADPT V2 are superior to
the previously introduced [242526313237] ADPT PI and especially to ADPT INV within
the first and the second maxima neighbourhoods (see Fig 10 and Tab 2) The MR damper
required force PMRreq (that is the same for each of the ADPT algorithms) tracking at 295 Hz
for ADPT PI and ADPT INV is inferior with respect to ADPT V1 and ADPT V2 especially
considering the time instants immediately following PMRmeas sign changes (all presented time
patterns have the same phase shifts see Figs 11-14) While observing Figs 16-19 the
difference of PMRreq force tracking precision at 435 Hz is more evident than at 295 Hz The
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
15
MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI
and especially for ADPT INV are incomparable to the respective patterns registered for
ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The
same may be concluded concerning PMRreq force tracking quality just before PMR
meas sign
changes although ADPT INV characteristics (Fig 16) could not be even described as
acceptable Concerning the MR damper residual force minimisation both ADPT V1 and
ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted
for the demagnetisation and response sharpening do the job properly The MR damper force-
displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along
with the friction (due to the MR damper residual force) phenomena at 295 Hz and the
positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper
measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not
differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2
however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash
as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated
according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of
nonlinear damping
As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one
may observe iMRreq signal rise at a time instant of 005 s while PMR
meas response modulus rise
is at ca 006 s what makes a real challenge for the follow-up-type-controller operational
quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations
present in Figs 13 and 14
5 CONCLUSION
The conducted experimental analysis proved the effectiveness of the proposed refined MR
damper force tracking algorithm in two versions The obtained output frequency response
function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels
former solutions (designated by ADPT PI and ADPT INV) and is comparable to the
frequency response of the ModGND system that previously demonstrated the best
performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range
while ModGND excels for frequencies higher than 435 Hz and marginally in the (300
320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope
best with the problem of the residual MR damper force magnetic remanence when zero
force is assumed due to the MR damper inability to generate active forces The
implementation of these logics for the ModGND algorithm along with the analysis of the
demanded value of γ for the real-world system with response time residual force and
inherent damping all of which are nonzero shall be a subject of the future research The
minimisation of the residual force negative effects and the quality of positive stiffness
tracking will also be investigated Based on these analyses results and laboratory model
measurements and considering the dynamic similarity study that includes determined time
and length scale factors [41] in combination with force scale factor [44] direct calculation of
the demanded control signal for a real-world full scale vibration reduction system MR TVA
will be possible
Acknowledgment
This work is supported by AGH University of Science and Technology under research
program No 1111130958
References
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL
[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech
Struct amp Mach (1996) 24 (2) 155-187
[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering
low structural damping and soil structure interaction European Wind Energy Association
Annual Event (2012) Copenhagen 16-19042012
[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic
damping of operational wind turbine modes from experiments European Wind Energy
Association Annual Event (2012) Copenhagen 16-19042012
[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z
wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)
209-216
[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M
Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European
Wind Energy Association Annual Event (2012) Copenhagen 16-19042012
[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p
harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen
16-19042012
[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor
speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)
Monaco
[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind
turbines on two floating platforms Mechatronics (2011) 21 691-703
[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY
[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation
test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013
[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu
M Wind turbine tower load reduction using passive and semiactive dampers European Wind
Energy Association Annual Event (2011) Brussels
[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace
Exposition (2010) Orlando
[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej
z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198
[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR
damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds
Lisse CRC Press
[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and
experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State
Phenomena (2011) 177 (Control engineering in materials processing) 102-115
[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR
shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)
[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical
and Applied Mechanics (2007) 45 (1) 133-146
[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension
system with MR shock absorbers Computers and Structures (2008) 86 379-385
[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the
Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32
(1+2) 67-80
[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based
vibration reduction system Bulletin Of The Polish Academy Of
Sciences-Technical Sciences (2011) 59 (1) 75-80
[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes
Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
15
MR damper residual force values (just after PMRmeas sign changes) measured for ADPT PI
and especially for ADPT INV are incomparable to the respective patterns registered for
ADPT V1 and ADPT V2 systems (again all time patterns have the same phase shifts) The
same may be concluded concerning PMRreq force tracking quality just before PMR
meas sign
changes although ADPT INV characteristics (Fig 16) could not be even described as
acceptable Concerning the MR damper residual force minimisation both ADPT V1 and
ADPT V2 (Figs 18 and 19) are superior to ModGND system (Fig 20) ndash the logics adopted
for the demagnetisation and response sharpening do the job properly The MR damper force-
displacement loops exhibit the negative stiffness (resulting from the equations (1)(2)) along
with the friction (due to the MR damper residual force) phenomena at 295 Hz and the
positive stiffness with the friction phenomena at 435 Hz Interestingly the MR damper
measured force and current patterns obtained for ModGND system (Figs 15 and 20) do not
differ fundamentally from the respective patterns obtained for ADPT V1 and ADPT V2
however PMRmeas force-displacement loops for ModGND (combined with the hypothetical ndash
as ModGND algorithm does not use required force pattern ndash PMRreq loops calculated
according to (1)(2) on the basis of x1ndashx2meas signal) indicate the additional presence of
nonlinear damping
As may be seen in eg Fig 18 the MR damper response time cannot be neglected ndash one
may observe iMRreq signal rise at a time instant of 005 s while PMR
meas response modulus rise
is at ca 006 s what makes a real challenge for the follow-up-type-controller operational
quality (part of that delay is iMRmeas delay Figs 22 (a)(b)) ndash see also the resultant oscillations
present in Figs 13 and 14
5 CONCLUSION
The conducted experimental analysis proved the effectiveness of the proposed refined MR
damper force tracking algorithm in two versions The obtained output frequency response
function of the tower tip horizontal displacement amplitude for the ADPT V1 system excels
former solutions (designated by ADPT PI and ADPT INV) and is comparable to the
frequency response of the ModGND system that previously demonstrated the best
performance [242526] ADPT V1 is superior to ModGND in the (345 415) Hz range
while ModGND excels for frequencies higher than 435 Hz and marginally in the (300
320) Hz range It was shown that the logics adopted for both ADPT V1 and ADPT V2 cope
best with the problem of the residual MR damper force magnetic remanence when zero
force is assumed due to the MR damper inability to generate active forces The
implementation of these logics for the ModGND algorithm along with the analysis of the
demanded value of γ for the real-world system with response time residual force and
inherent damping all of which are nonzero shall be a subject of the future research The
minimisation of the residual force negative effects and the quality of positive stiffness
tracking will also be investigated Based on these analyses results and laboratory model
measurements and considering the dynamic similarity study that includes determined time
and length scale factors [41] in combination with force scale factor [44] direct calculation of
the demanded control signal for a real-world full scale vibration reduction system MR TVA
will be possible
Acknowledgment
This work is supported by AGH University of Science and Technology under research
program No 1111130958
References
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL
[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech
Struct amp Mach (1996) 24 (2) 155-187
[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering
low structural damping and soil structure interaction European Wind Energy Association
Annual Event (2012) Copenhagen 16-19042012
[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic
damping of operational wind turbine modes from experiments European Wind Energy
Association Annual Event (2012) Copenhagen 16-19042012
[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z
wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)
209-216
[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M
Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European
Wind Energy Association Annual Event (2012) Copenhagen 16-19042012
[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p
harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen
16-19042012
[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor
speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)
Monaco
[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind
turbines on two floating platforms Mechatronics (2011) 21 691-703
[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY
[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation
test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013
[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu
M Wind turbine tower load reduction using passive and semiactive dampers European Wind
Energy Association Annual Event (2011) Brussels
[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace
Exposition (2010) Orlando
[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej
z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198
[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR
damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds
Lisse CRC Press
[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and
experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State
Phenomena (2011) 177 (Control engineering in materials processing) 102-115
[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR
shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)
[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical
and Applied Mechanics (2007) 45 (1) 133-146
[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension
system with MR shock absorbers Computers and Structures (2008) 86 379-385
[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the
Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32
(1+2) 67-80
[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based
vibration reduction system Bulletin Of The Polish Academy Of
Sciences-Technical Sciences (2011) 59 (1) 75-80
[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes
Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
16
[1] Jain P Wind Energy Engineering (2011) McGRAW-HILL
[2] Enevoldsen I and Mork KJ Effects of vibration mass damper in a wind turbine tower Mech
Struct amp Mach (1996) 24 (2) 155-187
[3] Butt UA and Ishihara T Seismic load evaluation of wind turbine support structures considering
low structural damping and soil structure interaction European Wind Energy Association
Annual Event (2012) Copenhagen 16-19042012
[4] Hansen MH Fuglsang P Thomsen K and Knudsen T Two methods for estimating aeroelastic
damping of operational wind turbine modes from experiments European Wind Energy
Association Annual Event (2012) Copenhagen 16-19042012
[5] Matachowski F and Martynowicz P Analiza dynamiki konstrukcji elektrowni wiatrowej z
wykorzystaniem środowiska Comsol Multiphysics Modelowanie Inżynierskie (2012) 13 (44)
209-216
[6] Bak C Bitsche R Yde A Kim T Hansen MH Zahle F Gaunaa M Blasques J Dossing M
Wedel-Heinen J-J and Behrens T Light rotor the 10-MW reference wind turbine European
Wind Energy Association Annual Event (2012) Copenhagen 16-19042012
[7] Shan W and Shan M Gain scheduling pitch control design for active tower damping and 3p
harmonic reduction European Wind Energy Association Annual Event (2012) Copenhagen
16-19042012
[8] Jelavić M Perić N and Petrović I Damping of wind turbine tower oscillations through rotor
speed control International Conference on Ecologic Vehicles amp Renewable Energies (2007)
Monaco
[9] Namik H and Stol K Performance analysis of individual blade pitch control of offshore wind
turbines on two floating platforms Mechatronics (2011) 21 691-703
[10] Den Hartog JP Mechanical Vibrations (1985) Dover Publications Mineola NY
[11] Oh S and Ishihara T A study on structure parameters of an offshore wind turbine by excitation
test using active mass damper EWEA Offshore (2013) Frankfurt 19-21112013
[12] Tsouroukdissian A Carcangiu CE Pineda Amo I Martin M Fischer T Kuhnle B and Scheu
M Wind turbine tower load reduction using passive and semiactive dampers European Wind
Energy Association Annual Event (2011) Brussels
[13] Rotea MA Lackner MA and Saheba R Active structural control of offshore wind turbines
48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace
Exposition (2010) Orlando
[14] Łatas W and Martynowicz P Modelowanie drgań układu maszt-gondola elektrowni wiatrowej
z tłumikiem dynamicznym Modelowanie Inżynierskie (2012) 13 (44) pp 187-198
[15] Kirkegaard PH et al Semiactive vibration control of a wind turbine tower using an MR
damper Struct Dynamics EURODYN (2002) GrundmannampSchueller SwetsampZeitlinger eds
Lisse CRC Press
[16] Kciuk S and Martynowicz P Special application magnetorheological valve numerical and
experimental analysis Diffusion and Defect Data ndash Solid State Data Pt B Solid State
Phenomena (2011) 177 (Control engineering in materials processing) 102-115
[17] Sapiński B and Martynowicz P Vibration control in a pitch-plane suspension model with MR
shock absorbers Journal of Theoretical and Applied Mechanics (2005) 43 (3)
[18] Sapiński B and Rosoacuteł M MR Damper performance for shock isolation Journal of Theoretical
and Applied Mechanics (2007) 45 (1) 133-146
[19] Sapiński B and Rosoacuteł M Autonomous control system for a 3 DOF pitch-plane suspension
system with MR shock absorbers Computers and Structures (2008) 86 379-385
[20] Krauze P Comparison of Control Strategies in a Semi-Active Suspension System of the
Experimental ATV Journal of Low Frequency Noise Vibration and Active Control (2013) 32
(1+2) 67-80
[21] Snamina J Sapinski B Energy balance in self-powered MR damper-based
vibration reduction system Bulletin Of The Polish Academy Of
Sciences-Technical Sciences (2011) 59 (1) 75-80
[22] Yazici H Azeloglu CO and Kucukdemiral IB Active Vibration Control of Container Cranes
Against Earthquake by the Use of Delay-Dependent Hinfin Controller Under Consideration of
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
17
Actuator Saturation Journal of Low Frequency Noise Vibration and Active Control (2014) 33
(3) 289-316
[23] Xia Z Wang X Hou J Wei S and Fang Y Non-linear dynamic analysis of double-layer semi-
active vibration isolation systems using revised Bingham model Journal of Low Frequency
Noise Vibration and Active Control (2016) 35 (1) 17-24
[24] Martynowicz P Wind turbines tower-nacelle model with magnetorheological tuned vibration
absorber ndash numerical and experimental analysis 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoring (IACSM) (2014)
Barcelona Spain 15-17072014
[25] Martynowicz P Vibration control of wind turbine tower-nacelle model with
magnetorheological tuned vibration absorber Journal of Vibration and Control (2015) doi
1011771077546315591445
[26] Martynowicz P Study of vibration control using laboratory test rig of wind turbine tower-
nacelle system with MR damper based tuned vibration absorber Bulletin of the Polish
Academy Of Sciences Technical Sciences (2016) 64 (2) 347ndash359
[27] Rosoacuteł M and Martynowicz P Implementation of LQG controller for wind turbine tower-nacelle
model with MR Tuned Vibration Absorber Journal of Theoretical and Applied Mechanics
(2016) 54 (4) 1109-1123
[28] Weber F Optimal semi-active vibration absorber for harmonic excitation based on controlled
semi-active damper Smart Mater Struct (2014) 23
[29] Batterbee DC and Sims ND Hardware-in-the-loop simulation of magnetorheological dampers
for vehicle suspension systems Proc IMechE (2007) 221 Part I J Systems and Control
Engineering
[30] Phu DX Shah K and Choi SB Damping Force Tracking Control of MR Damper System
Using a New Direct Adaptive Fuzzy Controller Shock and Vibration (2015) ID 947937
[31] Laalej H Lang ZQ Sapinski B and Martynowicz P MR damper based implementation of
nonlinear damping for a pitch plane suspension system Smart Mater Struct (2012) 21
doi1010880964-1726214045006
[32] Ho C Lang Z Q Sapinski B and Bilings SA Vibration isolation using nonlinear damping
implemented by a feedback-controlled MR damper Smart Mater Struct (2013) 22
doi1010880964-17262210105010
[33] Weber F BoucndashWen model-based real-time force tracking scheme for MR dampers Smart
Mater Struct (2013) 22
[34] Weber F and Maślanka M Frequency and damping adaptation of a TMD with controlled MR
damper Smart Mater Struct (2012) 21
[35] Weber F and Maślanka M Precise stiffness and damping emulation with MR dampers and its
application to semi-active tuned mass dampers of Wolgograd Bridge Smart Mater Struct
(2014) 23
[36] Weber F Robust force tracking control scheme for MR dampers Struct Control Health Monit
(2015) DOI 101002stc1750
[37] Sims ND Stanway R Johnson AR Peel DJ and Bullough WA Smart fluid damping shaping
the forcevelocity response through feedback control J Intell Mater Syst Struct (2000) 11
945-58
[38] Lord Rheonetic MR Controllable Friction Damper RD-1097-01 Product Bulletin (2002) Lord
Co
[39] TMS 60 Lbf Modal Shaker (2010) The Modal Shop Inc
[40] Martynowicz P Development of Laboratory Model of Wind Turbines Tower-Nacelle System
with Magnetorheological Tuned Vibration Absorber Solid State Phenomena (2014) 208 40-51
[41] Snamina J Martynowicz P and Łatas W Dynamic similarity of wind turbinersquos tower-nacelle
system and its scaled model Solid State Phenomena (2014) 208 29-39
[42] Martynowicz P and Szydło Z Wind turbines tower-nacelle model with magnetorheological
tuned vibration absorber the laboratory test rig Proceedings of the 14th International
Carpathian Control Conference (2013) 238-242
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
Control of an MR Tuned Vibration Absorber for Wind Turbine Application Utilising the Refined
Force Tracking Algorithm
18
[43] Rosoacuteł M and Martynowicz P Identification of Wind Turbine Model with MR Damper Based
Tuned Vibration Absorber Structural Engineering and Mechanics (in review)
[44] Snamina J and Martynowicz P Prediction of characteristics of wind turbines tower-nacelle
system from investigation of its scaled model 6WCSCM Sixth World Conference on
Structural Control and Monitoring proceedings of the 6th edition of the World conference of
the International Association for Structural Control and Monitoirng (IACSM) (2014)
Barcelona Spain 15-17072014
[45] Maślanka M Sapiński B and Snamina J Experimental Study of Vibration Control of a Cable
With an Attached MR Damper Journal of Theoretical and Applied Mechanics (2007) 45 (4)
893ndash917
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