an hydraulic test rig for the testing of quarter turn...
TRANSCRIPT
An Hydraulic Test Rig for the Testing of Quarter Turn
Valve Actuation Systems
Luca Pugi2* , Giovanni Pallini1, Andrea Rindi1, Nicola Lucchesi3
1Dept. of Industrial Engineering
University of Florence
Florence, Italy
2MDM TEAM SRL
(Spin Off of Florence University)
Florence, Italy
3VELAN ABV, SpA
Capannori (LU), Italy
Abstract - in this work, some preliminary design results
concerning the development of a rig for the fast prototyping and
the testing of the actuation system of large quarter turn valves
for power plants are shown. In particular, friction forces
generated on sealing and bushings by the internal pressurized
fluid influence opening and closing torques of large valves. In
order to test a valve actuation system, the proposed rig is able to
simulate the resisting torque and more generally the mechanical
impedance of pressurized quarter turn valve.
The proposed actuation of the rig is hydraulic. In this work design
and choosing of different solutions are discussed with a particular
attention to robustness and stability troubles of the rig respect
disturbances, limited bandwidth and interaction with partially
unknown tested system
I. INTRODUCTION
There are several kind of process valves used in Oil&Gas industry and more generally for large process plants whose opening state is controlled by imposing a rotation of about 90° as example ball or butterfly valves. Angular position of this kind of valves are usually controlled by linear pneumatic or hydraulic actuators whose linear motion is converted in a corresponding rotation using simple transmission systems such as for example the Scotch-Yoke system represented in the scheme of Figure 1. Also different solutions including electric actuators and toothed transmission systems, like gears of transmission belts, should be found in literature where most of the available documentation should be referred to patents concerning industrial applications.
For fail safe applications, a desired fail-state of the valve is usually assured by the preload of linear spring as visible in the example of Figure 1.
The actuation system of the valve is usually controlled by a closed position loop implemented on a component briefly called as valve positioner or simply positioner. The positioner is mainly composed by the following components:
Angular Position Feedback: angular position and consequently the state of the valve is continuously measured.
Regulator: a simple controller typically a PID (Proportional, Integral, Derivative ) position controller is implemented.
Valve or Drive: according a reference command produced by the regulator, a Drive system, typically a Valve for pneumatic or hydraulic cylinders is used to finally control the actuator.
Figure 1. Example of Quarter Valve actuation system using a pneumatic cylider and a scotch yoke transmission system
Aim of the proposed rig is to test the valve actuation system and positioner by simulating the opening/closing torque of a pressurized quarter turn valve. A simplified scheme is visible in Figure 2. The main advantage of this approach is to have the same actuation system running in different operating conditions and simulating different valves. This a quite interesting feature considering cost and encumbrances of valves and of the plant needed produce the pressurized flow in order to reproduce the typical operating conditions.
Tested valve actuator and positioner should be different both in terms of electro-mechanical layout and calibrations, as example in order to control different valves.
Therefore, there is the need to design the actuation and regulation of the rig to avoid potential troubles of stability due to the interaction with a tested system, whose behavior is only partially known.
Figure 2. Principle of Operation of the Proposed Test Rig
More generally this problem should be treated as a particular case of a SISO (Single Input, Single Output) torque controlled system which have to be robust as much as possible respect to an external disturbance which should be treated as an imposed position/kinematics.
This kind of trouble has been widely studied in robotics for the following applications:
force controlled or compliant end effectors [17]
robots interacting with humans or potentially sensitive environments [14]-[16].
walking robots were obstacles due to unstructured or partially unknown working environment should be treated as hard constraints or imposed position disturbances [18].
Similar problems are common on active or semi-active suspension systems, where the spectral content of the disturbances, that has to be rejected, should be far higher respect to the bandwidth of implemented control systems. Typical examples should be related to the control of railway pantograph with wire [19] or fluid [20] actuation systems. Also in the study of semi-active vehicular suspension, there is a robustness specification respect to a non-linear, bandwidth limited actuator [21].
Respect to previously cited applications, in this work attention is focused on an industrial application in which this kind of approach is quite uncommon. Furthermore, range of generated torque forces is quite rare respect to typical robotics or vehicular applications. Finally design has to be a compromise between cost, maintenance, ease of use specifications of an industrial applications against the necessity of performing a reliable Hardware in the Loop testing of positioners.
II. TESTING SPECIFICATIONS
Considering a wide variability of different positioners and actuators to be tested the specifications of the test rig are briefly summarized in: specifications in terms of maximum speed of
actuators are quite not demanding considering that a complete opening or closing run require about 10 seconds.
More demanding requirements concerns the simulated torque profile: for the same simulated valve the value of the maximum resisting torque should be three times greater than the minimum one as visible in the example of Figure 3.
Considering that the ratio between two torques exerted by the biggest and the smallest tested actuator has a value of about ten, torque profiles that have to be correctly simulated by the rig actuator should be variable of more than thirty times.
TABLE I. SPECIFICATIONS CONCERNING TESTED ACTUATORS
Figure 3. Example of simulated torque profile during an opening and a
closing run
III. DESIGN OF THE HYDRAULIC ACTUATOR
For the rig, an hydraulic actuation is preferred since it assure the possibility of exerting heavy torques with reduced encumbrances. Besides, it should be considered that the rig actuator has to be mostly regulated as brake able to dissipate a continuously controlled power. Management of electric drive is generally more complex in the braking phase, moreover it’s obvious to take into account penalties related to the limited quarter turn rotation and the impossibility of using gearings with high reduction ratio in order to reduce troubles related to friction, tooth backslash and friction.
Commercial hydraulic torque motors are available for sale in different size, however, considering cost specifications it was preferred a simple pivoted linear actuator linked to the rig using the transmission system described in the scheme of Figure 4.
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 11500
2000
2500
3000
3500
4000
4500
5000
5500
Angle [rad]
Tor
que[
Nm
]
opening run
closing run
Parameter min.NOM. MAX
VALUE
Angular Run [°] 80°-90°-100°
Max Angular
Speed[rad/s] 0.137- 0.143-0.157 [rad/s]
Max Acceleration
[rad/s2] 0.08-0.144-0.28[rad/s2]
Max Resisting
Torque [Nm] 1000-5000-10000[Nm]
Min. Resisting
Torque[Nm] 350-1600-3300[Nm]
An important advantage of this solution is the opportunity to scale the project depending on inputs: different solutions can be easily implemented to test bigger or smaller valves using commercial components. The main kinematic parameters of the transmission are described in TABLE II.
TABLE II. MAIN GEOMETRIC PARAMETERS OF TRANSMISSION
R xp yc
260[mm] 379[mm] 147[mm]
In particular solving this simple kinematics allows to calculate the ratio τ(α) between the exerted torque T and the corresponding linear force of the hydraulic cylinder, F (1).
22sincos
sincos
rxry
yxrl
F
T
pc
cp
(1)
Figure 4. Pivoted linear actuator connected to the rig using a simple
rotoidal joint
Figure 5. shows the behavior of τ(α) normalized respect to its value on the lower endrun. The normalized τ(α) profile is compared with τopt(α). τopt(α) is a reference ideal transmission ratio which makes possible the emulation of a typical valve torque profile using a linear actuator exerting a constant force, as example an hydraulic actuator fed with constant pressure. Unfortunately the chosen transmission system meets the optimal requirements on the end-run, despite this it provide a drastic reduction of the force exerted by the actuator, especially for intermediate positions corresponding to approximately null value of the angle α.
Figure 5. Normalized τ(α) compared with the reference τopt(α)
Considering the specifications of TABLE I. and the geometry described in TABLE II. It’s possible to size the hydraulic cylinder which is described in TABLE III.
TABLE III. MAIN GEOMETRIC PARAMETER OF THE CHOSEN HYDRAULIC
ACTUATOR
IV. HYDRAULIC PLANT DESIGN
The hydraulic plant of the rig is briefly described by the LMS Amesim™ scheme visible in Figure 6. The chosen plant configuration is selected in order to make possible the implementation of two different control strategies:
Strategy “A”: Proportional Flow Controller
Strategy “B”: Pressure Limitation with Adjustable Compliance
Figure 6. LMS Amesim™ scheme of the rig plant
A. Proportional Flow Controller
In this plant configuration the 4/3 distributor valve visible in Figure 7. is closed and the actuator is controlled by a proportional valve realizing the torque-force control scheme described in Figure 7. A proportional valve feed by a stabilized pressure source controls the actuator. The inlet pressure is stabilized using the servo-relief valve and the accumulator visible in the plant scheme of Figure 7.
Parameter Value Notes
Int. Diameter 63mm *Corresponding area
of about 15 cm2
Rod diameter 45 mm
Max flow 4.6 liters/minute
Calculated for an
augmented max speed of 0.04-0.05 m/s
Pressure 160-170bar To erogate a nominal
torque of 5000Nm
Figure 7. Architecture of the Proportional Flow Controller
In particular a reference torque profile Mref is reproduced using
a closed loop regulator that is implemented respect to a
feedback-measured torque Mfeed. To adopt this loop regulator
It is taken for granted that the feedback torque is in a limited
bandwidth assumed to be about 15-20Hz. The gain of the
regulator is scheduled in order to compensate system non-
linearities and especially the variable transmission ratio τ(α) of
the actuator.
Assuming a linearized model of valve and actuator available
in literature [20][22][23] it’s possible to calculate in the
Laplace domain the difference of pressure ΔP(s) between
actuator chambers as a function of two terms respectively
proportional to the valve spool state y(s) and to the position of
the actuator x(s) :
0 0
y
t t
b b
h AsP s y s x s
V Vh s h s
E E
(2)
In particular the following symbols are adopted:
A, V0 are respectively the area and the volume of the
actuators chambers supposed to be equal (system linearized
respect to the mean run).
hy and ht are parameters which reproduce respectively the
proportionality of flow respect to valve state and the
leakage of both valve and cylinder.
Eb is the bulk modulus of the oil
The spool state of the valve is usually controlled by an
amplification stage. as example in flapper or jet pipe servo-
valves [23]-[25] , or by an high performance linear motor, as
example in proportional valves [26]. In both cases, the relation
between the valve command i(s) and the corresponding state
y(s) is approximated by a second order transfer function which
is usually described in term of eigenfrequency ωn and damping
factor ε.
As a consequence the dynamical behaviour of ΔP(s) is better
described by (3).
21
0022
2
2
GsxGsisP
E
Vsh
Assx
E
Vsh
h
sssisP
b
t
b
t
y
nn
n
(3)
In particular the transfer function G2(s) describes the
relationship between a displacement of the cylinder and the
corresponding pressure variation of the cylinder.
G2(s) represents a cross coupling term between the rig
actuation dynamic and the corresponding tested system, which
should be cancelled or minimized to improve the dynamical
response of the system.
For this reason, in the control scheme of Figure 7. is also
implemented a velocity feedback contribution proportional to
cylinder speed. However, dynamical performances of the
system are negatively affected by both limited bandwidth of
the valve and compressibility effects of oil.
This approach, suggested by different sources in literature
[22][25], has been yet successfully applied by Allotta and
Pugi, on the force control of a railway pantographs [20].
It should be also noticed that an increase of compressibility
effects (corresponding to an increase of the V0/Eb ratio) and of
the leakage (ht) should produce a reduction of G2(s). However,
this solution has often limited benefits and potential drawbacks
since the increase of the above cited terms also drastically
reduce the dynamical response of the valve, corresponding to
G1(s).
B. Pressure Limitation with Adjustable Compliance
Tested positioner have a quite slow dynamical response
corresponding to valve opening times of about 10-12seconds,
so the high dynamical response granted by the previously
described controller it’s not so important. On the other hand
considering the high variability of tested components both in
terms of dynamical response and simulated torques profiles,
robustness, and stability performance of the controller are
more important and should justify the adoption of the less
conventional layout described in Figure 8.
In this case respect to the plant scheme of Figure 6. the
proportional valve is deactivated. Force exerted by the actuator
is controlled by regulating the pressure in one of the two
chambers of the cylinder while the other one is connected to
the oil tank. A 4/3 distributor is used to switch the connections
of the chamber respect to the opening or closing direction of
the valve.
Pressure is regulated using a servo-relief valve whose pressure
reference should be continuously controlled by an external
reference signal (typically an analog current reference).
As visible in the scheme of Figure 8. the reference command
pressure for the relief valve, Pref is calculated as the sum of two
contributions:
Pstat: once the desired torque profile Mref(α) is calculated
the corresponding pressure Pref(α) that the actuator have to
reproduce should be calculated according to equation (4),
which is calculated considering ideal static equilibrium of
the machine (no friction, neglected inertial contributions,
ideal hydraulic plant response):
1ref
stat
MP
A
(4)
Psl: Pstat is calculated considering a simplified static model
un-affected by disturbances. Psl is the contribution
calculated by a closed loop torque controller whose input
is the error between the desired torque Mref and the
meausured one Mfeed. Aim of the Psl contribution is to reject
as much as possible unmodeled dynamics as a disturbance.
This term is implemented as an high gain PI (proportional
integral) controller saturated to a known value.
The approach of the implemented controller resemble the
philosophy of sliding mode controllers [27].
Figure 8. Architecture of the Pressure Limitation with Adjustable
Compliance
In particular the proposed regulator is optimized in order to be
very robust respect disturbances introduced by the interaction
with a potentially stiff tested positioner.
In order to make more clear the followed approach the
simplified scheme of Figure 9. is considered:
The test rig is a treated as a torque controlled system which
have to reproduce the reference torque Mref.
The tested positioner is a position controlled system able
to follow a reference position αref
Both the interacting control systems have its own control loop
(transfer functions Gpos(s) e Grig(s)) and actuations systems
Ppos(s) e Prig(s). The coupling between the dynamical
behaviour of the two systems is modelled considering the
transfer functions Kpos(s) e Krig(s);
Since the dynamical response of the tested positioner is highly
variable, in order to assure an high robustness to the system
authors focused their attention in the optimization of rig
transfer functions with a particular attention to the equivalent
stiffness Krig(s) of the rig. In particular the module of Krig(s)
has to be minimized in order to reduce potentially dangerous
interactions between the two systems.
Figure 9. Simplified approach adopted to increase the robustness of the rig
control and actuation system
In particular considering the plant layout of Figure 6. the
dynamical behavior of the system is described by (5) in which
the following simplifications are assumed to be valid:
The pumping unit assures a constant flow Qpump
The flow delivered to the controlled cylinder chamber Q.
The servo-relief valve flow Qvalve is constrained to be
negative since the valve should be used only to discharge
the controlled capacities. For the sake of simplicity the flow
of the valve is supposed to be controlled by a proportional
regulator with a constant gain k. Valve dynamics is
reproduced as a second order system with an Eigen
frequency ωn of about 12Hz and a damping coefficient of
about 0.7,0.8.
0
2
*
*0
22
2
sPE
VAxs
Qss
PPkQQQ
b
pump
nn
nrefvalvepump
(5)
In (5) the equivalent compressibility term (V0*/Eb*) is higly
influenced by the presence of the air or nitrogenum filled
accumulator. In particular the compressibility of the
pneumatic accumulator is largerly dominant and should be
approximately calculated according (6) 1
0*
*k(P V )
acc
b init init
V VdV
E dP
(6)
Where the following symbology is adopted:
Vacc is the current volume of the pneumatic accumulator,
while Pinit and Vinit represent the initial (preload) pressure
and volume values
is the coefficient of the polytropic transformation which
is used to approximate the behavior of the gas in the
accumulator.
Solving (5), it’s possible to calculate the behavior of the
pressure P of the controlled chamber of the actuator as a
function of three inputs, Qpump, Pref, x.
skE
V
ssk
Asx
ssskE
VP
skE
V
ssk
QP
bnn
n
nn
nb
ref
bnn
n
pump
*
*0
22
2
22
2
*
*0
*
*0
22
2
2
21
1
2
1
(7)
Since the area of the actuator A and the transmission ratio τ(α)
are known, it’s possible to calculate from (7) the three transfer
functions Gpump(s),Gref(s),Krig(s), between the three inputs
Qpump, Pref, x and the torque M delivered by the actuator (8).
skE
V
ssk
sAsK
ssskE
V
AsG
skE
V
ssk
AsG
sxKsGPsGQM
bnn
n
rig
nn
nb
ref
bnn
n
pump
rigrefrefpumppump
*
*0
22
2
2
22
2
*
*0
2
*
*0
22
2
2
)(
21
2
)(
(8)
Some further considerations should be performed from (8):
Gpump(s): Qpump introduces a disturbance whose influence is
rejected by the pressure control loop of the relief valve. In
fact higher valve gain k decreases the module of Gpump(s).
Gref(s) : it’s possible to calculate a root locus of Gref(s)
parametrized respect to valve gain k as visible in Figure
10. For too high values of k the system became clearly
instable.
Figure 10. Root Locus of Gref(s)
Krig(s): this transfer function represent the coupling term
with the tested system. As a consequence to increase the
robustness without penalizing to much the gain k, Krig(s)
has to be carefully shaped. For position disturbances with
frequencies far higher than the frequency of the valve ωn,
Krig(s) is approximated by (9).
*0
*
2
V
EAsKs b
rign
(9)
From (9) it should be deduced that by moderately
increasing the compressibility term V0*/Eb* it’s possible to
reduce the value of Krig(s) without compromising to much
the bandwidth of the pressure controller which should be
calculated from the expression of Gref(s).
V. PRELIMINARY SIMULATION USING LMS AMESIM
A. Model Description
Using LMS Amesim™, authors developed a complete model of the rig whose main feature are visible in Figure 11.
In particular both rig and tested actuator mechanical behavior are reproduced in complete multibody model. The geometry of the rig is the same described in TABLE II. The tested actuator and positioner is supposed to be a scocth yoke transmission with the geometry described in Figure 1. Inertial properties of componets are taken directly from CAD geometries. Tested actuator is supposed to be fed with an air pressure corresponding to a maximum opening torque of about 5000Nm. The controller of the positioner is supposed to be an high gain PI (Proportional Integrator) regulator manually tuned with an equivalent impedance of the valve in order to obtain a feasible response. For the rig controller both the two regulator configurations are compared.
The response of hydraulic [26] and pneumatic components in terms of hydraulic losses and dynamical behavior is modelled including pipes which are modelled considering RI-C [28],[29], components in which resistive, inertial and capacitive effects working on fluid inside the pipe are evaluated.
Other important non linearities as friction and compliances on joints of mechanical components are modeled in order to further verify the robustness of the proposed controller. In particular on prismatic joints, kinematic and a static fricion factors are evaluated to be equal respectively to 0.15 and 0.3.
Also on rotoidal joints friction is applied considering the application of the same friction model [30] over a cylindrical surface with a radius of about 10mm.
Figure 11. LMS Amesim model of the HIL Test rig (example referred to the proportional flow controller)
Finally mechanical compliances on joints are introduced as equivalent springs/bushings which reproduce a limited deformation of the joint supposed to be linear respect to the applied load.
-250 -200 -150 -100 -50 0 50 100-200
-150
-100
-50
0
50
100
150
200
0.92
0.98
0.140.30.440.580.72
0.84
0.92
0.98
50100150200250
0.140.30.440.580.72
0.84
System: tftrafGain: 3.78e-009Pole: -27.9 + 36.3iDamping: 0.609Overshoot (%): 8.96Frequency (rad/s): 45.8
Root Locus
Real Axis (seconds-1)
Imagin
ary
Axis
(seconds
-1)
B. Preliminary Simulation Results
Using the model described above, authors compared the
performances of both the proposed controllers in terms of
robustness. Both proportional flow controller, and the pressure
limitation one have been successfully calibrated for a nominal
condition in which both the controller are able to produce an
almost equivalent performance. Then a Montecarlo simulation
with perturbed parameters is performed: the model is perturbed
considering some parametric variations, as example in the
simulated friction factor, or in the reference torque profile that
have to be simulated, and the effects in terms of robustness of
response of the system are evaluated. Some qualitative results
are summarized in TABLE IV. and in TABLE V.
TABLE IV. ROBUSTNESS ANALYSIS RESPECT TO PARAMETRIC
VARIATIONS OF TESTED POSITIONEER
TABLE V. ROBUSTNESS ANALYSIS RESPECT TO PARAMETRIC
VARIATIONS OF THE RIG
Preliminary simulations substantially confirm the behaviour
predicted by the theoretical analysis performed on linearized
models of the system: in particular, the second strategy seems
to be quite more robust respect to most of the uncertainties due
to parametric variations of the tested system. In particular, the
uncertainties of the simulated positioner were expressed in
terms of gains of its position loop and in terms of exerted
torque: a variation of the gain of the position loop of the
positioner was used to roughly reproduce the behaviour of a
system with different stability margins and performances. On
the other hand, the simulations of pneumatic actuators, scaled
to cover different torque categories, involved different system
sizing and consequent variations of the equivalent mechanical
impedance of the actuator virtually tested on the rig. In
particular in Figure 12. some results concerning the simulation
of different Mref profiles and the corresponding M measured
for different friction factor are shown: it’s clearly noticeable
that performances and robustness of the controller are more
influenced by a variation of the simulated torque profile
respect to even big variation of the simulated friction on joints.
As visible in Figure 13. the contribution in terms of actuator
pressure needed to compensate the friction is quite small,
explaining the reason of the relative robustness of the control
loop respect to friction variations.
Figure 12. Example of results, comparison considering different reference
torque profiles and different simulated friction factor on joints
Figure 13. Calculated pressure profiles for the nominal configuration
VI. CONCLUSIONS AND FUTURE DEVELOPMENTS
In this work the preliminary study of a Hardware in the loop
rig for the testing of quarter valve actuation and position
control system has been presented. In particular both actuation
and control system have been optimized in order to increase
robustness and performance respect to quite demanding
specifications especially in terms of robustness respect to
parametric uncertainties of the rig and variability of the tested
system. The major contribution of this work is the fruitful
Effect in terms of
Robustness
Parameter Perturbation(s)
State
Flow
Controller
Pressure
Limitation
Friction on
joints
No-Friction/
Doubled Friction
Robust Robust
Compliance
on Joints
No Compliance/
10X compliance
Sensitive Robust
Scaled Ref.
Torque
Profile
Max. Torque Profile Min. Torque Profile
Very
Sensitive
Sensitive
Variation of
the positioner loop Gains
Pos. Gain mult. x 0.5 Pos. Gain mult. x 10
Very sensitive
Robust
Effect in terms of
Robustness
Parameter Perturbation(s)
State
Flow
Controller
Pressure
Limitation
Friction on
joints
No-Friction/
Doubled Friction
Robust Robust
Compliance
on Joints
No Compliance/
10X compliance
Sensitive Robust
Valve Bandwidth
-20% +20%
Sensitive Less Sensitive
Bandwidth of
the torque feedback
-20%
+20%
Very
sensitive
Robust
transfer and application of know-how which is more frequently
used in robotics, to an industrial testing application. For the
next year the rig will be effectively put in service and authors
hope to be able to discuss performance and robustness of the
tested system with the support of fresh experimental data.
VII. ACKNOWLEDGEMENTS
This work was financed as a part of the project High
Efficiency Valves (CUP: D55C12009530007) financed by the
program POR CRO FESR of Regione Toscana (European
Funds for Regional Industrial R&D projects). Apart funding,
which is a fundamental contribution for research, authors wish
also to tanks engineering students of university of Florence for
their contribution and for their curious and enthusiastic
approach and in particular Giuseppe Occhipinti and Andrea
Pulcinelli. In addition authors wish to gratefully remember all
the people of Velan ABV SPA which have contributed to this
work with their experience and competence, in particular Fabio
Lapini and Michele Graziani.
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