[american institute of aeronautics and astronautics 48th aiaa aerospace sciences meeting including...

American Institute of Aeronautics and Astronautics

1

A Study of Dynamic Coupling and Composite Load Control for

Wind Turbines

Jeffrey K. Lazaro, Maria J. Chakiath*, and Karl A. Stol

†, Hazim Namik

‡

University of Auckland, Auckland, New Zealand

Wind turbine components are sized according to their expected fatigue loads and any

reduction in these would decrease costs and prolong working life. Wind turbine control is a

multivariable problem with large interaction across multiple control channels (inputs to

objectives). This article studies coupling and investigates a composite load controller for a

wind turbine, consisting of a linear quadratic regulator for the loads and a baseline power

controller for speed and torque regulation. The load objectives were to reduce tower fore-

aft, low speed shaft (LSS) tilt, and LSS yaw bending fatigue. Simulations in above rated

wind conditions evaluated the composite design against the baseline controller alone, as well

as a classical architecture with multiple single-input single-output (MSISO) loops. In this

way, it is important to compare to a control design that is not aware of any coupling. Results

showed significant mitigation of damage equivalent loads in the tower fore-aft, and LSS tilt

and yaw directions across both designs when compared to baseline. The composite controller

achieves better load reduction without the need for filtering out the effects of other channels,

as would be required in the MSISO design.

Nomenclature

A,B,C,D = linear state-space model matrices

J = linear quadratic regulation quadratic cost function

Ms,tilt = shaft bending moment in the tilt direction

Ms,yaw = shaft bending moment in the yaw direction

Q ,R = linear quadratic regulation state and input weighting matrix

Q’ = linear quadratic regulation output weighting matrix

Tg = generator torque command

u = input vector

x = state vector

y = output vector

θ = collective blade pitch angle

θc = cosine-cyclic pitch

θs = sine-cyclic pitch

τ = displacement in the tower top fore-aft direction

ψ = rotor azimuth angle

* Undergraduate Student, Department of Mechanical Engineering, Private Bag 92019

† Senior Lecturer, Department of Mechanical Engineering, Private Bag 92019, AIAA Senior Member

‡ PhD Candidate, Department of Mechanical Engineering, Private Bag 92019, AIAA Member

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition4 - 7 January 2010, Orlando, Florida

AIAA 2010-1600

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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I. Introduction

Wind turbines are growing larger and active control to reduce structural fatigue is an important field because

costs can be reduced and working life prolonged. A typical controller for a large wind turbine aims to maximise

power capture and decrease structural loads by actuating generator torque (Tg) and blade pitch (θ)1. There are

various control designs that can be used to meet these objectives and both single-input single-output (SISO) and

multi-input multi-output (MIMO) control has been used2-5

. Through the use of individual pitch control (IPC),

asymmetric loads such as tilt and yaw moments on various turbine components can be reduced. However, using

linear control design techniques with IPC gives rise to non-rotating inputs which are considered as separate

actuators, making the problem multivariable. With multiple objectives, the input-to-output channels are heavily

coupled and can have significant interactions.

A. MIMO Control

To avoid multiple control loops (and hence the possibility of conflicting control efforts), modern design methods

can be used to synthesise MIMO controllers, which aim to address several objectives simultaneously.

Using state feedback, an optimal controller finds a solution to a performance cost function for the competing

goals of state and input regulation, while guaranteeing stability. Researchers have tested state-space optimal

controllers and results indicate that it may exhibit improved performance over a classical SISO controller in terms of

dynamic load reduction and speed regulation2-4

. A disadvantage with MIMO control is that transition between below

and above rated wind can cause problems as it has difficulty with integral wind-up. A SISO proportional integral

(PI) pitch controller includes an integral reset to account for this, but in MIMO state-space designs this is not

straight-forward especially when state estimation is involved.

B. Individual Pitch Control

The possibility of individual blade pitching allows greater potential fatigue reduction for asymmetric loads.

Linear turbine models obtained for controller design are periodic with rotor azimuth angle. Commonly, averaging

the model to produce a linear time-invariant (LTI) system is sufficient for controller design as there is only weak

periodicity. However with rotating states, inputs, or outputs (e.g. when IPC is used) the linear system is highly

periodic and directly averaging gives reduced controller performance6. This is circumvented by using the multi-

blade coordinate transformation (MBC, also known as the Coleman or d-q axes transformation), which convert any

dynamics in a rotating frame into a non-rotating one7. Using IPC in a multi-variable controller, Bossanyi‟s

8 work

demonstrates a significant reduction in asymmetric loading, including fatigue on the individual blades. However,

this technique relies on the availability of sensors that can measure the asymmetric loads in either the rotating or

non-rotating part of the turbine. Moreover, Bossanyi describes techniques to incorporate IPC with classical PI

control.

C. Coupling

Coupling can be broadly defined as the interaction across multiple control input to output channels, whether

positive or negative. This interaction can be identified by Bode magnitude plots9. For SISO controllers, suitable

filters can be designed so that the control actions do not excite structural resonances or conflict with other paths.

Consideration must be made as to whether the coupling is helping or hindering load reduction. In this paper, these

assumptions are tested in simulation on a linear model.

D. Objective and Scope of Study

The goal of this study is to investigate coupling in a wind turbine load control scenario and to test the

performance of a composite controller against a traditional control architecture consisting of multiple SISO loops.

The composite controller comprises of a MIMO linear quadratic regulator (LQR) to reduce fatigue loads and a

baseline power controller for speed and torque management. The desired fatigue vibrations for attenuation are

bending moments in the tower fore-aft, low speed shaft (LSS) tilt, and LSS yaw directions and IPC is used to

address the afore-mentioned asymmetric loads. Because the composite model has a separate baseline controller for

power regulation, region transition is handled and the design can focus on load attenuation. Moreover, the MIMO

load control part of the composite design addresses interactive coupling in its internal design.

The particular turbine model considered in this project is the National Renewable Energy Laboratory (NREL)

5MW three-bladed horizontal axis baseline model and its properties are displayed in Table 1.


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Table 1. Properties of the NREL Baseline Wind Turbine1

Rated Power 5 MW

Rotor Orientation, Configuration Upwind, 3 Blades

Control Variable Speed, Variable Pitch

Gear Ratio 97:1

Rotor Diameter 126 m

Hub Height 90 m

Cut-In, Rated, Cut-Out Wind Speed 3 m/s, 11.4 m/s, 25 m/s

Cut-In, Rated Rotor Speed 6.9 rpm, 12.1 rpm

Rated Tip Speed 80 m/s

Rotor, Nacelle, Tower Mass 110,000, 240,000, 347,460 kg

II. Linear Turbine Model

The linear state-space model of the wind turbine used in this study has six degrees of freedom (tower fore-aft

motion, generator angle, LSS torsion, and three blade flap-wise motions) and is obtained numerically using FAST,

an aero-elastic simulation code for wind turbines10

. The operating conditions are rated generator torque and rotor

speed, a wind speed of 18 m/s, and a blade pitch angle of 14.9 degrees. The dynamic wind turbine plant in Eq. 1 can

be described by linear state space equations in terms of perturbations (∆) of the states (x), inputs (u) and outputs (y):

Δ𝒙 = 𝐴(ψ)Δ𝒙 + 𝐵(ψ)Δ𝒖 (1-1)

Δ𝒚 = 𝐶(ψ)Δ𝒙 + 𝐷(ψ)Δ𝒖 (1-2)

The model is highly periodic with rotor azimuth angle (ψ) and thus multi-blade coordinate transformation

(MBC) is used to transform any dynamics in the rotating frame to a fixed coordinate system7. The resulting system

is now weakly period and the state matrices are averaged without loss of information6, giving rise to the linear time

invariant (LTI) system in Eq. 2 with subscript „NR‟ referring to the non-rotating frame:

Δ𝒙 NR = 𝐴𝑁𝑅Δ𝒙NR + 𝐵𝑁𝑅Δ𝒖NR (2-1)

Δ𝒚NR = 𝐶𝑁𝑅Δ𝒙NR + 𝐷𝑁𝑅Δ𝒖NR (2-2)

The rotating inputs now become new coordinates in the non-rotating frame (transformed about ψ) that are called

collective (θ), cosine-cyclic (θ𝑐 ), and sine-cyclic (θ𝑠) components, as in Eq. 3:

θ1

θ2

θ3

=

1 cos(ψ) sin(ψ)1 cos(ψ + 2π/3) sin(ψ + 2π/3)

1 cos(ψ + 4π/3) sin(ψ + 4π/3)

θθ𝑐

θ𝑠

(3)

III. Controller Designs

The first design in Fig. 1a consists of multiple SISO (MSISO) controllers for fatigue load reduction and the

baseline controller for power regulation. The control loops are designed independently without knowledge of each

other and hence coupling between objectives is not considered. The controller that designs for coupling at a greater

level is the composite model (Fig. 1b). Here, the load objective dynamics are known by the controller. Addressing

coupling in the design of a controller can be advantageous in ensuring the objectives and subsequent corrective

actions do not conflict with each other. However the trade-off comes with increased complexity.

x


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A. Baseline Power Controller

The baseline power controller aims to keep rotor speed and power at the rated conditions. It consists of a SISO

PI algorithm that generates pitch commands from the input generator speed, and a torque command generated

independently which is inversely proportional to the generator speed1. This can be seen in Fig. 1. Note that the

baseline model is used to normalise results in testing.

B. Multiple SISO Loop Controller

The MSISO controller consists of three SISO loops (Fig. 1a) for the loads and the regular baseline controller for

power regulation. It is the model that considers the coupling between objectives the least as the control paths are

synthesised without knowledge of each other. The main advantage of SISO architectures is that classical design

techniques can be used which are well known and less complex than state-space methods. IPC is used so that the

three control paths take care of fatigue loads in the tower fore-aft, shaft tilt, and shaft yaw direction. Note that the

methods to design the load controller are those described by Bossanyi5,8,11

.

A simple proportional controller acting on the tower top fore-aft velocity (𝜏 ) and actuating collective blade pitch

has been demonstrated to sufficiently provide damping to the tower fore-aft structural mode5. Taking the tower

bending moment in the fore-aft direction as the controlled signal can be problematic because it is not desirable to

influence mean tower loading (dictated by the mean wind speed). Instead, acting on the velocity signal is

advantageous because it allows influence over the cyclic loading and does not overly conflict with speed regulation.

An accelerometer on the tower provides an acceleration measurement which is integrated to obtain the fore-aft

velocity. The reference for this is zero hence the error (e) can be considered to be equal to the velocity measurement

inverted which is shown in the block diagram in Figure 2.

PI PITCH CONTROL

TORQUE CONTROL

FORE-AFT P

CONTROL

WIND TURBINE

BASELINE POWER CONTROLLER

+

SHAFT TILT PI CONTROL

SHAFT YAW PI CONTROL

PI PITCH CONTROL

TORQUE CONTROL

WIND TURBINE

BASELINE POWER CONTROLLER

+

MIMO LOAD

CONTROLLER

Tg

θ

Output measurements

θ

Tg

System states

Figure 1. Multiple SISO controllers (a) and composite load control (b)

(a) (b)

Figure 2. Block diagram of fore-aft SISO loop

WIND TURBINE K

- + e(t) 𝜏

𝜏 1

𝑠

𝜏 𝑅𝑒𝑓 = 0

∆θ


5

Two separate SISO loops using PI control are required for shaft tilt and shaft yaw moments (Figure 3). Since

stationary load measurements for both of these are available in simulation and are already in a fixed coordinate

system, the forward MBC transformation is not necessary. Instead, a control action may be directly performed on

the measurements in the fixed frame before being transformed to the rotating one to produce individual pitch

commands as per Eq. 4. Note that the collective coordinate (θ) is not considered (this is already used for the tower

fore-aft loop) and so only cosine-cyclic (θ𝑐 ), and sine-cyclic (θ𝑠) are used:

θ1

θ2

θ3

=

cos(ψ) sin(ψ)cos(ψ + 2π/3) sin(ψ + 2π/3)

cos(ψ + 4π/3) sin(ψ + 4π/3)

θ𝑐

θ𝑠 (4)

The filtering element in Figure 3 can compose of a notch filter to remove blade passing frequency components

(three times the rotor revolution for a three-bladed turbine, called 3P loads) to avoid adversely affecting asymmetric

loads on the nacelle and tower, which are dominated by a peak at this point11

. Additional filters to avoid other

structural resonances may be added here as well.

C. Composite Controller

The composite architecture consists of a MIMO LQR controller for the fatigue loads and a baseline controller for

power regulation (Fig. 1b). This design has two advantages. Firstly, the load reduction objectives can be emphasised

in design and the controller incorporates any coupling present. This is desirable so that the control actions do not

overly conflict with each other. Secondly, transition between below and above rated wind conditions can be better

handled by the power controller as it deals with integral wind-up. This occurs when the integral term of the PI pitch

controller grows larger and larger in below rated conditions (as the rotor speed will never reach rated) so once it

becomes active in above rated conditions, the control action is incorrect. The PI pitch controller includes an integral

reset to account for this, but in MIMO state-space designs this is not as straight-forward especially when state

estimation is involved. In this study region transition is not considered so this advantage of the composite design is

not fully realised.

The LTI system is used to design an optimal full-state feedback (FSFB) controller using linear quadratic

regulation. A characteristic cost function describes the balance between the conflicting objectives of state regulation

and actuator usage and the solution that satisfies the FSFB control law is an LQR controller. Because two of the load

measurements are not states (LSS yaw and tilt) these must be regulated using output weightings. Tower fore-aft

velocity (𝜏 ) is the only state that we desire to explicitly regulate hence the output vector is:

𝒚 =

MS,tilt

MS,yaw

𝜏

For an optimal LQR design with the focus on output regulation, the characteristic quadratic cost function in

terms of non-rotating variables changes to Eq. 5:

𝐽 = 𝑦𝑁𝑅𝑇 𝑄′𝑁𝑅 𝑦𝑁𝑅 + 𝑢𝑁𝑅

𝑇𝑅𝑁𝑅 𝑢𝑁𝑅 𝑑𝑡

∞

0

(5-1)

PI CONTROLLER

PI CONTROLLER

MS,yaw

MS,tilt

θ𝑐

INVERSE

MBC θ𝑠

∆θ1 , ∆θ2 , ∆θ3

FILTERING

Figure 3. PI controllers acting on yaw and tilt moments


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𝑄𝑁𝑅 = 𝐶𝑁𝑅𝑇𝑄′𝑁𝑅 𝐶𝑁𝑅 (5-2)

In this way, the outputs can be regulated and the relationship between the familiar state weighting matrix Q and

the augmented Q’ that gives weightings to the outputs is shown in Eq. (5-2). This shows the relationship between the

states and the output signals through the C matrix and the outputs are being regulated through this mechanism. LQR

tools in MATLAB are used to calculate the final gain matrix and this is made periodic by inverse MBC

transformation to generate individual pitch commands. As a final note, gains for the generator angle and speed are

set to zero so as not to conflict with speed regulation in the baseline controller.

IV. Dynamic Coupling in the Closed Loop

To discuss the coupling present in the scenario we consider, it is first useful to examine the Bode magnitude

plots shown in Figure 4. The inputs are the pitch commands in the non-rotating frame (considered as three separate

actuators for the following discussion) while the outputs are the bending moments we are aiming to regulate.

Figure 4. Bode magnitude plots of the non-rotating inputs to the load outputs

It is evident from Figure 4 that collective pitch action has a large affect on the asymmetric shaft moments at low

frequencies and there is a large interaction between the asymmetric loads. Additionally, the cosine and sine cyclic

pitch signals to the asymmetric shaft load channels show a drop-off in magnitude after 0.6 Hz (blade passing

frequency), implying that these inputs are not as effective at high frequencies.

There are other methods to measure coupling and select input and output pairings such as the concept of the

relative gain array (RGA) and singular value decomposition (SVD)12

. RGA involves calculating the ratio of open

loop and closed loop gains with other loops closed at steady-state. Using the linear model this analysis can be

performed however it only shows that the multi-variable scenario is complex and there are many interactions. In

other words, there is no actuator which can fully affect a measured output without interactions from the other

actuators, which is what we initially expect. In addition, these methods are only useful at steady-state, do not


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incorporate dynamic effects, and are only valid for the particular linear model. For a realistic wind condition it is

necessary to look at the entire frequency response as in the Bode diagram.

A. Testing of Coupling

SISO load controllers such as in the design presented earlier essentially ignore the coupling in the other channels

(6 of the 9 diagrams in Figure 4). It is assumed that the interactions are not significant or if they are, they will be

constructive i.e. reduce other loads inadvertently, or require custom filter designs. To test this assumption, the three

SISO load controllers are tested separately with other loops inactive and no additional filtering. They are tuned to

achieve as much load reduction as possible while matching speed and power tracking of the baseline controller

tested alone. The performance metric for structural fatigue is damage equivalent loads (DEL) and this is calculated

by the rain-flow counting method13

. Note that the test conditions are covered in more detail in Section VI and the

DEL results are presented in Table 2, normalised to the baseline power controller alone.

Table 2. Results for coupling tests

As expected, the DEL is reduced for the particular load objective that the controller is aiming for. Collective

action also reduces the asymmetric shaft loads slightly due to constructive interaction. The Bode magnitude plot

shows collective actuation clearly gives the most powerful actuation for these loads at steady state (i.e. static loads)

however because of the turbulent wind profiles used for testing, the DEL reductions are only modest.

On the other hand, sine-cyclic and cosine-cyclic signals tend to interact negatively with the tower fore-aft. It is

recommended that these controller loops include an additional filter to avoid exciting the structure at the first tower

fore-aft resonant peak (0.33 Hz, shown in Figure 4). Moreover, the cosine and sine cyclic loops affect the

asymmetric load that they are not designed to regulate. These interactions are positive and the channels show similar

frequency responses with no large peaks so structural resonances are not seen. In fact, it is possible to swap the

inputs (i.e. yaw to cosine and tilt to sine), account for any phase shift, and still reduce the desired load.

V. Results for Composite Controller

The designed controllers are tested using FAST to simulate the non-linear wind turbine with the same six

degrees of freedom as in the linear model. A fully flexible turbine was not chosen because the goal of this study is to

isolate the coupling present and not propose a controller for immediate testing. The wind files are created using

TurbSim, a stochastic, full field, turbulent-wind simulator14

.

Five percent turbulent wind profiles including wind shear are used over a 100 second test period and analysis

begins at 20 seconds to ignore start-up transients. For fair testing, the controller gains are tuned to achieve the same

power and speed tracking as baseline at the operating point chosen. RMS pitch rate is a useful quantity to show that

the controllers have similar actuation activity and RMS power error is from the rated 5 megawatts. Note that the

results have been normalised to baseline and these are shown in Table 3.

Fore-aft - Collective Alone

Shaft Yaw – Sine Cyclic Alone

Shaft Tilt – Cosine Cyclic Alone

Tower Fore-Aft DEL 0.54 1.02 1.03 Shaft Yaw DEL 0.95 0.73 0.96 Shaft Tilt DEL 0.95 0.95 0.76

Table 3. Results for composite and multiple SISO loop controller

MSISO Composite

RMS Power Error 1.05 1.00 RMS Speed Error 1.04 1.04 RMS Pitch Rate 5.87 5.23 Tower FA DEL 0.62 0.54 Shaft Yaw DEL 0.71 0.39 Shaft Tilt DEL 0.68 0.45


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The RMS power and speed error are both close to baseline (near a value of 1.0) indicating fair testing.

Additionally, RMS pitch rates for both controllers are similar. Tower fore-aft sees a large reduction in DEL of 38%

and 46% for the MSISO and composite designs respectively. While the MSISO controller reduces yaw and tilt by

30%, the composite controller clearly shows superior results here.

In order for the MSISO design to match the composite one, it is necessary to further tune the gains with all three

loops active. In this case, each loop was tuned separately then combined with no further refinement and it is shown

that the tower fore-aft DEL is worst than for a single fore-aft to collective loop (see Table 2). As mentioned

previously, additional filtering for the cosine and sine cyclic loops would be necessary to decouple the channels.

On the other hand, multivariable design can reduce the loads without the need for filtering since the coupling is

taken care of in its internal design. It must be kept in mind that it uses FSFB to regulate the outputs and this is reliant

on an accurate, flexible LTI model (i.e. with many degrees of freedom and thus many states). Fatigue is mainly

caused by cyclic loading and because the controller is acting on state velocities as well as displacements, the

superior DEL reductions are not surprising. In essence, the composite controller is adding more damping to the

states. For a more robust design and under greater turbulence when the operating condition is far away from the

linearisation point, drifting of the control outputs would be problematic. This is beyond the scope of this project but

in order to avoid this, it is suggested that either the integral of the outputs be added as regulation objectives or that

gains on state displacements are set to zero.

The power spectral density plots below in Figure 5 show the magnitude of the loads at various frequencies for

each controller and for baseline control alone. The tower fore-aft loads are unaffected at low frequencies but the

resonant peak at 0.33 Hz is attenuated by both load controller designs, as are frequency components around 1 Hz.

Looking at the shaft yaw and tilt moments, the MSISO and composite designs are both effective at mitigating

these loads at low frequencies around the once-per-revolution loads (1P), but only the composite model reduces

higher frequency components as well (also shown in the greater DEL reduction in Table 3).

Figure 5. Power spectral density plots for the loads


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VI. Conclusions

The composite and multiple single-input single-output loop (MSISO) controllers showed attenuations of 46

and 38 percent respectively for the tower fore-aft damage equivalent loads (DEL) and up to 60 and 30

percent for the asymmetric shaft loads. In order for the MSISO controller to match the multi-variable

approach, suitable filtering and more rigorous tuning would be necessary.

There is a lot of coupling interaction in wind turbine control scenarios and before any design is undertaken,

these must be analysed to justify either a SISO or multi-variable control solution.

The main advantage of the MSISO controller is that it is easy to understand and utilises well known

classical design techniques. The disadvantage of this design is that creating multiple control loops can

create unnecessary conflicts with the competing regulation objectives and thus filtering is necessary to

decouple the channels.

Tuning each SISO loop separately and then combining may not give optimal results and additional

refinement is needed with all loops active. This may be problematic and it is another drawback of MSISO

designs.

The main advantage of the composite design is that it incorporates coupling between the load objectives. It

can achieve higher load reductions than MSISO architectures without any additional filtering. The

drawback is that it relies on a flexible model and for full-state feedback, multiple sensors and/or state

estimation would be needed for practical implementation.

VII. Future Work

To fully investigate the performance of a composite controller it is recommended that future work investigate

operation over a wider wind range, especially in below rated conditions and in region transition. During region

transition, the composite load control design is likely to be superior to a single MIMO controller. In addition, more

load objectives could be added to fully take advantage of multi-variable designs.

References 1Jonkman, J., " Dynamics Modeling and Loads Analysis of an Offshore Floating Wind Turbine," PhD Thesis, University of

Colorado. 2Boukhezzar, B., Lupu, L., Siguerdidjane, H, and Hand, M. " Multivariable control strategy for variable speed, variable pitch

wind turbines," Renewable Energy, Vol 32, 2007, pp 1273-1287. 3Lescher, F, Zhao, J.Y, Martinez, A, “LQG Multiple Model Control of a Variable Speed Pitch Regulated Wind Turbine” 17th

IMACS World Congress, Paris, France, 2005 4Wright, A.D and Fingersh, L.J, "Testing State-Space Controls for the Controls Advanced Research Turbine," 44th AIAA

Aerospace Sciences Meeting and Exhibit, National Renewable Energy Laboratory, Reno, Nevada, 2006. 5Bossanyi, E and Hassan, G., "The Design of Closed Loop Controllers for Wind Turbines," Wind Energy, Vol. 3, 2000, pp.

149-163 6Stol, K.A, Mol, H., Bir, G. and Namik, H. "A Comparison of Multi-Blade Coordinate Transformation and Direct Periodic

Techniques for Wind Turbine Control Design." 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and

Aerospace Exhibition, Orlando, Florida, 2009. 7Bir, G., "Multi-Blade Coordinate Transformation and Its Application to Wind Turbine Analysis." 27th American Society of

Mechanical Engineers (ASME) Wind Energy Symposium, Reno, Nevada, 2008. 8Bossanyi, E and Hassan, G., "Individual pitch control for load reduction," Wind Energy, Vol. 6, 2003, pp. 119-128. 9Selvam, K, Kanev, S., van Wingerden, J.W, van Engelen, T, and Verhaegen, M, "Feedback-feedforward individual pitch

control for wind turbine load reduction," International Journal of Robust and Nonlinear Control, Vol. 19, 2009, pp. 72-91. 10Jonkman, J. and Buhl Jr, M. "FAST User's Guide," NREL NREL/EL-500-38230, 2005. 11Bossanyi, E and Hassan, G., "Further Load Reductions with Individual Pitch Control," Wind Energy, Vol. 8, 2005, pp. 481-

485. 12van de Wal, M. and de Jager, B "A review of methods for input/output selection" Automatica, Vol. 37, 2001, pp. 487-510. 13Downing, S.D. and Socie, D.F, "Simple Rainflow Counting Algorithms," International Journal of Fatigue, Vol. 4, 1982,

pp. 31-40. 14Jonkman, B.J. and Buhl Jr, M.L. "TurbSim User's Guide," Version, Vol. 1, pp. 500-41136.

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