National Renewable Energy Laboratory 

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A national laboratory of the U.S. Department of Energy

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NREL is operated by Midwest Research Institute ● Battelle Contract No. DE-AC36-99-GO10337 

Testing State-Space Controls 

for the Controls Advanced 

Research Turbine 

Preprint 

A.D. Wright and L.J. Fingersh 

National Renewable Energy Laboratory 

M.J. Balas 

University of Wyoming

To be presented at the 44th AIAA Aerospace Sciences 

Meeting and Exhibit 

Reno, Nevada 

January 9–12, 2006 

Conference Paper 

NREL/CP-500-39123 

January 2006 
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Testing State-Space Controls for the Controls Advanced 

Research Turbine 

Alan D. Wright*†, Lee J. Fingersh‡ 

National Renewable Energy Laboratory 

Golden, Colorado 80401 

Mark J. Balas§

University of Wyoming 

Laramie, Wyoming 82071 

Control can improve wind turbine performance by enhancing energy capture and 

reducing dynamic loads. At the National Renewable Energy Laboratory, we are 

implementing and testing state-space controls on the Controls Advanced Research Turbine 

(CART), a turbine specifically configured to test advanced controls. 

We show the design of control systems to regulate turbine speed in Region 3 using rotor 

collective pitch and reduce dynamic loads in Regions 2 and 3 using generator torque. These 

controls enhance damping in the first drive train torsion mode. We base these designs on 

sensors typically used in commercial turbines. 

We evaluate the performance of these controls by showing field test results. We also 

compare results from these modern controllers to results from a baseline proportional 

integral controller for the CART. Finally, we report conclusions to this work and outline 

future studies. 

I. Introduction 

Typical variable-speed wind turbines have different regions of operation. In Region 2, the goal is to maximize 

energy production by using generator torque control to operate at optimum tip-speed ratio. In Region 3, generator 

torque is held constant, and blade-pitch control is used to maintain constant turbine speed. Another important goal of 

turbine control is to reduce structural dynamic loads. 

In previous papers, we have shown the design of state-space controllers to regulate turbine speed in Region 3 and 

enhance damping of flexible turbine modes.1,2 Those papers showed the advantages of using full-state feedback to 

place turbine plant poles to enhance transient response and increase stability. When limited turbine measurements 

are available, state estimation must be used to estimate plant states.3

 Successful use of state estimation is based on 

just a few turbine measurements, such as generator speed and tower-top fore-aft acceleration. Other researchers 

designed controls using state-space methods in Region 2 to maximize energy extraction and reduce fatigue loads 

with pitch control. 4 In that study, individual pitch control was shown through simulation to reduce fatigue damage 

equivalent blade loads by 11%. 

 

*

 This work has been authored by Midwest Research Institute under Contract No. DE-AC36-99GO10337 with the 

U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for 

publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, 

worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United 

States Government purposes. †

 Senior Engineer II, National Wind Technology Center, 1617 Cole Blvd., Mailstop 3811, AIAA nonmember 

‡

 Senior Engineer, National Wind Technology Center, 1617 Cole Blvd., Mailstop 3811, AIAA nonmember 

§

 Department Head and Professor, Electrical and Computer Engineering Department, AIAA fellow

1
There is a great need to implement and test these advanced control algorithms on field-test turbines to 

demonstrate their load-alleviating capability and to resolve issues regarding implementation of these controls in 

commercial turbines. Load reduction is important to reduce cost of energy (COE). Performance of these modern 

control algorithms must be compared to simpler controls based on classical methods to demonstrate intended load 

reductions. To date, few sources have published results on the implementation and testing of state-space controls on 

a real turbine. When a robust pitch controller was compared to a proportional integral (PI) controller through fullscale tests,5

 the robust controller produced about the same performance with less pitch activity than the PI controller, 

but the 3P frequency load attenuation was improved. Further implementation and testing of state-space control 

designs was reported in (Ref. 7), where two state-space controllers for regulating turbine speed in Region 3 were 

designed, implemented, and tested in the Controls Advanced Research Turbine (CART) at the National Wind 

Technology Center (NWTC). These controls were designed to add significant damping to flexible modes which 

ordinarily have small amounts of damping in open-loop operation. Poor design of controllers can destabilize these 

modes and increase fatigue loads. It is important that the controllers designed in both Regions 2 and 3 stabilize these 

modes. A smooth transition between Region 2 and 3 controllers must be achieved to maintain stability of these lowdamped modes so that fatigue loads are not increased. 

In this paper, we show the design of controls to enhance the damping in the first drive train torsion mode in both 

Regions 2 and 3, thereby reducing drive train torque loads. These controls must maximize energy in Region 2 and 

maintain constant turbine speed in Region 3. We show the results of designing a smooth transition between Regions 

2 and 3. We then show preliminary results of implementing and testing these controls in the CART. We describe 

lessons learned from implementing these controls on a field-test turbine, state conclusions, and outline future work. 

Now we describe the field-test machine. 

II. CART Configuration 

The CART (Fig. 1) is a two-bladed, teetered, upwind, active-yaw wind turbine. This machine is used as a test 

bed to study aspects of wind turbine controls technology on medium- to large-scale machines.8

 

The two-bladed teetering upwind turbine is variable speed, and each blade is capable of being independently 

pitched with its own electromechanical servo. The pitch system can pitch the blades up to 18 degrees per second 

(deg/s) with pitch accelerations up to 150 degrees per second per second (deg/s/s). The squirrel cage induction 

generator with full power electronics can control torque from minus rating (motoring) to plus rating (generating) at 

any speed. The torque control loop has a very high rated bandwidth of 500 radians per second. 

Rated electrical power (600 kW at a low-speed shaft [LSS] speed of 41.7 RPM) is maintained in Region 3 in a 

conventional variable-speed approach. Power electronics are used to command constant torque from the generator 

and full-span blade pitch controls the rotor speed. In Region 2, the machine torque is varied to produce variable rotor 

speed to maintain optimum aerodynamic power coefficient . Cp

The machine is equipped with a full complement of instruments that gather meteorological data at four heights. 

Blade-root flap and edge-strain gauges, tower-bending gauges, and LSS and high-speed shaft (HSS) torque 

transducers gather loads data. Absolute position encoders gather data on pitch, yaw, teeter, LSS, and HSS positions. 

These data are sampled at 100 Hz. The custom-built control system collects this data and controls the turbine at a 

control-loop cycle rate of 100 Hz. This system is PC-based and very flexible. 

For the baseline turbine controls, the generator torque is varied in Region 2 according to the expression 

, where T is generator torque, is a constant, and w is rotor speed. 2 T kw = k 8

 In Region 2, blade pitch is constant. 

In Region 3, generator torque is fixed and blade pitch is varied with a simple PI control loop to maintain constant 

rotor speed. 8 

One of the challenges of wind turbine control design is meeting multiple control objectives. While maximizing 

energy in Region 2 and maintaining constant turbine speed in Region 3, we must also reduce dynamic loads to 

obtain longer turbine lifetimes and reduce COE. If controls are not carefully designed to account for the flexible 

modes of the wind turbine, we can actually increase dynamic loads through destabilization of low-damped modes. 

Figure 2 shows excitation of the CART’s first drive train torsion mode in Region 3 when controlled with the simple 

PI baseline controller. It is clear that advanced controls must be designed to enhance damping in these modes. We 

2
now describe the design of state-space controls for Region 2 and Region 3 that allow us to meet primary objectives 

in these regions while also enhancing the damping in the first drive train torsion mode. 

III. State-Space Control Design 

Our control objective is to maximize power in Region 2 and maintain constant rotor speed in Region 3. We also 

want to design the controller to enhance damping in the first drive train torsion mode. We must also design a smooth 

transition between Region 2 and Region 3 to avoid exciting flexible turbine modes, which increase dynamic loads. 

In (Ref. 10), a multi-controller approach to state-space control of variable-speed wind turbines over the entire 

operating envelope was shown. Separate state-space controllers were designed for Region 2 and Region 3. In Region 

2, the state-space controller was designed using Disturbance Tracking Control (DTC) theory. 9. This control design 

approach allows us to use full-state feedback to achieve desired transient response and stability, while tracking 

optimum . In Region 3, the controller was designed using Disturbance Accommodating Control (DAC), an 

approach also allowing full-state feedback. The DTC and DAC controllers were then combined in a multi-controller 

system that switched between the two controllers when the variable-speed turbine operation transitioned between 

Regions 2 and 3. 

Cp

We apply this technique to the design of a generator torque controller to enhance drive train torsion damping in 

Regions 2 and 3. This controller tracks wind disturbances to maintain constant in Region 2. In Region 3, its 

only objective is to add damping to drive train torsion. In the transition region, we perform a linear interpolation of 

generator torque control between Regions 2 and 3 to provide a smooth transition. A pitch controller is also designed 

using DAC to regulate turbine speed in Region 3 and mitigate the effects of wind speed disturbances. 

Cp

To apply linear control theory to the design of a Region 2 or 3 controller, a linear state-space turbine model is 

needed. Such a model is described by 

 

d x Ax Bu u

y Cx

= + +Γ

=

& (1) 

where x is the state vector, u is the control input, Du is the disturbance input, y is the measured output, A is the 

state matrix, B is the control input distribution matrix, is the disturbance input distribution matrix, and C

relates the measured output 

Γ

y to the turbine states. 

The disturbance inputs ud are derived using a Disturbance Waveform Generator 9. 

0

() ()

( ) ( );

(0) = 

d d d

d d d

d d

z t Fz t

ut zt

z z

θ

=

=

&

 (2) 

where d z are the disturbance states, and the matrices , and are assumed to be known, while Fd θ d

0

d z is 

unknown (the waveform of the disturbance is known but the amplitude is not). For a step waveform for representing 

the uniform component of wind speed over the rotor disk, 0 , and . Fd ≡ θ d ≡ 1

The control law is assumed to be the superposition of a term corresponding to state feedback of the plant states 

x and a term involving the disturbance d z : 

u Gx G z = + d d (3) 

3
A. Generator Torque Control Design 

For the generator torque control design in either Region 2 or 3, a linear model that describes the generator 

rotational speed as well as first drive train torsion mode is: 

[ ]

d d

1 1

2 d d2

3 3 d d

gen gen gen gen

rot rot rot rot

1

2

3

 - C ) -1 C

x x 0

x K 0 -K x + 0 + 0 

x x C 1 -C -1 0

 . 

(

I II I

I II I

x

y = 0 0 1 x

x

Tgen w

α

=

⎡ ⎤⎡ ⎤ ⎡ ⎤ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎡ ⎤ ⎡ ⎤ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎢ ⎥⎢ ⎥ ⎢ ⎥

⎣ ⎦⎣ ⎥ ⎢ ⎦ ⎣ ⎦

⎡ ⎤

⎢ ⎥

⎢ ⎥

⎢ ⎥ ⎣ ⎦

&

&

&

g

d d

 

⎥

 (4) 

where, 

1

2 d

3

( )

 perturbed rotor-speed: 

 perturbed drive-train torsion spring force: K

 perturbed generator speed: 

rot

rot gen

gen

x

x

x

δ

δψ δψ

δ

Ω

−

Ω

=

=

=

Here δψ rot is the perturbed rotor azimuth angle, δψ gen the perturbed generator azimuth angle, the 

perturbed rotational speed of the rotor, and 

δΩrot

δΩgen the rotational speed of the generator. is the rotor rotational 

inertia, is the generator rotational inertia, is the spring constant describing the torsional stiffness of the 

LSS, is the torsional damping constant, is the partial derivative of rotor aerodynamic torque with respect to 

blade pitch angle, and is the partial derivative of rotor aerodynamic torque with respect to rotor speed. 

rot I

gen I Kd

Cd α

g

We model the disturbance state in (1) with just one state: perturbation of the uniform wind speed over the rotor 

disk dw . Our control input is Tgen d , perturbation in generator torque. State estimation is used to estimate 

unmeasured plant states using the single turbine measurement perturbed generator rotational speed . x3

We designed the Region 2 generator torque controller from this state-space model generated by FAST 13 at the 

turbine operating point: 

Wind speed = 8 m/s 

Rotor speed = 27.1 RPM 

Pitch angle = -1 degree (normal Region 2 “run-pitch”). 

The goal of state-space control design is to use state feedback to place the poles of the plant to obtain desired 

stability and transient response. In open-loop, the eigenvalues of the A matrix at this operating point have the values 

-0.0004 ± 3.57i (Hertz [Hz.].), -0.0044. The pole pair corresponds to the first drive train torsion mode, having a 

natural frequency of 3.57 Hz. We chose the gains G in the feedback law so that the closed-loop eigenvalues were 

-0.6 ± 3.57i (Hz.), -0.1. This resulted in greatly enhanced damping in the first drive train torsion mode. The gain 

corresponding to the uniform wind disturbance was chosen to track wind speed disturbances using the theory of 

DTC.

Gd

 9.

4
For the Region 3 generator torque controller, a linear model with the same states as in (4) was generated by 

FAST at the turbine operating point. 

Wind speed = 18 m/s 

Rotor speed = 41.7 RPM 

Pitch angle = 11 degrees. 

The goal is to again use state feedback to place the poles of the plant to obtain desired stability and transient 

response. In open-loop, the eigenvalues of the A matrix had the values -0.0016±3.5712i (Hz.), -.016. We chose the 

gains G in the feedback law so that the closed-loop poles would have values -0.6±3.57i (Hz.), -0.15. 

In Region 3 control, the generator torque is usually constant. Blade-pitch control is then used to maintain a 

constant turbine rotational speed, thereby fixing power at “rated power.” Here we allow only small perturbations in 

generator torque to enhance damping in the first drive train torsion mode. The gain corresponding to the uniform 

wind disturbance ( ) was set to zero for the Region 3 torque controller to prevent tracking or canceling wind 

speed disturbances, which would cause large variations in generator torque. 

Gd

B. Region 2 to 3 Generator Torque Control Transition 

In the Region 2 to 3 transition, we switched between the Region 2 and Region 3 generator torque controllers 

based on the equation: 

21 1 2 1 ( )( ) /( ) T TT = − Ω −Ω Ω −Ω + rot T1 (5) 

where is generator torque, is the Region 2 torque, is the Region 3 torque, is rotor speed, is the 

rotor speed at the start of Region 2 to 3 transition (39.2 RPM), and the rotor speed at the start of Region 3 (41.3 

RPM). 

T T1 T2 Ωrot Ω1

Ω2

C. Region 3 Pitch Controller 

Control of turbine speed in Region 3 is performed by the rotor collective pitch controller. Here we use DAC to 

design the controller to mitigate wind speed disturbances. The rotor collective pitch controller is designed from a 

state-space model with the following states: 

1

2

3

4

5

6

 perturbed rotor symmetric flap displacement

 perturbed rotor symmetric flap velocity

 perturbed generator speed

 perturbed actuator pitch angle

 perturbed actuator pitch rate

 pert

x

x

x

x

x

x

=

=

=

=

=

=

urbed uniform wind disturbance over the rotor disk

We found it necessary to include actuator dynamics in the model for control design as described in (Ref. 7), as 

reflected in selection of states 4 x and 5 x above. 

For design of this controller, this state-space model was generated by FAST at a turbine operating point of 

Wind speed = 18 m/s 

Rotor speed = 41.7 RPM 

Pitch angle = 11 degrees. 

We chose the gains G in the feedback law so that the closed-loop poles would have values -4.6±13.5i (Hz.), -2, 

-10, and -59. The first pair of poles corresponds to the perturbed rotor first symmetric flap mode. The next pole 

5
corresponds to the perturbed rotor rotational speed state, and the next two states correspond to the perturbed actuator 

blade-pitch angle and perturbed pitch rate. In this operating region, the control objective for the pitch controller is to 

regulate speed in the presence of persistent wind disturbances. The gain corresponding to the wind disturbance 

is chosen to mitigate wind disturbances uniform over the rotor disk using DAC.

Gd

 9 

We ran test simulations in FAST before implementing these controllers on the real machine. During one test, we 

wanted to compare the rotor speed predicted by FAST when using the state-space controllers to the baseline Region 

2 and Region 3 controllers. Figure 3 shows this comparison. In this simulation, we input step winds, beginning with 

a wind speed of 6 m/s and increasing to 12 m/s in steps during 60 seconds of simulation. Over the entire wind speed 

range, the state-space controller results in slightly higher rotor speeds compared to the baseline controller. The larger 

discrepancy at the low end of Region 2 may be a result of designing only one controller in Region 2, at one 

operating point (wind speed of 8 m/s). A solution may be to design several controllers at different Region 2 

operating points and to transition between controllers using gain scheduling. In addition, it was shown in (Ref. 4) 

that certain state-space models may result in imperfect optimum tip-speed ratio tracking using Disturbance Tracking 

Control Theory. We will investigate these issues in future work. 

We now describe various implementation issues regarding testing this Region 2 and Region 3 controller in the 

CART. 

IV. Implementation Issues and Lessons Learned 

There are various issues in implementing and testing wind turbine controls. Sensor limitations, data sampling 

rates, and actuator dynamics are important, as reported in (Ref. 7). In addition, the control algorithm must be 

correctly coded in the turbine-control software. Each of the previously described controllers is implemented into the 

CART-control software. All programming bugs are removed. Before these algorithms are field tested, the control 

code is tested using a simple simulator built into the control software. This simulator integrates a single-state (rotor 

speed) and uses a lookup table for aerodynamic torque. These tests are useful for catching C-code implementation 

bugs, highlighting region transition problems, and as an independent check of speed-regulation performance. One 

weakness of this simulator is that it does not account for turbine flexible modes. In addition, because the simulator 

does not produce many of the measurement signals that the more complex state-space controllers assume, there are 

situations in which the simulator predicts dynamic instability when the other simulator models (FAST) or actual 

turbine do not. However, this is a very useful test to conduct before the controller is tested on the real machine. 

There are also situations in which testing a new controller on the real machine results in unstable behavior, even 

though the simulations do not reveal this behavior. When first testing a new controller, turbine behavior must be 

closely monitored to ensure stable operation. The first Region 2 generator torque controller we implemented and 

tested in the CART resulted in unstable generator torque upon startup, as shown in Fig. 4. None of our simulations 

predicted this behavior. This controller was designed from a linear model generated at a turbine operating point 

closer to Region 3 than the final design. When the controller was redesigned at the operating point described in the 

control design section above, we obtained stable generator torque upon startup. 

Another issue was correctly implementing the Region 2 to 3 transition. Early implementation of these generator 

torque controls resulted in a rough transition. Instead of adding damping to the first drive train torsion mode, we 

were actually destabilizing this mode. Figure 5a shows turbine response while being controlled by the first 

implementation of the transition Eq. (5). In this first implementation, we used unfiltered rotor rotational speed in (5). 

This signal (LSS RPM) contains high-frequency noise, as seen in the figure. Figure 5a also shows commanded 

generator torque and LSS torque. Between 160 and 163 seconds, the turbine is entirely in transition since the rotor 

speed is above the entrance to transition (39.2 RPM). The resulting demanded generator torque (Torque Demand) 

contains much of the same high-frequency content as the LSS RPM signal. This noise acts to excite the drive train 

torsion instead of adding damping, as seen in the LSS torque signal in Fig. 5a. We then filtered rotor speed in Eq. (5) 

with a first-order filter with a time constant of 1 second. The resulting measured demanded generator torque, LSS 

torque, and LSS RPM (unfiltered LSS RPM values shown in this plot) are shown in Fig. 5b. Now, except for the 

point at which the turbine enters transition, the commanded generator torque is much smoother than in Fig. 5a. The 

LSS Torque signal shows much less response at the first drive train torsion mode. 

6
A further problem occurred at the limit points of the Region 2 to 3 transition (lower limit 39.2 RPM, upper limit 

41.3 RPM). Figure 5b shows discontinuities in demanded generator torque when the lower limit of 39.2 RPM is 

reached. These discontinuities are caused by a mismatch of rotor speed used in Eq. (5) and rotor speed used in the 

decision to enter transition. At any instant of time, the unfiltered and filtered values of rotor speed will be unequal. 

From Eq. (5) we see that for a rotor speed of 39.2 RPM, the demanded generator torque should equal (Region 2 

torque at 39.2 RPM). If there is a mismatch in the rotor speed used in Eq. (5) and the rotor speed used in the decision 

to enter transition test, the demanded generator torque will not equal , and there will be a discontinuity in 

demanded generator torque upon entering or exiting the transition region. Figure 5c shows the result of using filtered 

rotor speed in both Eq. (5) and the decision test. In this figure, the rotor speed passes through both the lower and 

upper limit points (39.2 and 41.3 RPM). Now the commanded generator torque is smooth without discontinuities. 

T1

T1

Another problem concerned interaction between the Region 3 torque controller and the Region 3 pitch controller. 

Previous control simulation tests failed to show this interaction 3 (Fig. 6). Both the generator torque and blade pitch 

controllers were designed assuming generator speed (HSS RPM) as the control input. As can be seen from Fig. 6a, 

the HSS RPM signal contains high cyclic amplitude at the first drive-train torsion frequency. Also from Fig. 6a, we 

see that the LSS Torque and the demanded Generator Torque all contain response at this frequency. Because HSS 

rotational speed is the input to the pitch controller as well, the pitch controller also responds at this natural 

frequency. The pitch controller and torque controller interact in an undesirable way. 

We then changed the control input to the blade pitch controller to LSS RPM instead of HSS RPM. This signal 

does not contain a response at the first drive-train torsion frequency because the large rotor inertia acts as a filter, 

filtering out response at this frequency (3.5 Hz). Now, the blade pitch controller no longer responds at the first drivetrain torsion frequency, and the generator torque controller no longer interacts with the pitch controller (Fig. 6b). 

Even though the pitch controller was not designed from a state-space model containing a description of the first 

drive-train torsion mode, it interacts with the torque controller when high-speed RPM is used as the control input. 

Inputting rotor speed (LSS RPM) instead of generator speed (HSS RPM) solves this problem. 

We now make some preliminary comparisons of the state-space controller to the baseline controller in Regions 2 

and 3. 

V. Field Test Results and Comparisons 

We collected data on the CART while testing the Region 2 state-space controller. We then compared the test 

results to a case from the baseline control in Region 2. Because these controllers were tested at different times, a 

direct results comparison is difficult. Our objective was to show trends, such as load mitigation. We attempted to 

examine both datasets and extract smaller sections of data in which turbine operating parameters (such as wind 

speed and direction, yaw error, etc.) were similar. The results of our comparison are preliminary, and we need many 

more hours of operation for realistic statistical comparisons between the controllers. 

Table 1 shows the statistics of two datasets used for comparison. Each dataset consisted of 300 seconds of data. 

Listed in this table are the mean and standard deviation (std) of the wind speed (at a height of 36.6 meters [m]), rotor 

speed (LSS RPM), generator torque (Torque Demand), and LSS torque. 

Figure 7 shows plots of wind speed, LSS rotational speed, LSS torque, and demanded generator torque for the 

two datasets. Figure 7a corresponds to the baseline controller and Fig. 7b the state-space controller. Although the 

wind speeds do not match, the deviations in wind speed for the two cases are similar, with somewhat greater 

deviations occurring during operation with the state-space controller. We also calculated the Damage Equivalent 

Load (DEL) for the LSS torque for the two datasets. 14 The state-space controller resulted in slightly lower DEL than 

the baseline controller. 

We also calculated the power spectral density (PSD) of the LSS and demanded generator torque for the two 

cases, as shown in Fig. 8. The peak in the PSD for the LSS torque (Fig. 8a) corresponds to the first drive-train 

torsion natural frequency. It is interesting to note that this peak is lower for the state-space control case because we 

have used full state feedback to place the poles corresponding to this mode to have higher damping, resulting in 

reduced loads at this frequency. The peak for the state-space control case is displaced slightly to the right of the 

7
baseline case because we have placed the pole to have a natural frequency at 3.57 Hz. The natural frequency of the 

first drive-train torsion mode in open-loop is probably about 3.3 Hz., as seen by the peak response for the baseline 

case. This represents a slight discrepancy between the FAST-predicted natural frequency (3.57 Hz.) and the openloop natural frequency of this mode in the real machine, due to modeling uncertainty. 

 

Figure 8b shows the PSD of the demanded generator torque. For the baseline control case, the peak at 3.57 Hz. is 

absent because the controller is not adding damping to this mode. For the state-space case, the large peak at 3.57 Hz. 

indicates the action of the generator controller to add damping to this mode as desired. Table 1 indicates (std of 

demanded generator torque) that the generator torque activity is actually lower for the state-space case compared to 

the baseline case. Further data collection and comparisons are needed before we can assess the effects of these 

additional control objectives on the actuator duty cycle of the generator. 

Next we compared the Region 3 state-space controller to the Region 3 baseline PI controller. Table 2 compares 

statistics of 300 seconds of CART data during operation with the PI controller and the state-space controller. Figure 

9 shows plots of different data channels for these two cases. The mean and std of wind speed are slightly lower for 

Table 1: Preliminary Comparison of Baseline and FAST State-Space Controllers for Region 2 

Operation 

Statistics and Performance 

Measure 

Baseline Control 

(05031750.DAT) 

State-Space 

Control 

 (07191751.DAT) 

Wind speed (m/s) 

 

 

 mean 8.45 

std 1.44 

mean 8.22 

std 1.53 

Rotor speed (rpm) 

 

 

mean 28.53 

std 3.86 

mean 27.3 

std 3.35 

Generator torque (kNm) 

 

 

mean 1340 

std 361 

mean 1190 

std 341 

Low-speed shaft torque 

(kNm) 

 

 

mean 59.4 

std 15.9 

fatigue DEL 7.63 

mean 53.3 

std 14.1 

fatigue DEL 6.83 

Table 2. Comparison of Baseline and FAST State-Space Controller for Region 3 Operation 

Statistics and Performance 

Measure 

Baseline Control 

 (05212101.DAT) 

State-Space Control 

 (09092110.DAT) 

Wind speed (m/s) mean 15.85 

std 2.31 

mean 15.74 

std 2.11 

Rotor speed (rpm) mean 41.67 

std 0.30 

mean 41.26 

std 0.49 

Generator torque (kNm) mean 3501 

std 112.9 

mean 3409 

std 160.2 

Low-speed shaft torque (kNm) mean 154.10 

std 8.08 

fatigue DEL 18.27 

mean 149.84 

std 7.92 

fatigue DEL 8.92 

8
the state-space controller, as seen in the table. The mean rotor speed is also slightly lower, although the std is 

slightly higher than for the baseline case. A lack of turbine data for the turbine operating entirely in Region 3 meant 

that there was some operation in the transition region. The std of demanded generator torque is higher for the statespace controller than for the baseline case. This may be due to operation in the transition region. For the baseline 

controller operating entirely in Region 3, the standard deviation of demanded generator torque should be zero. A 

direct assessment of actuator duty for the state-space controller is difficult. We also calculated the DEL for the LSS 

torque, with a large reduction in load for the state-space controller compared to the baseline controller. 14 

Figure 10 shows the PSDs of LSS and generator torque for the two control cases. Again, we see in Fig. 10a a 

significant reduction in the peak at the first drive-train torsion mode for the state-space case because of the damping 

enhancement provided by the generator controller. The PSD of generator torque shows a peak at 3.57 Hz. for the 

state-space case, indicating that the generator is adding damping to the first drive-train torsion mode. 

Although these results are preliminary, Tables 1 and 2 seem to show the potential to reduce LSS torque loads 

with the state-space controllers. This is due to the enhanced damping of the first drive-train torsion mode with these 

controllers. The load reduction seems to be greater in Region 3 than in Region 2. This may be due to nonlinear 

behavior of the turbine in Region 2. Improved performance might be obtained by designing controllers at several 

operating points in Region 2 and transitioning between them using gain scheduling. In this study we designed a 

controller at a single operating point in Region 2. In addition, we need to re-design the Region 2 controller to place 

the poles farther to the left in the complex plane, further increasing the damping in the first drive-train torsion mode. 

More data must be collected with the state-space controllers and comparisons made to the baseline controller before 

firm conclusions can be reached. In this preliminary study, the trends indicate potential for load alleviation using 

state-space control designs. 

VI. Conclusions 

In this paper, we have shown the design, implementation, and testing of controls using generator torque in 

Regions 2 and 3 to enhance damping in the first drive-train torsion mode. Rotor collective pitch control is used in 

Region 3 to regulate turbine speed. We described various controls implementation issues, such as Region 2 to 3 

transition. We also described correctly implementing the generator torque control and blade pitch control in Region 

3 to prevent interactions between these two controllers. We showed preliminary test results after implementing and 

testing these controls in the CART in both Regions 2 and 3, indicating that these state-space controls reduce 

structural dynamic loads compared to a baseline PI controller. These results are preliminary, and many more hours 

of operation are needed for realistic statistical comparisons between the controllers. 

Future Work 

Directions for future work include further field-testing of the controls already implemented in the CART. We 

need to obtain many more hours of test data to show statistically that loads are reduced compared to baseline control 

results. Implementation and testing of independent pitch control to mitigate spatially varying wind disturbances 

across the rotor disk will be tested. Design of controls using generator torque and blade pitch to add damping to the 

tower side-side and fore-aft modes will be implemented and tested. Controls will also be designed and implemented 

on a 3-bladed version of the CART. 

References 1

Wright, A.D., and Balas, M., “Design of State-Space-Based Control Algorithms for Wind Turbine Speed Regulation,” 21st

ASME Wind Energy Conference, Reno, Nevada, 14-17 January, 2002. 

2

Wright, A.D., and Balas, M., “Design of Controls to Attenuate Loads in the Controls Advanced Research Turbine,” 23rd

ASME Wind Energy Conference, Reno, Nevada, 5-8 January, 2004. 

3

Wright, A.D., “Control Design for Flexible Wind Turbines,” Ph.D. Dissertation, Department of Aerospace Engineering 

Sciences, University of Colorado, Boulder, Colorado, 2003. 

4

Stol, K., “Disturbance Tracking and Blade Load Control of Wind Turbines in Variable-Speed Operation,” 22nd ASME Wind 

Energy Conference, Reno, Nevada, 6-9 January, 2003. 

9
5

Knudsen, T., Andersen, P., and Toffner-Clausen, S., “Comparing PI and Robust Pitch Controllers on a 400KW Wind 

Turbine by Full Scale Tests,” Presented at EWEC97, Dublin, Ireland, 5-9 October, 1997. 7

Wright, A., Stol, K., and Fingersh, L., “Progress in Implementing and Testing State-Space Controls for the Controls 

Advanced Research Turbine,” 24th ASME Wind Energy Conference, Reno, Nevada, 10-13 January, 2005. 

8

Fingersh, L., and Johnson, K., “Baseline Results and Future Plans for the NREL Controls Advanced Research Turbine,” 23rd

ASME Wind Energy Conference, Reno, Nevada, 5-8 January, 2004. 

9

Balas, M.J., Lee, Y.J., and Kendall, L., “Disturbance Tracking Control Theory with Application to Horizontal Axis Wind 

Turbines,” 17th ASME Wind Energy Conference, Reno, Nevada, 12-15 January, 1998. 

10Allen, S., Balas, M.J., and Counts, L., “A Multi-Controller Approach to Horizontal Axis Wind Turbines,” 18th ASME Wind 

Energy Conference, Reno, Nevada, 11-14 January, 1999. 

11Stol, K., and Balas, M., “Periodic Disturbance Accommodating Control for Speed Regulation of Wind Turbines,” 21st

ASME Wind Energy Conference, Reno, Nevada, 14-17 January, 2002. 

12Stol, K., and Fingersh, L., “Wind Turbine Field Testing of State-Space Control Designs,” National Renewable Energy 

Laboratory, NREL/SR-500-35061, Golden, Colorado, Sept. 2004. 

13Jonkman, J.M., and Buhl, M.L., “FAST User’s Guide,” National Renewable Energy Laboratory, NREL/EL-500-38230, 

Golden, Colorado, August 2005. 

14Sutherland, H.J., “On the Fatigue Analysis of Wind Turbines,” Sandia National Laboratories, SAND99-0089, Albuquerque, 

New Mexico, June 1999. 

10
Low-Speed Shaft Torque

0

50

100

150

200

250

300

176 177 178 179 180 181 182 183 184 185

Time (sec.)

Torque (kNm)

CART Measured Data

Figure 2. Measured shaft torque 

showing drive train excitation in Region 

3 using classical control. 

Figure 1. The Controls Advanced 

Research Turbine (CART). 

-4000

-2000

0

2000

0246

Time (sec)

Generator Torque (kNm)

Unstable Torque

Stable Torque 10

15

20

25

30

35

40

45

20 30 40 50 60 70 80

Time (sec)

Generator Speed (rpm)

Baseline

State-space

Figure 3. FAST-simulated generator 

speed for the baseline and state-space 

controllers excited by step winds spanning

Regions 2 and 3. 

Figure 4. Measured generator torque 

showing stable and unstable behavior 

during startup for two implemented 

controllers. 

11
160 162 164 39

39.2

39.4

39.6

LSS RPM, RPM

160 162 164 80

100

120

140

160

180 LSS Torque, kN-m

160 162 164 2200

2400

2600

2800 Torque Demand, N-m

time, seconds

Lower Transition Limit (39.2 RPM) 

18 19 20 21 22 23 24 25 26 27 28 39

39.2

39.4

39.6

39.8

40

LSS RPM, RPM

18 19 20 21 22 23 24 25 26 27 28 80

100

120

140

160

180

LSS Torque, kN-m

18 19 20 21 22 23 24 25 26 27 28 2200

2400

2600

2800

Torque Demand, N-m

time, seconds

Lower Transition Limit (39.2 RPM) 

Fig 5a. Fig 5b. 

34 35 36 37 38 39 40 41 42 43 44 45 38

39.2

41.3

43

LSS RPM, RPM

34 35 36 37 38 39 40 41 42 43 44 45 80

120

160

LSS Torque, kN-m

34 35 36 37 38 39 40 41 42 43 44 45 2000

3000

4000

Torque Demand, N-m

time, seconds

Upper transition limit (41.3 rpm) 

Lower transition limit (39.2 rpm) 

Fig 5c. 

Figure 5. Measured CART data during

transition from Region 2 to Region 3. 

12
First Controller Revised Controller 

28 29 30 31 32 33 34 35 36 37 38 8

10

12

14

Blade 1 Pitch, deg

28 29 30 31 32 33 34 35 36 37 38 1760

1800

1850

1900

HSS RPM, RPM

28 29 30 31 32 33 34 35 36 37 38 100

200

300

LSS Torque, kN-m

28 29 30 31 32 33 34 35 36 37 38 3480

3580

Torque Dem and, N-m

time, seconds

440 441 442 443 444 445 446 447 448 449 450 8

10

12

14

Blade 1 Pitch, deg

440 441 442 443 444 445 446 447 448 449 450 1750

1800

1850

1900

HSS RPM, RPM

440 441 442 443 444 445 446 447 448 449 450 100

200

300

LSS Torque, kN-m

440 441 442 443 444 445 446 447 448 449 450 3300

4300

tim e, seconds

Torque Dem and, N-m

Fig 6a. Fig 6b. 

Figure 6. Measured CART data during

operation in Region 3, showing generator 

pitch interaction in first controller. 

Baseline Control Case State-Space Control Case 

100 150 200 250 300 350 400 5

10

15

20

Windspeed 36.6m, mps

100 150 200 250 300 350 400 20

30

40 LSS RPM, RPM

100 150 200 250 300 350 400 0

50

100

150

LSS Torque, kN-m

100 150 200 250 300 350 400 0

1000

2000

3000

Torque Dem and, N-m

tim e, seconds

50 100 150 200 250 300 350 5

10

15

20

Windspeed 36.6m, m ps

50 100 150 200 250 300 350 20

30

40 LSS RPM, RPM

50 100 150 200 250 300 350 0

50

100

150

50 100 150 200 250 300 350 0

1000

2000

3000

Torque Dem and, N-m

tim e, seconds

LSS Torque, kNm

Fig 7a. Fig 7b. 

Figure 7. Measured CART data for Region 

2 control for the baseline and state-space 

case. 

13
0.001

0.010

0.100

1.000

10.000

100.000

1000.000

234 5

0.100

1.000

10.000

100.000

1000.000

2345

Frequency (Hz.)

Generator Torque 

(kNm)^2/Hz.

state-space

baseline

Frequency (Hz.)

Low-Speed Shaft 

Torque (kNm)^2/Hz.

baseline

state-space

Fig 8a. Fig 8b. 

Figure 8. Power spectral density of lowspeed shaft and generator torque for the 

Region 2 baseline and state-space cases. 

Baseline Control Case State-Space Control Case 

150 200 250 300 350 400 450 0

10

20

30 Windspeed 36.6m, mps

150 200 250 300 350 400 450 39

41

43

45

LSS RPM, RPM

150 200 250 300 350 400 450 100

150

200

250

LSS Torque, kN-m

150 200 250 300 350 400 450 2500

4500

Torque Dem and, N-m

tim e, seconds

50 100 150 200 250 300 0

10

20

30

Windspeed 36.6m, mps

50 100 150 200 250 300 39

41

43

45

LSS RPM, RPM

50 100 150 200 250 300 100

150

200

250

LSS Torque, kNm

50 100 150 200 250 300 2500

4500

Torque Dem and, N-m

tim e, seconds

Fig 9a. Fig 9b. 

Figure 9. Measured CART data for Region 

3 control for the baseline and state-space 

case. 

14
0.001

0.010

0.100

1.000

10.000

100.000

1000.000

10000.000

2345

Frequency (Hz.)

Low-Speed Shaft 

Torque (kNm)^2/Hz.

baseline

state-space

0.100

1.000

10.000

100.000

1000.000

2345

Frequency (Hz.)

Generator Torque 

(kNm)^2/Hz.

baseline

state-space

Fig 10a. Fig 10b. 

Figure 10. Power spectral density of lowspeed shaft and generator torque for the 

Region 3 baseline and state-space cases. 

15
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4. TITLE AND SUBTITLE

Testing State-Space Controls for the Controls Advanced Research 

Turbine: Preprint 

5c. PROGRAM ELEMENT NUMBER

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NREL/CP-500-39123 

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WER6 2109 

6. AUTHOR(S)

A.D. Wright, L.J. Fingersh, and M.J. Balas 

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National Renewable Energy Laboratory 

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14. ABSTRACT (Maximum 200 Words)

Control can improve wind turbine performance by enhancing energy capture and reducing dynamic loads. At the 

National Renewable Energy Laboratory, we are implementing and testing state-space controls on the Controls 

Advanced Research Turbine (CART), a turbine specifically configured to test advanced controls. We show the 

design of control systems to regulate turbine speed in Region 3 using rotor collective pitch and reduce dynamic loads 

in Regions 2 and 3 using generator torque. These controls enhance damping in the first drive train torsion mode. We 

base these designs on sensors typically used in commercial turbines. We evaluate the performance of these 

controls by showing field test results. We also compare results from these modern controllers to results from a 

baseline proportional integral controller for the CART. Finally, we report conclusions to this work and outline future 

studies. 

15. SUBJECT TERMS

wind energy; wind turbines; control systems; CART; Controls Advanced Research Turbine 

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