1. AIAA Aerospace Sciences Meeting 2009
Adaptive Control of a Utility-Scale Wind Turbine Operating in Region 3
Susan A. Frost
Intelligent Systems Division
NASA Ames Research Center
Susan.A.Frost[at]nasa.gov
Mark J. Balas
Wind Energy Research Center (WERC)
University of Wyoming
Mbalas[at]uwyo.edu
Alan D. Wright
National Wind Technology Center
National Renewable Energy Laboratory
Alan_Wright[at]nrel.gov
research on
acknowledge coauthors
National Wind Technology Center Golden, Colorado

2. Outline Utility-Scale Wind Turbines Adaptive Control Theory
Region 3 Adaptive Pitch Controller
Controls Advanced Research Turbine (CART)
Simulation Results
Conclusions
click on RIGHT after CART

3. Utility-Scale Horizontal Axis Wind Turbine
Utility-Scale HAWT’s
Rotor Diameter:
40-95 m Onshore
m Offshore
Tower: meters
Capacity:
0.1-3 MW Onshore
3-6 MW Offshore
Start up wind speed: 4-5 mps
Max operating wind speed ~16 mps
Low speed shaft: RPM
High speed shaft: RPM
WT manufactures are undoubtedly building larger wind turbines
Image: NWTC

4. Operating Regions Control Goals: Maximize power generation in Region 2
Maintain rated power in Region 3

5. Pitch-Controlled Wind Turbines
Region 2:
Control generator torque to yield optimum power
Hold blade pitch constant
Region 3:
Control blade pitch to maintain constant rotor speed
Generator torque held constant
like this picture b/c of people in tower

6. Wind Turbine Actuation
Blade Pitch
Nacelle Yaw
Generator Torque
collective pitch control
Pitch Actuators
Control Actions

7. Adaptive Control in Wind Turbines
Adaptive Control = uses output of Plant to determine control inputs
Good for poorly modeled plants with uncertain operating environments
Requires less modeling of turbine & its operating conditions
Can reduce controller design & verification time since less tuning required than for PID
Changes to existing turbine may require no controller modification
Adaptive vs PID

8. Direct Adaptive Control
Direct Model Reference Adaptive Control (DMRAC) with Rejection of Persistent Disturbances
Plant is linear time-invariant (LTI)
where x is plant state, u is control input, y is sensor output, uD is disturbance input
Disturbance input vector, uD, comes from a Disturbance Generator:
See: Johnson,C.D., 1976.
where zD is disturbance state

9. Disturbance Generator
Disturbances are of known form, but unknown amplitude
Ex: Step disturbance:
Ex: Sinusoidal disturbance:
Convenient form of Disturbance Generator:

10. Reference Model Output Tracking
Known Reference Model:
Reference model parameters are known
Plant parameters are unknown
Control Objective: Cause Plant output y to asymptotically track Reference Model output ym
Need to show error goes to zero and gains are bounded
LOOK at AUDIENCE!!
Output error:
Adaptive Control Law:
See: Wen, Balas, JMAA, Fuentes, Balas, JMAA, 2000.

11. Ideal Trajectories & Model Matching Conditions
Define ideal trajectories for plant:
Matching conditions are necessary and sufficient for existence of ideal trajectories
where
Model Matching Conditions are obtained by substituting ideal trajectories into above:
If CB>0, then solutions to matching conditions exist
Solutions to matching conditions must exist for analysis purposes, BUT they don’t need to be known for adaptive controller design!

12. Adaptive Controller Analysis
State tracking error:
Ideal output error:
For analysis, form:
Using the above definitions and adaptive control law:
Substitute into equation for to obtain:
where is the vector of available information

13. Adaptive Gain Laws Form the Tracking Error System:
where is the vector of available information
Specify the Adaptive Gain Laws:
where is an arbitrary, positive definite matrix.
The Adaptive Gain Laws can be written as:
The adaptive gain laws are chosen to be simple and effective
For Closed-Loop Stability Analysis, see: Frost, Balas, Wright, IJRNC (2009)

14. Closed-Loop Stability Result
Theorem: Suppose the following are true:
All um are bounded (i.e., all eigenvalues of Fm are in the closed left-half plane and any eigenvalues on the jω-axis are simple);
The reference model, is stable;
is bounded (i.e., all eigenvalues of F are in the closed left-half plane and any eigenvalues on the jω-axis are simple);
(A,B,C) is Almost Strict Positive Real (ASPR) (i.e and the open-loop transfer function is minimum phase)
Then the adaptive gains are bounded, and asymptotic tracking occurs, i.e.
Don’t know where the gains are bounded

15. Adaptive Pitch Control in Region 3
Objective: Regulate generator speed in Region 3 and reject step disturbances
Controller designed w/ extended DMRAC approach to collectively pitch blades & hold generator torque constant
Region 3 operation requires regulation, so no reference model is used, i.e and are identically zero
Disturbance can be modeled by a step function of unknown amplitude, so
Adaptive control law:
Several papers published demonstrating that changes in wind speed across the rotor surface are well modeled by step functions
Note: not considering wind shear

16. Adaptive Pitch Control Law
The adaptive collective pitch control law is given by:
Adaptive controller gains were tuned to minimize generator speed error while keeping the blade pitch rate in a range similar to baseline PI controller’s
The actual values of the gains used in the adaptive controller were: and

17. Controls Advanced Research Turbine (CART)
NWTC, Golden, Colorado

18. CART Specifications CART Specifications
Low-speed Shaft
High-speed Shaft
Tower
Nacelle
Generator
Gearbox
Blade
Hub
Rotor
CART Specifications
Variable-speed, two-bladed, teetered, upwind, active-yaw
Rotor Diameter: 43.3 m
Hub Height: 36.6 m
Rated electrical power: 600 kW at 42 RPM in region 3
Region 3 Rated generator speed: 1800 RPM
Power electronics command constant generator torque
Blade pitch rate limit: ±18 deg/sec
Baseline PI Pitch Controller
utility scale, but small
blade pitch rate limit +-18
baseline pi pitch controller for region 3 control

19. FAST Simulator for CART
FAST= Fatigue, Aerodynamics, Structures, and Turbulence
Aeroelastic simulator capable of predicting extreme and fatigue loads of HAWTs
AeroDyn subroutine package (Windward Engineering) generates aerodynamic forces along turbine blades
Turbine modeled as combination of rigid and flexible bodies
Versatile high fidelity simulation of CART with controller included in the loop with switches for DOFs, etc.
Good folks at NREL developed a high fidelity simulator of the CART
Uses Kane’s method to set up equations of motion

20. Simulink Model of Adaptive Pitch Controller
Look at audience

21. Simulation Conditions
Simulation time: seconds
Integration step size: seconds
Generator DOF switch on
All other DOF switches turned off
Wind turbine had fixed yaw with no yaw control
Aerodynamic forces were calculated during runs
Two types of wind inflow: step and turbulent wind
These are the simulation conditions

22. Step Wind Inflow – Generator Speed Errors
time scale starts at 20 secs after transients
Pitch Controller
Normalized Generator Error
Baseline PI
RPM
Adaptive
RPM
Generator Speed Errors
Relative difference: 48%
Normalized Generator Speed Errors for Step Wind

23. Step Wind: Pitch Angle Rate
Baseline PI Controller Pitch Rate
Adaptive Controller Pitch Rate

24. Turbulent Wind Inflow – Generator Speed Errors
Pitch Controller
Normalized Generator Error
Baseline PI
RPM
Adaptive
RPM
Relative difference: 68%
Normalized Generator Speed Errors for Turbulent Wind

25. Turbulent Wind: Pitch Angle Rate
adaptive controller is much quicker to respond to the changes in the wind so more pitch activity
Baseline PI Controller Pitch Rate
Adaptive Controller Pitch Rate

26. Robustness to Modeling Errors
Turbulent Wind Inflow
Generator speed errors with 5% perturbation in chord length
Generator speed errors with 15% perturbation in aerodynamic twist

27. Operation with Flexible Modes Enabled
Turbulent Wind Inflow
Generator errors when drive train rotational flexibility DOF switch is turned on
Generator errors when drive train rotational flexibility, first fore-aft tower bending-mode, and first side-to-side tower bending-mode DOF switches are turned on

28. Conclusions & Future Work
Adaptive controller was easy & quick to design
Adaptive controller showed improved generator speed regulation when compared with baseline PI controller
Pitch rate was comparable for both controllers with step wind
Both controllers performed in robust manner under parameter variations
Future work
Investigate parameter modifications which would require redesign of PI controller, but no change to adaptive controller
Incorporate a tracking model representing an ideal wind turbine to be used in design of adaptive controller
Apply adaptive control to Region 2 and 2.5
Test adaptive controller on CART

29. References
Johnson, C.D. Theory of disturbance-accommodating controllers. Control & Dynamic Systems, Advances in Theory and Applications, Leondes, CT. ed. Academic Press: New York, 1976; 12:
Wen, J.T, Balas, M.J. Robust adaptive control in Hilbert space. Journal of Mathematical Analysis and Application 1989; 143(1): 1-26.
Fuentes, R.J., Balas, M.J. Direct adaptive rejection of persistent disturbances. Journal of Mathematical Analysis and Applications 2000; 251(1):
Frost, S.A., Balas, M.J., Wright, A.D., Direct adaptive control of a utility-scale wind turbine for speed regulation, International Journal of Robust and Nonlinear Control, 2009, 19(1): 59-71, DOI: /rnc.1329.
Fingersh, L.J., Johnson, K.E. Baseline results and future plans for the NREL Controls Advance Research Turbine. Proceedings of the 23rd AIAA Aerospace Sciences Meeting and Exhibit Wind Energy Symposium 2004;