Susan A. FrostSusan A. FrostIntelligent Systems DivisionIntelligent Systems DivisionNASA Ames Research CenterNASA Ames Research CenterSusan.A.Frost[at]nasa.govSusan.A.Frost[at]nasa.gov

Mark J. BalasMark J. BalasWind Energy Research Center (WERC)Wind Energy Research Center (WERC)University of WyomingUniversity of WyomingMbalas[at]uwyo.eduMbalas[at]uwyo.edu

Alan D. WrightAlan D. WrightNational Wind Technology CenterNational Wind Technology CenterNational Renewable Energy LaboratoryNational Renewable Energy LaboratoryAlan_Wright[at]nrel.govAlan_Wright[at]nrel.gov

Adaptive Control of a Utility-Scale Wind Turbine Operating in Region 3

National Wind Technology Center Golden, Colorado

AIAA Aerospace Sciences Meeting 2009

Outline

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Utility-Scale Wind Turbines Adaptive Control Theory Region 3 Adaptive Pitch

Controller Controls Advanced Research

Turbine (CART) Simulation Results Conclusions

Utility-Scale Horizontal Axis Wind Turbine

Utility-Scale HAWT’s Rotor Diameter:

– 40-95 m Onshore– 90-114 m Offshore

Tower: 25-180 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: 30-60 RPM

High speed shaft: 1000-1800 RPM

Image: NWTC3

Operating Regions

Plot of Turbine Power Versus Windspeed

rated power

0

100

200

300

400

500

600

700

4 6 8 10 12 14 16 18 20

Windspeed (m/s)

Pow

er (k

W)

Region 3Region 2

rated windspeed

Control Goals: Maximize power

generation in Region 2

Maintain rated power in Region 3

4

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

5

Wind Turbine Actuation

Nacelle Yaw

Blade Pitch

Control ActionsPitch Actuators

Generator Torque

6

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

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Direct Adaptive Control

Plant is linear time-invariant (LTI)

0)0(;

)(xxCxy

uBuΑxx D

Disturbance input vector, uD, comes from a Disturbance Generator:

0)0(; zzzFz

zu

DDD

DD

See: Johnson,C.D., 1976.

where x is plant state, u is control input, y is sensor output, uD is disturbance input

where zD is disturbance state

Direct Model Reference Adaptive Control (DMRAC) with Rejection of Persistent Disturbances

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Disturbance Generator

Disturbance Generator:

0)0(; zzzFz

zu

DDD

DD

Ex: Step disturbance:

2

0 1Let , then 1 0 ,

0D

DD D

uz F

u

unknown is andknown are and where D DD A Ex: Sinusoidal disturbance:

Let zD uD , then 1, F 0

uD a0 1, where a0 is unknown

uD (t) AD sin(Dt D ),

Disturbances are of known form, but unknown amplitude

uD zDzD LD

where D is a vector of known basis functions;

and (L, ) can be unknown

Convenient form of Disturbance Generator:

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Reference model parameters are known

Reference Model Output Tracking

0 tmy yye

DDyemumm GeGuGxGu

mmmmm

mmmmm

mmmmm

0

0

)0(;

)0(;

uuuFu

xxxCy

uBxAx

Plant parameters are unknown

Control Objective: Cause Plant output y to asymptotically track Reference Model output ym

(A,B,C,,)

(Am ,Bm,Cm ,Fm )

Output error:

Adaptive Control Law:

See: Wen, Balas, JMAA, 1989 Fuentes, Balas, JMAA, 2000.

Known Reference Model:

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Ideal Trajectories & Model Matching Conditions

where0

( ); (0)

D

m

x Ax Bu u

y Cx y x x

Define ideal trajectories for plant:

x S11 xm S12

um S13* zD

u S21 xm S22

um S23* zD

Matching conditions are necessary and sufficient for existence of ideal trajectories

Solutions to matching conditions must exist for analysis purposes, BUT they don’t need to be known for adaptive controller design!

Model Matching Conditions are obtained by substituting ideal trajectories into above:

()

AS11 BS21

S11Am;AS12

BS22 S11

Bm S12 Fm

CS11 Cm;CS12

0;AS13 BS23

S13 F;CS13

0

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Adaptive Controller Analysis

For analysis, form:

Gu Gu S22 ; Gm Gm S21

Ge Ge Ge; GD GD S23

* L

uu u Guum Gmxm Ge Ge ey GDD

Using the above definitions and adaptive control law:

*

e u m e D

C

e Ae B u A BG C e B G G G G

A e B G

Substitute into equation for to obtain:

where is the vector of available informationTTD

Ty

Tm

Tm ][ exu

e

State tracking error:

e* x x** where e Ae B u u u u

ey y ym y y* Cx Cx* Ce*

Ideal output error:

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Adaptive Gain Laws

Form the Tracking Error System:

*

*

Cee

GBeAe*

y

C

Specify the Adaptive Gain Laws:HeG Ty

where is an arbitrary, positive definite matrix. The Adaptive Gain Laws can be written as:

11

22

33

44

Tu y m

Tm y m

Te y y

TD y D

h

h

h

h

G e u

G e xG

G e e

G e

For Closed-Loop Stability Analysis, see: Frost, Balas, Wright, IJRNC (2009)

H

13

where is the vector of available informationTTD

Ty

Tm

Tm ][ exu

Closed-Loop Stability Result

Theorem: Suppose the following are true:1. 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);2. The reference model, is stable;3. is bounded (i.e., all eigenvalues of F are in the closed left-half

plane and any eigenvalues on the jω-axis are simple);4. (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.

),,,( mmm CBA

D

ey y ym Ce* t 0

Gu, Gm , Ge, and GD

CB 0

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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:

mG uG

1D

DyeDDye GeGGeGu

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Adaptive Pitch Control Law

• The adaptive collective pitch control law is given by:

4444

33

hh

h

yDyD

Tyye

Dye

eeG

eeG

GeGu

• 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: and1433 h

h44 0.5

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Controls Advanced Research Turbine (CART)

NWTC, Golden, Colorado 17

CART Specifications

Low-speed Shaft

High-speed Shaft

Tower

Nacelle

GeneratorGearbox

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

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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.

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Simulink Model of Adaptive Pitch Controller

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Simulation Conditions

• Simulation time: 0-100 seconds• Integration step size: 0.006 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

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Step Wind Inflow – Generator Speed Errors

Step Wind Inflow

Generator Speed ErrorsPitch Controller Normalized Generator Error

Baseline PI 0.0922 RPM

Adaptive 0.0479 RPM

Normalized Generator Speed Errors for Step Wind

Relative difference: 48%

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Step Wind: Pitch Angle Rate

Baseline PI Controller Pitch Rate Adaptive Controller Pitch Rate

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Turbulent Wind Inflow – Generator Speed Errors

Turbulent Wind Inflow

Pitch Controller Normalized Generator Error

Baseline PI 0.2435 RPM

Adaptive 0.0781 RPM

Normalized Generator Speed Errors for Turbulent Wind

Relative difference: 68%

Generator Speed Errors

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Turbulent Wind: Pitch Angle Rate

Baseline PI Controller Pitch Rate Adaptive Controller Pitch Rate

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Robustness to Modeling Errors

Generator speed errors with 5% perturbation in chord length

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Generator speed errors with 15% perturbation in aerodynamic twist

Turbulent Wind Inflow

Operation with Flexible Modes Enabled

Generator errors when drive train rotational flexibility DOF switch is turned on 

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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

Turbulent Wind Inflow

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

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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: 387-489.

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): 28-39.

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: 10.1002/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; 87-93.

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