## Abstract

This article solves the problem of regulating the rotor speed tracking error for wind turbines in the full-load region by an effective robust adaptive control strategy. The developed controller compensates for the uncertainty in the control input effectiveness caused by a pitch actuator fault, unmeasurable wind disturbance, and nonlinearity in the model. Wind turbines have multilayer structures such that the high-level structure is nonlinearly coupled through an aggregation of the low-level control authorities. Hence, the control design is divided into two stages. First, an $L2$ controller is designed to attenuate the influence of wind disturbance fluctuations on the rotor speed. Then, in the low-level layer, a controller is designed using a proposed adaptation mechanism to compensate for actuator faults. The theoretical results show that the closed-loop equilibrium point of the regulated rotor speed tracking error dynamics in the high level is finite-gain $L2$ stable, and the closed-loop error dynamics in the low level is globally asymptotically stable. Simulation results show that the developed controller significantly reduces the root mean square of the rotor speed error compared to some well-known works, despite the largely fluctuating wind disturbance, and the time-varying uncertainty in the control input effectiveness.

## References

1.
Bianchi
,
F. D.
,
De Battista
,
H.
, and
Mantz
,
R. J.
,
2006
,
Wind Turbine Control Systems: Principles, Modelling and Gain Scheduling Design
,
,
London
.
2.
Palejiya
,
D.
, and
Chen
,
D.
,
2015
, “
Performance Improvements of Switching Control for Wind Turbines
,”
IEEE Trans. Sustainable Energy
,
7
(
2
), pp.
526
534
.
3.
Imran
,
R. M.
,
Hussain
,
D. A.
, and
Soltani
,
M.
,
2014
, “
Dac With LQR Control Design for Pitch Regulated Variable Speed Wind Turbine
,”
2014 IEEE 36th International Telecommunications Energy Conference (INTELEC)
,
,
Sept. 28–Oct. 2
,
IEEE
, pp.
1
6
.
4.
Kalbat
,
A.
,
2013
, “
Linear Quadratic Gaussian (LQG) Control of Wind Turbines
,”
2013 3rd International Conference on Electric Power and Energy Conversion Systems
,
Istanbul, Turkey
,
Oct. 2–4
,
IEEE
, pp.
1
5
.
5.
,
H.
,
2013
, “
L1-Optimal Control of Variable-Speed Variable-Pitch Wind Turbines
,” Master’s thesis,
,
.
6.
Sarkar
,
S.
,
Fitzgerald
,
B.
, and
Basu
,
B.
,
2020
, “
Nonlinear Model Predictive Control to Reduce Pitch Actuation of Floating Offshore Wind Turbines
,”
IFAC-PapersOnLine
,
53
(
2
), pp.
12783
12788
.
7.
Qi
,
K.
,
De-hui
,
S.
,
Zheng-xi
,
L.
,
Shu-juan
,
Q.
,
Yan-jiao
,
H.
, and
Yun-tao
,
S.
,
2014
, “
H Fault Tolerant Control of Wind Turbine System With Actuator Faults
,”
IFAC Proc. Volumes
,
47
(
3
), pp.
5838
5843
.
8.
Benlahrache
,
M. A.
,
Laib
,
K.
,
Othman
,
S.
, and
Sheibat-Othman
,
N.
,
2017
, “
Fault Tolerant Control of Wind Turbine Using Robust Model Predictive Min-Max Approach
,”
IFAC-PapersOnLine
,
50
(
1
), pp.
9902
9907
.
9.
Jiao
,
X.
,
Yang
,
Q.
,
Fan
,
B.
,
Chen
,
Q.
,
Sun
,
Y.
, and
Wang
,
L.
,
2020
, “
EWSE and Uncertainty and Disturbance Estimator Based Pitch Angle Control for Wind Turbine Systems Operating in Above-Rated Wind Speed Region
,”
ASME J. Dyn. Syst. Meas. Control.
,
142
(
3
), p.
031006
.
10.
Ma
,
M.
,
Chen
,
H.
,
Liu
,
X.
, and
Allgöwer
,
F.
,
2014
, “
Moving Horizon $H∞$ Control of Variable Speed Wind Turbines With Actuator Saturation
,”
IET Renewable Power Generation
,
8
(
5
), pp.
498
508
.
11.
Simani
,
S.
, and
Castaldi
,
P.
,
2012
, “
Adaptive Fault-Ttolerant Control Design Approach for a Wind Turbine Benchmark
,”
IFAC Proc. Volumes
,
45
(
20
), pp.
319
324
.
12.
Simani
,
S.
, and
Castaldi
,
P.
,
2013
, “
Data-Driven and Adaptive Control Applications to a Wind Turbine Benchmark Model
,”
Control. Eng. Pract.
,
21
(
12
), pp.
1678
1693
.
13.
Wang
,
H.
, and
Zhang
,
Q.
,
2020
, “
Adaptive Fault-Tolerant Control of Variable Pitch System of Wind Power Generator Based on Clustering-Type Fuzzy Neural Network
,”
IET Renewable Power Generation
,
14
(
17
), pp.
3541
3549
.
14.
Zuo
,
Z.
,
Wang
,
Y.
, and
Yang
,
W.
,
2015
, “
L2-Gain Fault Tolerant Control of Singular Lipschitz Systems in the Presence of Actuator Saturation
,”
J. Robust. Nonlinear. Control.
,
25
(
12
), pp.
1751
1766
.
15.
van der Schaft
,
A. J.
, and
Van Der Schaft
,
A.
,
2000
,
L2-Gain and Passivity Techniques in Nonlinear Control
, Vol.
2
,
Springer
,
London
.
16.
Anubi
,
O. M.
,
2013
,
Variable Stiffness Suspension System
,
University of Florida
,
Gainesville, FL
.
17.
Jonkman
,
J.
,
Butterfield
,
S.
,
Musial
,
W.
, and
Scott
,
G.
,
2009
, “Definition of a 5-MW Reference Wind Turbine for Offshore System Development,”
National Renewable Energy Lab.(NREL)
,
Golden, CO
, Technical Report, NREL/TP-500-38060.
18.
Wasynczuk
,
O.
,
Man
,
D.
, and
Sullivan
,
J.
,
1981
, “
Dynamic Behavior of a Class of Wind Turbine Generators During Random Wind Fluctuations
,”
IEEE Trans. Power Apparatus Syst.
,
PER 1
(
6
), pp.
2837
2845
.
19.
Odgaard
,
P. F.
, and
Johnson
,
K. E.
,
2013
, “
Wind Turbine Fault Detection and Fault Tolerant Control—An Enhanced Benchmark Challenge
,”
2013 American Control Conference
,
Washington, DC
,
June 17–19
,
IEEE
, pp.
4447
4452
.
20.
Rudin
,
W.
,
1964
,
Principles of Mathematical Analysis
, Vol.
3
,
McGraw-Hill
,
New York
.
21.
Anubi
,
O. M.
, and
Crane
,
C.
,
2014
, “
A New Semiactive Variable Stiffness Suspension System Using Combined Skyhook and Nonlinear Energy Sink-Based Controllers
,”
IEEE Trans. Control Syst. Technol.
,
23
(
3
), pp.
937
947
.
22.
Anubi
,
O. M.
, and
Crane
,
C. D.
, III,
2013
, “
Roll Stabilisation of Road Vehicles Using a Variable Stiffness Suspension System
,”
Vehicle Syst. Dyn.
,
51
(
12
), pp.
1894
1917
.
23.
Khalil
,
H. K.
, and
Grizzle
,
J. W.
,
2002
,
Nonlinear Systems
, Vol.
3
,
,
NJ
.
24.
Jonkman
,
B. J.
,
2009
, “Turbsim User’s Guide: Version 1.50,”
National Renewable Energy Lab. (NREL)
,
Golden, CO
, Technical Report NREL/TP-500-46198.