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A Fault Tolerant Control Approach to Sustainable Offshore Wind Turbines

Part of the Advances in Industrial Control book series (AIC)


The main challenges for the deployment of wind turbine systems are to maximise the amount of good quality electrical power extracted from wind energy. This must be ensured over a significantly wide range of weather conditions simultaneously with minimising both manufacturing and maintenance costs. In consequence to this, the fault tolerant control (FTC) and fault detection and diagnosis (FDD) research have witnessed a steady increase in interest in this application area as an approach to maintain system sustainability with more focus on offshore wind turbines (OWTs) projects. This chapter focuses on investigations of different aspects of operation and control of wind turbine systems and the proposal of a new FTC approach to sustainable OWTs. A typical non-linear state space model of a wind turbine system is described and a Takagi-Sugeno (T-S) fuzzy model of this system is also presented. A new approach to active sensor fault tolerant tracking control (FTTC) for OWT described via T-S multiple models. The FTTC strategy is designed in such way that aims to maintaining nominal wind turbine controller without change in both fault and fault-free cases. This is achieved by inserting T-S proportional state estimators augmented with multiple-integral feedback (PMI) fault estimators to be capable to estimate different generator and rotor speed sensors fault for compensation purposes. The material in this chapter is presented using a non-linear benchmark system model of a wind turbine offered within a competition led by the companies Mathworks and KK-Electronic.


  • Wind turbine control
  • Active fault tolerant control
  • Fault estimation
  • T-S fuzzy systems
  • Tracking control

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  • DOI: 10.1007/978-3-319-08413-8_7
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Fig. 7.17


\(P_{\text{cap}} , P_{\text{wind}}\) :

Aerodynamic, wind power

ρ :

Air density

R :

Rotor radius

\(C_{p} , C_{q}\) :

Power, torque coefficients

\(\beta , \beta_{r}\) :

Actual, reference blade pitch angle

\(\lambda , \lambda_{\text{opt}}\) :

Actual, optimal tip-speed-ratio

\(v, v_{ \hbox{min} } , v_{ \hbox{max} }\) :

Point, minimum, and maximum wind speed

\(\omega_{r} , \omega_{ \hbox{min} } , \omega_{ \hbox{max} } , \omega_{{r{\text{opt}}}}\) :

Actual, minimum, maximum, and optimal rotor speed

T a :

Aerodynamic torque

\(T_{g} , T_{gr} , T_{gm} ,\) :

Actual, reference, measured generator torque

\(J_{r} , J_{g}\) :

Rotor, generator inertia

\(B_{r} , B_{g}\) :

Rotor, generator external damping

ω g :

Generator speed

n g :

Gearbox ratio

\(K_{{{\text{d}}t}} ,B_{{{\text{d}}t}}\) :

Torsion stiffness, damping coefficients

\(\theta_{\Delta }\) :

Torsion angle

ζ :

Damping factor

ω n :

Natural frequency

τ g :

Generator time constant

\(C_{{p{ \hbox{max} }}}\) :

Upper bound of power coefficient

\({\mathcal{A}}_{\text{wind}} ,\text{ }\,{\mathcal{A}}, \,{\mathcal{A}}_{2}\) :

Upstream, disc, downstream, areas

\(P^{ + } ,\, P^{ - }\) :

Pressure before, after actuator disc

F d :

Thrust exerted on the actuator disc

α :

Axial interference factor

t b ,t w :

Blade, turbulence times

S :

Length of the disturbed wind

n :

Number of blades

f s :

Sensor fault signal

\(e_{t} , \,e_{x} ,\, e_{v}\) :

Tracking, state estimation, wind measurement errors

\(K\left( p \right), \,L_{a} \left( p \right)\) :

Controller, observer gains

\(P_{1} ,\,P_{2} ,\,\gamma , \,\mu , \,X_{1}\) :

LMI variables

\(A\left( p \right),\,B,\, E\left( p \right), \,C, \,D_{f}\) :

System matrices

\(\bar{A}\left( p \right),\, \bar{B}, \,\bar{E}\left( p \right), \,R, \bar{C},\, \bar{D}_{f}\) :

System matrices augmented with tracking error integral

\(A_{a} \left( p \right), \,B_{a} , \,E_{a} \left( p \right), \,R_{a} , \,G, \,C_{a}\) :

Observer augmented matrices


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Shaker, M.S., Patton, R.J. (2014). A Fault Tolerant Control Approach to Sustainable Offshore Wind Turbines. In: Luo, N., Vidal, Y., Acho, L. (eds) Wind Turbine Control and Monitoring. Advances in Industrial Control. Springer, Cham.

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