## 1 Introduction  
Wind power generation is the most mature, largest and most promising power generation method for new energy [1]. Wind power plants are generally located in complex terrain and bad climates. The WECS, an important part of the wind power generation system, has a high fault rate, especially in its sensor and actuator, which seriously affect the performance of the system, even causing system paralysis, and cause immeasurable losses [2]. Therefore, realizing the fault tolerant control of WECS is an important guarantee for improving the operation reliability of wind power generation systems. Fault-tolerant control aims to ensure a stable and safe operation of the controlled system under the requirements of a certain performance index when it fails [3]. Passive fault-tolerant control strategy cannot control the unknown faults of the system, while active fault tolerance can redesign the controller by using a priori knowledge of all kinds of faults [4]. Active fault-tolerant control is applied to various practical projects. An active fault-tolerant tracking controller is proposed for vehicle dynamics systems in [5], and the uncertain dynamic model of the vehicle is established. the vehicle dynamic states with sensor faults are estimated by the description observed and a fault-tolerant tracking controller based on linear matrix inequalities is designed. A robust \(H_{\infty}\) output-feedback control strategy applied to the path following an autonomous ground vehicle is presented in [6], and a robust \(H_{\infty}\) static output-feedback controller based on mixed genetic algorithms/linear matrix inequality is used to realize the path-following without the information of the lateral velocity. Active fault-tolerant control has also been widely studied and applied in WECS. An adaptive fault observer is designed for WECS, which detects the faults of the transmission part of the conversion system, and an active fault tolerant controller is designed to ensure the reliable and stable operation of the system [7]. An active tolerant controller based on \(H\infty\) is designed to obtain the high performance in extreme wind speed profile, and a sliding mode fault detection and isolation system is applied to reconstruct and compensate a wind turbine's sensor faults in [8]. The T-S fuzzy model proposed by [PERSON] etc. is an effective method to solve the problem of nonlinear system control [9]. A proportional integral observer based on T-S fuzzy control is designed for the fault estimation of the actuator and sensor in [10]. Through the Lyapunov stability theory and \(L_{2}\) performance analysis, the sufficient design conditions for simultaneous estimation of two kinds of faults are given, and the proposed conditions are solved under linear matrix inequalities constraints and the proportional integral observer gains are calculated. Aiming at the potential faults of the system, fuzzy modeling and the recognition method are used to automatically correct the potential faults of the system based on online diagnosis information, so as to ensure that the motor torque can be reliably adjusted when the actuator fails [11]. A multi-observer scheme based on Calman filter and maximum shift strategy is presented for the additive and multiplicative faults of sensors, and the fault types are diagnosed by generating new residual values in [12]. Sliding mode control can effectively deal with the uncertainty and interference of complex dynamic systems and adjust the dynamic behavior of the system by selecting sliding function [13] so that the nonlinear system has strong robustness, and this is widely applied in engineering practice, such as CNC machine tools [14], four-rotor helicopters [15], wind turbines [16] and so on.