# Control of a Variable Blade Pitch Wind Turbine Subject to Gust Wind and Actuators Saturation
## 1 Introduction  
The dynamic and control of large and medium-size wind turbines remain a considerable challenge for scientists and engineers despite the substantial research done in the last few decades, for instance, considering the wind turbine complex nonlinear dynamics, the convoluted behavior of the wind, the maximum power that can be withdrawn from the system being constrained by the Betz Equation [1], and the overall performance affected by the disturbances. The stability analysis in the presence of disturbances of a complex system was widely investigated, a synopsis of novel methods is cited in [2]. Concerning control system design applied to the wind turbine technology, an ample amount of literature is cited in [3; 4; 5; 6; 7; 8; 9; 10; 11; 12]. Over the last decades, the design of controllers using fuzzy logic approach has been used widely as a substitute to traditional control technic especially for nonlinear systems [13]. The Takagi-Sugeno (T-S) fuzzy model is considered one of the most popular forms of fuzzy systems [14]. The stability analysis of a dynamic system represented by the (T-S) fuzzy model can be performed using a Lyapunov function approach [15]. Therefore, many control problems have been concluded, and some excellent results have been disclosed in the literature. The (T-S) fuzzy model was expanded to include systems undergoing external disturbances. A considerable amount of work was done to prove the stability of disturbed dynamic systems. For instance, [PERSON] et al. [16] developed an output feedback control for a (T-S) fuzzy system with multiple time-varying delays and unmatched disturbances. In [17], the author proposed a fuzzy sliding mode control method combined with a deep learning algorithm to approximate the dynamics model and to counteract the disturbances. The Takagi-Sugeno-Kang is used in [18] to derive a robust fuzzy control for a Magnetic Bearing System Subject to Harmonic Disturbances. [PERSON] et al. [19] proposed a robust \(H_{\infty}\) to reduce the disturbance of uncertain discrete-time fuzzy systems. [PERSON] [20] design a stable filter with disturbance attenuation of Takagi-Sugeno fuzzy systems with unmeasurable premise variables. An innovative fuzzy-observer-design technic for Takagi-Sugeno fuzzy models with unknown output disturbances is presented in [21]. [PERSON] and [PERSON] [22] designed an observer and a Controller for Takagi-Sugeno (T-S) fuzzy systemswith an enlarged class of disturbances. In [23], a fuzzy disturbance observer controller is developed and applied to a nonlinear system under internal and external disturbances. A robust adaptive sliding-mode control for fuzzy systems with mismatched uncertainties and exogenous disturbances in which the uncertainties in state matrices are mismatched and norm-bounded. In contrast, the exogenous disturbances are assumed to be bounded with an unknown bound, which is estimated by a simple and effective adaptive approach is developed in [24]. In [25], the author analyzes the unknown slippage in wheeled mobile robots and proposes a fuzzy adaptive tracking control method to counteract the dynamic disturbances. [PERSON] et al. [26] proposed a novel-function approximator; the authors use the Fourier series expansion and fuzzy-logic system to model unknown periodically disturbed systems. Then, an adaptive backstepping tracking-control scheme is developed. Other advanced methods like output feedback [27; 28], neuro-fuzzy [29], genetic algorithm [30], model predictive [31], and interval type-2 fuzzy systems [32] were used. This paper introduces a (T-S) fuzzy control method for disturbance rejection applied to a medium-size wind turbine subject to extreme gust wind and actuators saturation. The wind turbine is equipped with a blade pitch mechanism to adjust the blade pitch angle accordingly to minimize the effect of the disturbances mainly caused by the extreme variation of the wind.