# A Study on \(H_{\infty}\)-Fuzzy Controller for a Non-Linear Wind Turbine with Uncertainty
## 1 Introduction
To improve the stability of the controller in regions with high wind speed, a multiple-input, single-output (MISO) \(H_{\infty}\) controller was designed for load reduction. This controlled simulated normal and extreme wind conditions, and the results showed that the proposed MISO \(H_{\infty}\) control algorithm was able to reduce the load on the tower [13]. In one study, the iterative \(\mu\) synthesis-based \(H_{\infty}\) control algorithm was designed and simulated in MATLAB. The simulation results showed the ability of the proposed \(H_{\infty}\) controller to reduce the pitch angle oscillations caused by the model uncertainty and thus maintain robustness [14]. In another study, an \(H_{\infty}\) robust control algorithm was designed by increasing the blade mass simulation model, and the results showed that, with model uncertainty, the \(H_{\infty}\) controller was more stable compared to conventional PI control [15]. Additionally, in the simulation study of a pitch \(H_{\infty}\) controller designed exclusively for the rated power region, the authors showed that the pitch \(H_{\infty}\) control algorithm reduced the standard deviation in the rotor speed of a wind turbine in the rated power region compared to the conventional control algorithm, especially in environments with sensor noise and extreme wind conditions [16]. The aforementioned studies in the literature validated the stability and load reduction performance of the controller for a specific wind speed range. However, they had limitations in terms of a failure to provide complete control strategies capable of covering the entire operating regions of wind turbines, including below-rated, rated, and above-rated wind speed regions, including the nonlinearity and uncertainty associated with wind turbines. Recent studies have started to adapt fuzzy logic, an adaptive control technique, to wind turbine control. A wind turbine controller with fuzzy logic combines linear systems according to the operating region of the wind turbine in order to apply gains and weights with consideration of nonlinearity [17]. One study found that using the conventional maximum power point tracking (MPPT) control led to the development of a fuzzy-maximum power point tracking control algorithm, which was proposed to improve the power and stability of the controller in regions with low wind speed [18]. The results showed that,in these regions, the use of the fuzzy MPPT control algorithm can improve the stability and power performance of the wind turbine compared with the use of the conventional MPPT control algorithm. In another study, the proposed fuzzy PI-scheduling control algorithm was able to reduce the load of the tower base by up to 21.5% compared with the conventional PI control algorithm [19]. The optimal control algorithm using fuzzy control was also previously investigated. A linear-quadratic regulator control algorithm based on fuzzy control was proposed. Researchers found that its use to improved stability and load reduction performance compared with the conventional PI control algorithm [20; 21]. In previous studies on wind turbine control, the uncertainty of the model was considered using \(H_{\infty}\) control and the nonlinearity of the wind turbine was addressed via fuzzy logic. However, there were few attempts to simultaneously address both model uncertainty and nonlinearity simultaneously. Therefore, in this study, we revisited our previous study on the pitch \(H_{\infty}\) control algorithm and designed a fuzzy logic-based \(H_{\infty}\) control algorithm to improve controller performance in operational wind turbine situations with nonlinearity and uncertainty effects. Additionally, in order to compare the performance of the proposed controller, we designed PI control algorithms using the baseline control structure presented by the National Renewable Energy Laboratory (NREL) and a linear-quadratic regulator based on the fuzzy logic (LQRF) control algorithm from our previous work [22; 23].