# A Study on \(H_{\infty}\)-Fuzzy Controller for a Non-Linear Wind Turbine with Uncertainty
## 1 Introduction  
The globally installed capacity of new wind turbines reached 93.6 GW in 2021, an increase of 53% from 2020 [1]. However, as the number of installed wind turbines increases, fewer potential sites remain available for the development of onshore wind farms. This requires wind turbines to increasingly operate on more complex terrain and in harsher environments, or otherwise be installed at sites with less favorable resources [2, 3]. With the view of pursuing the efficient utilization of wind resources and ensuring the energy productivity of wind turbines, there is a need to develop wind turbine systems with higher capacities, larger rotor diameters, and higher hub heights [4]. Recently, wind turbine prototypes with capacities of 14 MW or larger have been developed by the world's leading wind turbine manufacturers and installed at onshore test sites for type certification [5]. Larger wind turbines are desirable for their ability to generate electricity more efficiently within limited spaces for wind farms. However, they inevitably require longer blades to extract more power from the wind, with the result of wind turbines experiencing larger wind speed variations vertically (known as wind shear), producing larger fatigue loads with more fluctuations [6, 7]. Therefore, the design of the wind turbine controller becomes increasingly critical for larger wind turbines. The control algorithm must not only ensure good power performance in normal operation conditions, but also maintain reasonable operating performances with disturbances under unexpected conditions. The goal of wind turbine control is to enable wind turbines to operate automatically while responding appropriately to changes in wind speed. In regions where the wind speed falls below the rated value, the generator torque is controlled for the purpose of producing maximum power. Producing maximum power can be achieved by controlling the generator speed so that the tip speed ratio (ratio of wind speed and blade tip speed) remains constant when the power coefficient (i.e., aerodynamic efficiency) of the wind turbine is at its maximum [8]. This method is known as maximum power point tracking (MPPT), and the generator torque is controlled to be proportional to the square of the generator speed [9]. The blade pitch angle is maintained at a fine-pitch angle. In regions where the wind speed exceeds the rated value, the generator torque is either kept constant at the rated torque or controlled to be inversely proportional to the generator speed for the purpose of maintaining the rated power. The blade pitch angle is controlled to keep the generator speed at its rated value [8]. In addition to the general control goal, the wind turbine, which is a plant of the control system, is always exposed to an environment where various disturbances, including turbulence, gusts, sensor noise, and failure, exist. Therefore, the application of robust control techniques for wind turbines has been investigated with the aim of improving the stability of these turbines [10] by reducing the impacts of the disturbances. Considering the feasibility of a robust controller, a robust proportional-integral (PI) control algorithm was designed based on the conventional PI control algorithm to reduce power fluctuations and improve system stability by adjusting the cross-frequency and stability margin using frequency responses. However, this did not significantly improve the load reduction performance [10; 11]. To reduce the effects of sensor noise interference and model uncertainty on the control algorithm, a sliding mode robust control was suggested for use to improve the stability performance and power performance of the controller in regions characterized by low wind speed [12]. Although the sliding mode control was found to contribute to the robustness of the torque control algorithm, the role of the pitch control algorithm was not studied sufficiently to make any determinations.