## 1 Introduction
[13] proposed a solution to the yaw tracking control problem of unmanned helicopters, transforming non-affine nonlinear equations into simplified affine models, estimating unknown parameters using the Levenberg-Marquardt algorithm, and implementing autonomous flight using an adaptive controller based on Lyapunov. [PERSON] and [PERSON] [14] investigated a new control mechanism to generate the yaw control torque of a hovering robot hummingbird. This method generates the yaw moment of the wing by modifying the kinematics of the wing, while minimizing its impacts on the roll and pitch moments. [PERSON] and [PERSON] [15] introduced a fatigue load controller design for a semi-submersible floating offshore wind turbine. The designed controller was used to manipulate the pitch angles of three blades and minimize the fatigue load at the tower base, with the turbine position controlled by the cabin yaw angle and average wind speed. Therefore, with the expansion of wind turbines, the yaw effect and yaw control of wind turbines, especially megawatt wind turbines, are also worth studying. Various advanced control methods and theories have been applied and implemented. For example, [PERSON] et al. [16] summarized and discussed the yaw control system, considering various control strategies for multi-objective control technology in different operating areas. For each control system, the different control algorithms are usually divided into classical, modern computing, and artificial intelligence. Modern and soft computing technologies have shown significant improvements in the system's performance with minimal costs and faster responses. For example, soft computing control algorithms, such as fuzzy logic control, sliding mode control, and maximum power point tracking, have shown superior performances. [PERSON] et al. [17] established a dynamic coupling model for a multi-source driven yaw system. Different yaw angle control modes were studied, including comparative control and servo control. This model establishes a multi-channel electronic supply system, gearbox system, and hydraulic braking subsystem, achieving the coupling of the multi-channel yaw subsystem. Since the wind direction is random and time-varying, it is difficult to accurately and immediately predict the wind direction and the target yaw angle. Yaw control based on the predicted wind direction is limited by the accuracy of the wind direction prediction, which leads to a small improvement of the energy capture efficiency of wind turbines. To address this issue, a stochastic model based on the intelligent scene generation (SG) was proposed to predict yaw actions to improve the energy capture efficiency [18]. In addition, over the years, comprehensive research has been conducted on the physical characteristics and effectiveness of the active yaw control of wind turbines under different wind conditions based on wind tunnel experiments and various analytical wind farm models [19]. These studies extensively discussed the distribution and relationship of the optimal yaw angle, wind farm size, and peak power gain, elucidating the effects of turbulence intensity and flow spacing on active yaw control. The stability and time response analyses of the yaw motion and stability of the controller itself are also important topics in yaw system research, which requires that the proposed control method supplies the controlled object with better stability and motion trajectory, and also has the convenience of software development and the physical feasibility of hardware implementation, so as to further improve the maneuverability of active control and provide a theoretical basis for the design of wind turbine structures and yaw control strategies considering dynamic yaw operations [14; 20; 21]. For example, [PERSON] et al. proposed a robust fractional proportional integral derivative (PID) controller design for yaw control systems [22], including a three-dimensional stable region analysis method for achieving fractional order control.