## 1 Introduction
Unlike other traditional stable region analysis methods, the proposed method [22] optimized other parameters based on robust design criteria for parameter uncertainty. Therefore, the controlled system can tolerate different parameter uncertainties, meet the transient performance index demands, and maintain the stability of the system. Based on the nonlinear fuzzy observation, active rear-steering and direct-yaw moment coordinated control were carried out, and the stability of the fuzzy sliding mode controller was proved by using the Lyapunov method to improve the yaw and roll stability control under extreme conditions [23]. Meanwhile, the combination of HITL simulation technology with LabVIEW/Casim demonstrates that the proposed fuzzy controller greatly improves yaw stability under extreme conditions. The LabVIEW 2020/Casim 2019 software suite can predict the braking performance, smoothness, power performance, and economy of the yaw turning motion. For the megawatt wind turbine yaw system, a typical low-speed servo motion system is composed of a yaw sliding bearing and yaw drive system. Therefore, a friction self-excited vibration in low-speed motion, that is, a yaw crawling motion, inevitably occurs in the megawatt wind turbine yaw system during its operation, which affects the stability of the yaw motion and the accuracy of the yaw system [24]. Therefore, engineers and technicians have investigated the kinematics mechanism of the yaw system from the perspective of tribology, established the crawling kinematics model on the basis of equilibrium position, and analyzed the motion law and influencing factors of the yaw system, which had positive practical significance for the engineering application of megawatt units. As for the controlled system with a repetitive crawling motion, especially for the nonlinear crawling vibration system, iterative learning control [25] has unique tracking and estimation advantages for nonlinear repetitive crawling vibration. Especially, by using PID controllers, reinforcement learning techniques can promote the convergence of system responses and accelerate the running speed of the iteration process [26]. On the one hand, it can have a good tracking effect on the target value; on the other hand, it can be combined with a PID controller to limit the controlled object within the allowable error range and force the controlled object to exhibit a convergence trend [27]. The LS vibration is a rapid shaking phenomenon based on the aforementioned crawling phenomenon, which is a special case of crawling phenomenon. In extreme wind conditions, it is more likely to cause destructive effects. In the present study, the iterative learning control for the nonlinear LS vibration amplitude of a wind turbine in yaw motion is investigated. Aiming at amplitude suppression for the LS vibration of the yaw system of megawatt wind turbines, the kinematics mechanism of the yaw system is studied from the perspective of tribology, and the kinematics model of the yaw system based on the equilibrium position is established. On the basis of this model, the nonlinear mathematical model of the LSJ system is constructed. Inspired by the dual-driven parallel control mechanism of pitch and yaw servos [2], based on the conventional lead gear of yaw driving, the auxiliary gear of yaw driving is designed and mounted. Based on the open-loop PD control and the iterative learning control methods of the time-varying continuous system, the stability control and jitter suppression of the yaw system are realized by using the combined driving torques provided by the lead and auxiliary gears. From the stability and convergence of the time-domain response and the convergence of the iterative error, the effectiveness of the iterative learning control method is verified. The feasibility of the physical realization and engineering application of the control algorithm is verified using C-HITL simulation technology. The content of this study is engineering application-oriented.