## 1 Introduction
A polishing end-effector with an MR-based damper and a magnetic spring mechanism is designed, the damping and stiffness model is built, the vibration dynamic model is established, and the vibration characteristics are theoretically analyzed. [PERSON], [PERSON] and [PERSON] et al. [18] described a position/force decoupled polishing system, which consists of a tool path control subsystem and a pneumatic servo-based polishing force control subsystem. A dynamic model of the pneumatic servo system was established based on the system output, and an integral sliding mode controller consisting of switching control and equivalent control was designed based on the dynamic model. Nonlinear control systems have dead zone effects, friction characteristics, and relay characteristics. The traditional PID control strategy makes it difficult to achieve the expected control effect [19; 20; 21; 22]. The sliding mode control algorithm has a fast response speed and strong robustness and does not require online system identification, which has good control effects on nonlinear systems. However, when the state trajectory reaches the sliding mode surface, it is difficult to slide strictly along the sliding mode surface to the equilibrium point. Instead, it passes back and forth on both sides of the sliding mode surface, resulting in high-frequency chattering [23; 24; 25; 26; 27]. Saturation functions, dynamic sliding mode, filtering, and switching gain reduction can effectively reduce the high-frequency chattering of sliding mode control, which increases the steady-state control error and increases the difficulty of controller design [28; 29; 30]. In recent years, many researchers have applied intelligent control technology to practical projects and achieved good control effects. [PERSON] [31] is the first to consider the tank bidirectional stabilization system with a fully electric actuator as a fuzzy mechanical system with inequality constraints and conduct an optimization design after proposing an error-controllable control strategy. In the Literature [32], a dynamic-free adaptive sliding mode control (adaptive-SMC) methodology for the synchronization of a specific class of chaotic delayed fractional-order neural network systems in the presence of input saturation is proposed. Literature [33] addresses the attitude-tracking control problem of multiple rigid bodies in the presence of completely unknown inertial information. In order to reduce the impact of unknown parameters on the control system, a neural network algorithm is used to select unknown nonlinear terms from the controller model. In the Literature [34], under the framework of stochastic Lyapunov stability, sufficient conditions are constructed to ensure the mean-square stability of the closed-loop networked MJSs, and the sliding region is reached around the specified sliding surface. Furthermore, a sliding mode control based on a genetic algorithm is proposed by optimizing the objective function to reduce the convergence area around the sliding mode surface. In this article, a polishing equipment is introduced, the polishing process is theoretically analyzed, and a calculation model of polishing pressure is established. AFSMC is designed to replace the traditional PID controller. For time-varying and nonlinear polishing force control systems, traditional PID algorithms cannot effectively, stably, and accurately control them. SMC relies on accurate system mathematical models and parameter adjustments. If the model has errors or cannot be accurately measured, the control effect will be poor. When the state trajectory reaches the sliding mode surface, it is difficult to slide strictly along the sliding mode surface to the equilibrium point. Instead, it crosses back and forth on both sides of the sliding mode surface, causing high-frequency chattering. According to these issues, we try to apply AFSMC to the polishing force control system.