RBF neural network dynamic sliding mode control based on lambert W function for piezoelectric stick-slip actuator

This paper presents a novel approach for increasing the precision of high-precision positioning control experiments for a piezoelectric stick-slip actuator system. This is achieved through dynamic sliding mode control with a radial basis function neural network (RBFNN) based on the Lambert W function. The proposed control strategy is divided into two parts: scanning mode control and stepping mode control. For scanning control, a dynamic sliding mode controller was designed to solve the jitter problem in traditional sliding mode control. The introduction of the RBFNN avoids the effects of uncertainty terms and unknown disturbances in the model; reduces the controller gain, which must be adjusted; and improves the robustness of the system to disturbances. The stability of the dynamic sliding mode controller based on the RBFNN was verified through a Lyapunov analysis, and the Lambert W function was introduced to optimize the controller parameters responsible for the time lag in the closed-loop control system. This optimization improved the system's robustness against time delays, which can adversely affect its performance. Simulation and experimental results indicated that the proposed control strategy achieved a positioning control accuracy of <40 nm during the scanning phase and was robust in the presence of a load. In long-distance positioning control experiments, the control strategy achieved a control target of 40 μm while maintaining the positioning control accuracy and reducing the impact of time lag on the system.