An improved dynamic Prandtl–Ishlinskii hysteresis model and a PID-type adaptive sliding mode controller for piezoelectric micro-motion platform

Abstract Piezoelectric actuators are widely used in the field of micro-nano driving due to their advantages of fast frequency response, high displacement resolution, large stiffness, small size, and low heat generation. However, the hysteresis non-linearity of piezoelectric actuators severely affects their positioning accuracy during operation. Therefore, the study of hysteresis model and compensation control for piezoelectric actuators has always been a hot topic in the field of micro-nano driving. However, existing hysteresis models and control methods cannot well describe the dynamic hysteresis curve of piezoelectric actuators and track the desired trajectory. To address this issue, this paper proposes an improved dynamic Prandtl–Ishlinskii (IDPI) model and a finite-time trajectory tracking adaptive sliding mode control method based on PID-type. Firstly, this paper introduces the construction and parameter identification method of the IDPI model. Secondly, the accuracy of the IDPI model in describing hysteresis curves under different input signals is verified through experiments, and the effectiveness of the feedforward controller based on the IDPI model is validated experimentally. Then, considering the modeling uncertainty, unmodeled internal dynamics, and external environmental disturbances of the piezoelectric micro-motion platform, a finite-time trajectory tracking adaptive sliding mode controller based on PID-type is designed to suppress the non-linear characteristics of the piezoelectric micro-motion platform. Finally, the performance of the compensator is verified through simulation experiments.