PID-type sliding mode-based adaptive motion control of a 2-DOF piezoelectric ultrasonic motor driven stage

This paper presents a new scheme of adaptive sliding mode control (ASMC) for a piezoelectric ultrasonic motor driven X–Y stage to meet the demand of precision motion tracking while addressing the problems of unknown nonlinear friction and model uncertainties. The system model with Coulomb friction and unilateral coupling effect is first investigated. Then the controller is designed with adaptive laws synthesized to obtain the unknown model parameters for handling parametric uncertainties and offsetting friction force. The robust control term acts as a high gain feedback control to make the output track the desired trajectory fast for guaranteed robust performance. Based on a PID-type sliding mode, the control scheme has a simple structure to be implemented and the control parameters can be easily tuned. Theoretical stability analysis of the proposed novel ASMC is accomplished using a Lyapunov framework. Furthermore, the proposed control scheme is applied to an X–Y stage and the results prove that the proposed control method is effective in achieving excellent tracking performance.