An ARX-Based PID-Sliding Mode Control on Velocity Tracking Control of a Stick-Slip Pi-ezoelectric-Driven Actuator

Piezoelectric-driven stick slip actuators have been drawn more and more attention in the nano- positioning application due to the high accuracy and theoretical unlimited displacement. However, the hysteresis of piezoelectric actuator (PEA) and the nonlinear friction force between the end- effector and the stage make control of piezoelectric-driven stick slip actuator challenge. This paper presents the development of an autoregressive exogenous (ARX)-based proportional-integral-derive (PID)-sliding mode control (SMC) for the velocity tracking control of the piezoelectric-driven stick slip actuator. Stability is guaranteed by rigorously choosing the appropriate PID parameters and the zero steady state error is achieved. To verify the effectiveness of the proposed method, experiments were carried out on a commercially-available piezoelectric-driven stick slip actuator. The tracking errors were compared with the traditional PID controller, illustrating that in spite of existing of modeling error, the ARX-based PID-SMC is able to better improve the velocity tracking performance of piezoelectric-driven stick slip actuator, compared with the traditional PID controller.