Tracking control of piezoelectric stack actuator using modified Prandtl–Ishlinskii model

Abstract

This article presents the development of Prandtl–Ishlinskii hysteresis model and tracking control of piezoelectric stack actuator with severe hysteresis. Classical Prandtl–Ishlinskii model is a linearly weighted superposition of many backlash operators with different threshold and weight values, which inherits the symmetric property of the backlash operator at about the center point of the loop formed by the operators. To describe the asymmetric hysteresis of piezoelectric stack actuators, two modified operators were developed, one for ascending branches and another for descending branches. Based on this modified model, a feedforward controller was designed to compensate the hysteresis. Since the modified model describes the inverse of hysteresis, the feedforward controller and the hysteresis of piezoelectric stack actuator canceled each other. To attenuate the creep effect and reduce tracking error, a feedback controller was proposed to work with the feedforward controller. Experimental results show that this control scheme that combines feedforward and feedback controllers greatly improves the tracking of the piezoelectric actuator and the error is less than 0.15 µm.