Tracking Control of Piezoelectric Stack Actuator Using Modified Prandtl–Ishlinskii Model

This paper presents the development of Prandtl–Ishlinskii hysteresis model and tracking control of piezoelectric stack actuator with severe hysteresis. Classic Prandtl–Ishlinskii model which is a linearly weighted superposition of many backlash operators with different threshold and weight values, inherits the symmetry property of the backlash operator at about the center point of the loop formed by the operator. To describe the asymmetric hysteresis of piezoelectric stack actuators, two sets of weighting parameters are proposed to modify the weight values of backlash operators in the ascending and descending branches. Hence, two weight values correspond to one operator. Each pair of the weight values slides smoothly from one to another when the output of their corresponding operator is at a desired threshold. A feedforward controller was designed based on the modified model, which can precisely describe the inverse of the hysteresis. Then the modified model and the hysteresis of the piezoelectric stack actuator cancelled each other. A feedback controller was design to compensate for actuator creep. Different types of signal are used to test the feedforward and feedback controllers. The results show that the proposed hysteresis control scheme which combines feedforward and feedback controllers greatly improves the tracking accuracy of the piezoelectric actuator and the error is less than 0.15 μm.