Modeling and Compensation of Hysteresis of Piezoelectric Actuators by Utilizing Asymmetric Play Operator

Piezoelectric ceramic actuators have been widely used for developing nano-positioning stages. However, their inherent hysteresis property remarkably hinders the positioning accuracy. The classical Prandtl-Ishlinskii model is effective for characterizing symmetric hysteresis loop, but real-world hysteresis is often asymmetric. To address this limitation, this paper presents an improved Prandtl-Ishlinskii model by employing asymmetric play operators, enabling the accurate characterization of the asymmetric hysteresis loop. Furthermore, play operators with unevenly spaced thresholds are introduced, replacing the traditionally evenly spaced ones, which allows for a more effective modeling, also, with higher accuracy. To compensate for the hysteresis property, the inverse of the improved Prandtl-Ishlinskii model is derived and applied as a feedforward compensator.