Compensation of hysteresis nonlinearity for a piezoelectric actuator using a stop operator-based Prandtl-Ishlinskii model

Piezoelectric actuators exhibit limited tracking performance in precision control due to their inherent hysteresis nonlinearity. In this paper, the hysteresis behavior is described by a play operator-based Prandtl-Ishlinskii (PPI) model. And a corresponding stop operator-based Prandtl-Ishlinskii (SPI) model is utilized as a feedforward compensator for canceling the hysteresis effect in piezoelectric actuators. For this purpose, the two parameters describing the SPI model, the thresholds and the weights, are analytically derived from the PPI model, which constitutes a main contribution of the paper. As an illustration, the effectiveness of the compensator is demonstrated through simulation and experimental results attained with a piezoelectric micro-positioning stage. Both the simulation and experimental results show that the SPI model can serve as an effective feedforward hysteresis compensator and can thus enhance the tracking/positioning precision of the piezoelectric actuators.