Compensation of play operator-based Prandtl-Ishlinskii hysteresis model using a stop operator with application to piezoelectric actuators

Abstract

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