Novel models for one-sided hysteresis of piezoelectric actuators

The hysteretic behavior of a plant with a non-negative input, referred to as one-sided hysteresis, is characterized by an initial ascending curve and hysteresis loops. It is observed that the widely-used classical Preisach hysteresis model and its modifications cannot represent such one-sided hysteresis due to the limitation of the Preisach hysteresis operator. To address this issue, a novel hysteresis operator modified from the Preisach hysteresis operator is proposed in this study and on this basis, a rate-independent hysteresis model and a rate-dependent hysteresis model are developed with methods to estimate their parameters. An algorithm to invert the rate-independent hysteresis model and its application to tracking control are also presented. The models and control schemes developed were verified experimentally on a commercially-available piezoelectric actuator. The results obtained show that the models developed are promising to represent the one-sided hysteresis of the piezoelectric actuator and that the inverting algorithm of the rate-independent hysteresis model is effective as applied to the tracking control of piezoelectric actuators.