A Modified Prandtl-Ishlinskii Model for Modeling Asymmetric Hysteresis of Piezoelectric Actuators

Piezoelectric actuators can offer high resolution of displacement and this makes them suitable for precise driving tasks. However, most piezoelectric actuators are made of piezoceramics which have a major drawback related to their natural hysteresis nonlinearity. To compensate the hysteresis nonlinearity of piezoelectric actuators, many hysteresis models have been proposed such as the Preisach model, the classical Prandtl-Ishlinskii model, and so on. This paper provides a new approach to model the asymmetric hysteresis nonlinearity of piezoelectric actuators. Unlike the classical Prandtl-Ishlinskii model, the proposed model is based on a combination of two asymmetric operators which can independently simulate the ascending branch and descending branch of hysteresis. Moreover, the proposed model can be calculated using the recursive least-squares method and this makes the model easy and convenient to be calculated. The validity of the proposed model is demonstrated by comparing its simulation results with experimental measurements. The results show that the proposed model is capable of modeling asymmetric hysteresis of piezoelectric actuators with very high accuracy.