A new approach to hysteresis modelling for a piezoelectric actuator using Preisach model and recursive method with an application to open-loop position tracking control

This paper proposes a novel recursive approach to model and control of a piezoelectric actuator featured by inherent hysteresis behaviors. It is known that the classical Preisach model consisting of triangle elements is ideal for discontinuous relays, but the output values jump at frontiers of the consecutive relays. In order to overcome this disadvantage, in this work a new solution approach is proposed in which the fundamental elements are suggested so that their weights concentrate just along their own diagonal. With such elements, there is neither jump at frontiers of consecutive elements nor any interpolation needed to obtain an output. In addition, a recursive method, which requires very few computational load, is proposed to determine the output of the model. Based on the proposed approach to hysteresis modelling, an open-loop control algorithm for compensating a rate-independent hysteresis is formulated without utilizing an inverse model. It is verified through experimental implementation that the effectiveness of the hysteresis identification is high and position (displacement) tracking control results achieved from the proposed approach without compensator inversion are excellent.