Modeling and Identification of Hysteresis in Piezoelectric Actuators

In this paper, a model and the associated identification procedure are proposed to precisely portray the hysteresis behavior in piezoelectric actuators. The model consists of basic physical elements and utilizes a Maxwell-slip structure to describe hysteresis. By analyzing the model, the influence of initial strain/charges on the hysteresis behavior is revealed. It is also found that if all the spring elements in the model are linear, the resultant hysteresis loop is anti-symmetric and does not match the experimental behavior. To account for this mismatch, a nonlinear spring element is included into the model. The constitutive relation of the nonlinear spring and the parameters of the basic elements in the model are identified from experimental data by linear programming. Simulations of the identified model indicate that the model can reproduce the major as well as the minor hysteresis loops. An inverse control is further implemented to validate the accuracy of the identified model. Experiments show that hysteresis is effectively canceled and accurate tracking of a reference trajectory is achieved.