A Generalized Asymmetric Prandtl-Ishlinskii Model for Characterizing Hysteresis Nonlinearities

Smart material actuators, as an example, invariably exhibit hysteresis that may be either symmetric or asymmetric depending upon the actuation principle. A classical Prandtl-Ishlinskii model is normally used to describe the symmetric hysteresis. A generalized play operator is formulated and integrated to the Prandtl - Ishlinskii model together with density function to describe asymmetric hysteresis nonlinearities. This hysteresis operator is analysed using different envelop functions in order to illustrate the influence of these functions on the outputs of the generalized Prandtl-Ishlinskii model. Parameters identification for the envelope functions of the generalized play operator and the proposed density function are carried out using a nonlinear optimization technique. The validity of the generalized model is demonstrated by comparing its displacement responses with the measured asymmetric responses obtained for magentostrictive actuator. The results suggest that unlike the classical Prandtl-Ishlinskii model, the generalized Prandtl-Ishlinskii can effectively characterize asymmetric hysteresis properties.