A modified Prandtl–Ishlinskii modeling method for hysteresis

A modified Prandtl–Ishlinskii modeling method for rate-independent hysteresis in piezoelectric actuators is proposed in this paper. In this method, a generalized backlash operator (GBO) regarded as the elementary operator is introduced into the model so as to be more flexible for modeling of complex hysteresis. Moreover, the Levenberg–Marquardt algorithm is used to estimate the parameters of the model. Thus, all the parameters of the modified PI model can be determined automatically. From this way, it avoids the tedious procedure for the selection of the operator parameters by trial and error. Then, a group of proper Clarke subgradients of the GBO outputs with respect to their parameters at a non-smooth point is obtained based on the bundle method. Finally, the experimental results of applying the proposed method to the modeling of hysteresis in a piezoelectric actuator and an ultrasonic motor (USM) are illustrated, respectively.