Generalized Prandtl-Ishlinskii Hysteresis Model: Hysteresis Modeling and Its Inverse for Compensation in Smart Actuators

Smart actuators such as magnetorestrictive actuators, shape memory alloy (SMA) actuators, and piezoceramic actuators exhibit different hysteresis loops. In this paper, a generalized Prandtl-Ishlinskii model is utilized for modeling and compensation of hysteresis nonlinearities in smart actuators. In the formulated model, a generalized play operator together with a density is integrated to form the generalized Prandtl-Ishlinskii model. The capability of the formulated model to characterize hysteresis in smart actuators is demonstrated by comparing its outputs with experimental results obtained from different smart actuators. As an example, hysteresis nonlinearities of the magnetostrictive and SMA actuators are characterized by the generalized Prandtl-Ishlinskii model. Furthermore, an analytical inverse of the generalized Prandtl-Ishlinskii model is derived for compensations in different smart actuators. In other words, exact inverse of the generalized Prandtl-Ishlinskii model is achievable and it can be implemented as a feedforward compensator to migrate the effects of the hysteresis in different types of smart actuators. Such compensation is experimentally illustrated by piezoceramic actuator.