A Generalized Play Operator for Modeling and Compensation of Hysteresis Nonlinearities

Abstract

Smart actuators, such as shape memory alloy and magnetostrictive actuators, exhibit saturation nonlinearity and hysteresis that may be symmetric or asymmetric. The Prandtl-Ishlinskii model employing play operators has been used to describe the hysteresis properties of smart actuators that are symmetric in nature. In this paper, the application of a generalized play operator capable of characterizing symmetric as well as asymmetric hysteresis properties with output saturation is explored in formulating a generalized Prandtl-Ishlinskii model. Since the proposed generalized model is a mere extension of the analytically invertible Prandtl-Ishlinskii model, an inverse of the generalized model is formulated using the inverse of the Prandtl-Ishlinskii model together with those of the envelope functions of the generalized play operator. The effectiveness of the inverse of the generalized model in compensating for the hysteresis effects is subsequently investigated through simulations and experiments performed on a piezoceramic actuator. The simulation results suggest that the inverse of the generalized Prandtl-Ishlinskii model can be conveniently applied as a feedforward controller to compensate for hysteresis nonlinearities.