A generalized Prandtl–Ishlinskii model for characterizing the hysteresis and saturation nonlinearities of smart actuators

Smart actuators, such as shape memory alloy (SMA) and magnetostrictive actuators, exhibit saturation nonlinearity and hysteresis that may be symmetric or asymmetric. The Prandtl–Ishlinskii model employing classical play operators has been used to describe the hysteresis properties of smart actuators that are symmetric in nature. In this study, 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. The generalized play operator employs different envelope functions under increasing and decreasing inputs to describe asymmetric and saturated output–input hysteresis loops. The validity of the proposed generalized model to characterize symmetric and asymmetric hysteresis properties is demonstrated by comparing the model responses with the measured major and minor hysteresis loops of three different types of actuator, namely SMA, magnetostrictive, and piezoceramic actuators. The simulation results suggest that the proposed generalized Prandtl–Ishlinskii model can be directly applied for modeling the hysteresis loops of different smart actuators together with the output saturation.