Development of rate independent Prandtl-Ishlinskii model for characterizing asymmetric hysteresis nonlinearities of SMA actuators

Shape memory alloy actuators (SMA) show asymmetric hysteresis loops between the input current and output displacement. Furthermore, the SMA actuators exhibit saturated output displacement at maximum and/or minimum input. A generalized Prandtl-Ishlinskii model is formulated to model hysteresis nonlinearities of SMA actuators. In this model, a generalized play hysteresis operator is proposed and integrated with a density function to construct generalized Prandtl-Ishlinskii model. The formulated generalized Prandtl-Ishlinskii model can also describe hysteresis loops with saturated output displacement. The results suggest that unlike the classical Prandtl-Ishlinskii model, the proposed Prandtl-Ishlinskii can effectively characterize hysteresis nonlinearities of the SMA actuators.