Experimental comparison of some phenomenological hysteresis models in characterizing hysteresis behavior of shape memory alloy actuators

Abstract

Among the phenomenological hysteresis models, the Preisach model, Krasnosel’skii–Pokrovskii model, and Prandtl–Ishlinskii model have found extensive applications for modeling hysteresis in shape memory alloys and other smart actuators. Since the mathematical complexity of the identification and inversion problem depends directly on the type of phenomenological hysteresis modeling method, choosing a proper phenomenological model among the mentioned models for modeling the hysteretic behavior of shape memory alloy actuators is a task of crucial importance. Moreover, the accuracy of the hysteresis modeling method in characterizing shape memory alloy hysteretic behavior consequently affects the whole compensator design task. In this article, the accuracy of the mentioned phenomenological models in characterizing and predicting the hysteretic behavior of shape memory alloy actuators is experimentally compared. It will be shown that although, unlike the Preisach and Krasnosel’skii–Pokrovskii models, the identification process of the Prandtl–Ishlinskii model is a time-consuming process, it leads to the best results when the outputs of these models are compared with the experimental data. Since the Prandtl–Ishlinskii model is also analytically invertible and can be easily implemented as a feed-forward controller for compensating the hysteretic nonlinearity behavior of shape memory alloy actuators, it seems to be the best model for modeling and compensating the hysteretic behavior of shape memory alloy actuators.