In this paper, a first-order system with hysteretic characteristics is used to describe the hysteresis caused by the inertia of the internal magnetic domain of magnetostrictive materials. A shape function is introduced to describe the interaction of different magnetic domains inside of magnetostrictive materials and the saturation properties of the hysteresis. Under a proposed frame of “first-order system (inertial system) + shape function” (ISSF-Duhem model), a new hysteresis model is proposed for magnetostrictive actuators. Specifically, the expression of the first-order system is constructed based on its general expression, and the Grompertz function is employed as the shape function. Feasibility and capability of the hysteresis model are verified and evaluated by describing and predicting the hysteresis of a commercial magnetostrictive actuator.
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