Abstract
Hysteresis of the actuators based on magnetostrictive materials influences the control performance of the application systems. It is of importance and significance to establish an effective hysteresis model for the magnetostrictive actuators for precision engineering. In this paper, based on the analysis of the Duhem model, a first-order inertial system with hysteresis characteristic under harmonic input is used to describe the hysteresis caused by the inertia of the magnetic domains of magnetostrictive materials. Shape function is employed to describe the pinning of domain walls, the interactions of different magnetic domains of magnetostrictive materials, and the saturation properties of the hysteresis. Specifically, under an architecture of “inertial system + shape function” (ISSF-Duhem model), firstly a new hysteresis model is proposed for magnetostrictive actuators. The formulation of the inertial system is constructed based on its general expression, which is capable of describing the hysteresis characteristics of magnetostrictive actuators. Then, the developed models with a Grompertz function-based shape function, a modified hyperbolic tangent function-based shape function employing an exponential function as an offset function, a one-sided dead-zone operator-based shape function are compared with each other, and further compared with the classic modified Prandtl–Ishlinskii model with a one-sided dead-zone operator. Sequentially, feasibility and capability of the proposed hysteresis model are verified and evaluated by describing and predicting the hysteresis characteristics of a commercial magnetostrictive actuator.
Highlights
Magnetostrictive materials, a smart material, produce mechanical stress and strain when exposed to external magnetic fields [1]
A differential equation of the inertial system is used to represent the hysteresis caused by the inertia in the motion of magnetic domains, and a general expression of the inertial system describing the hysteresis is established
Based on the analyses of the Duhem model and the causes of hysteresis of magnetostrictive materials, introducing the concept of inertial system and shape function, the ISSF-Duhem model for describing the hysteresis of magnetostrictive actuators featured with saturation and asymmetry is proposed and investigated in this paper
Summary
Magnetostrictive materials, a smart material, produce mechanical stress and strain when exposed to external magnetic fields [1]. Similar to other smart material-based actuators [4,5,6,7,8], such as piezoelectric ceramic-based actuators and shape memory alloy-based actuators, the magnetostrictive actuators behave strong hysteresis nonlinearity [9,10]. Such hysteresis nonlinearity would decrease the actuating accuracy and degrade control system performance.
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