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A differential model for the hysteresis in magnetic shape memory alloys and its application of feedback linearization

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Abstract

Magnetic shape memory alloys (MSMAs) are materials with strong nonlinearity, which will show hysteresis when it works. In the current paper, a differential model is proposed to describe the hysteresis in MSMAs caused by magnetic field induced martensite reorientation based on Landau theory of phase transitions. First, the three-dimensional model is simplified into a one-dimensional case, and the hysteresis in MSMAs is described by three martensite variant orientations. Then, a traditional Landau free energy is introduced, and the traditional Landau model is obtained by using the Euler–Lagrange equation. However, it is found that the prediction accuracy of the model is not ideal compared with the experimental data. Thus, an improved model is proposed, and the traditional Landau free energy is replaced by a function that can be determined by the easily measured physical quantities in the experimental curve. Numerical experiments show that the prediction effect of the improved model is much better than the traditional Landau model, and the stress dependence is also demonstrated. Moreover, the proposed improved model has the advantages for dynamic analysis and control with its differential form. Therefore, the frequency dependence of the improved model is demonstrated and a feedback linearization control methodology is proposed to make the system develops in the desired trajectory.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51575478 and 61571007).

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Authors and Affiliations

  1. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Haoyuan Du, Yuxiang Han & Linxiang Wang

  2. MS2Dicovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, N2L 3L5, Canada

    Roderick Melnik

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  1. Haoyuan Du
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  2. Yuxiang Han
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Correspondence to Linxiang Wang.

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Du, H., Han, Y., Wang, L. et al. A differential model for the hysteresis in magnetic shape memory alloys and its application of feedback linearization. Appl. Phys. A 127, 432 (2021). https://doi.org/10.1007/s00339-021-04533-6

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