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Mathematical models of shape memory alloy behavior for online and fast prediction of the hysteretic behavior

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Abstract

In this contribution, a new closed form of a mathematical model of Nickel–Titanium (NiTi) shape memory alloy (SMA) and its thermo-mechanical wire hysteresis behavior is developed. The approach is based on experimental data. The behavior of the heated and naturally cooled wire is modeled by mathematical expression. The cycle of heating and cooling is performed under a constant load. The prediction of the hysteretic behavior is realized through models adaptation, as predetermination, or real time determination of the models values, is developed and presented in detail. Simulations for position control using PID controller is shown for comparison purposes. The developed approach is incorporated in a feed forward control scheme. A comparison between the actual position and the predicted models position shows promising results.

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Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering, Birzeit University, Birzeit, Palestine

    Hassan Shibly

  2. Chair of Dynamics and Control, Faculty of Engineering Sciences, University of Duisburg-Essen, 47048, Duisburg, Germany

    Dirk Söffker

Authors
  1. Hassan Shibly
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  2. Dirk Söffker
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Correspondence to Hassan Shibly.

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Shibly, H., Söffker, D. Mathematical models of shape memory alloy behavior for online and fast prediction of the hysteretic behavior. Nonlinear Dyn 62, 53–66 (2010). https://doi.org/10.1007/s11071-010-9698-2

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  • DOI: https://doi.org/10.1007/s11071-010-9698-2

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