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Inverse rate-dependent Prandtl-Ishlinskii operators and applications

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Abstract

In the past years, we observed an increased interest in rate-dependent hysteresis models to characterize complex time-dependent nonlinearities in smart actuators. A natural way to include rate-dependence to the Prandtl-Ishlinskii model is to consider it as a linear combination of play operators whose thresholds are functions of time. In this work, we propose the extension of the class of rate-dependent Prandtl-Ishlinskii operators to the case of a whole continuum of play operators with time-dependent thresholds. We prove the existence of an analytical inversion formula, and illustrate its applicability in the study of error bounds for inverse compensation.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Memorial University, St. John’s, Newfoundland, A1B 3X5, Canada

    Mohammad Al Janaideh

  2. Faculty of Civil Engineering, Czech Technical University, Thákurova 7, 166 29, Praha 6, Czech Republic

    Pavel Krejčí

  3. Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67, Praha 1, Czech Republic

    Giselle Antunes Monteiro

Authors
  1. Mohammad Al Janaideh
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  2. Pavel Krejčí
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  3. Giselle Antunes Monteiro
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Corresponding author

Correspondence to Giselle Antunes Monteiro.

Additional information

The research was supported by GAČR Grant No. 20-14736S, RVO: 67985840 and by the European Regional Development Fund, Project No. CZ.02.1.01/0.0/0.0/16_019/0000778.

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Al Janaideh, M., Krejčí, P. & Monteiro, G.A. Inverse rate-dependent Prandtl-Ishlinskii operators and applications. Appl Math 68, 713–726 (2023). https://doi.org/10.21136/AM.2023.0231-22

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  • DOI: https://doi.org/10.21136/AM.2023.0231-22

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