Inverse rate-dependent Prandtl-Ishlinskii operators and applications

Mohammad Al Janaideh; Pavel Krejčí; Giselle A. Monteiro

Applications of Mathematics (2023)

  • Volume: 68, Issue: 6, page 713-726
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Al Janaideh, Mohammad, Krejčí, Pavel, and Monteiro, Giselle A.. "Inverse rate-dependent Prandtl-Ishlinskii operators and applications." Applications of Mathematics 68.6 (2023): 713-726. <http://eudml.org/doc/299366>.

@article{AlJanaideh2023,
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.},
author = {Al Janaideh, Mohammad, Krejčí, Pavel, Monteiro, Giselle A.},
journal = {Applications of Mathematics},
keywords = {hysteresis; Prandtl-Ishlinskii operator; inverse rate-dependent Prandtl-Ishlinskii operator},
language = {eng},
number = {6},
pages = {713-726},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Inverse rate-dependent Prandtl-Ishlinskii operators and applications},
url = {http://eudml.org/doc/299366},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Al Janaideh, Mohammad
AU - Krejčí, Pavel
AU - Monteiro, Giselle A.
TI - Inverse rate-dependent Prandtl-Ishlinskii operators and applications
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 6
SP - 713
EP - 726
AB - 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.
LA - eng
KW - hysteresis; Prandtl-Ishlinskii operator; inverse rate-dependent Prandtl-Ishlinskii operator
UR - http://eudml.org/doc/299366
ER -

References

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