Geodesic
Inverse rate-dependent Prandtl-Ishlinskii operators and applications
Applications of Mathematics, Tome 68 (2023) no. 6, pp. 713-726 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.2023.0231-22
Classification : 47J40, 74N30
Keywords: hysteresis; Prandtl-Ishlinskii operator; inverse rate-dependent Prandtl-Ishlinskii operator 
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     title = {Inverse rate-dependent {Prandtl-Ishlinskii} operators and applications},
     journal = {Applications of Mathematics},
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Al Janaideh, Mohammad; Krejčí, Pavel; Monteiro, Giselle Antunes. Inverse rate-dependent Prandtl-Ishlinskii operators and applications. Applications of Mathematics, Tome 68 (2023) no. 6, pp. 713-726. doi: 10.21136/AM.2023.0231-22

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