Dither in Systems with Hysteresis

Abstract : This paper deals with differential inclusion containing an hysteresis nonlinearity and two inputs: a control input and a dither input of high frequency. Conditions are introduced under which its solution admits asymptotic behavior when the dither frequency goes to infinity. According to asymptotic growth of the dither amplitude, two different behaviors appear: the nonlinearity is smoothed (resp. quenched) if the velocities induced by the dither are asymptotically bounded (resp. unbo- unded). Convergence results for finite and infinite time intervals are given, and linked with the averaging principle. The case of bounded dithering velocities is of interest in a mechanical context, where hysteresis is used to model dry friction. A very interesting feature is that the averaged hysteresis operator may be linearized for small velocities. The hypotheses on the dither include periodicity, $F$-repetitiveness and (asymptotic) almost-periodicity.
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Rapport
[Research Report] RR-2690, INRIA. 1995
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https://hal.inria.fr/inria-00074001
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Soumis le : mercredi 24 mai 2006 - 14:16:23
Dernière modification le : vendredi 25 mai 2018 - 12:02:04
Document(s) archivé(s) le : dimanche 4 avril 2010 - 21:31:04

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  • HAL Id : inria-00074001, version 1

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Pierre-Alexandre Bliman, Alexander M. Krasnosel'Skii, Michel Sorine. Dither in Systems with Hysteresis. [Research Report] RR-2690, INRIA. 1995. 〈inria-00074001〉

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