HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Reports

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.
Document type :
Reports
Complete list of metadata

https://hal.inria.fr/inria-00074001
Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Wednesday, May 24, 2006 - 2:16:23 PM
Last modification on : Thursday, February 3, 2022 - 11:16:01 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:31:04 PM

Identifiers

  • HAL Id : inria-00074001, version 1

Collections

Citation

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

Share

Metrics

Record views

135

Files downloads

260