# P.I. Control of Nonlinear Oscillations for a System with Delay

Abstract : We study the periodic oscillations of a 1st order delayed linear system with relay output and proportional$+$integral feedback and describe the behavior of the general solutions of the closed loop. We present results on control of the oscillations and on rejection of the perturbations. For the system under study, we first exhibit a countable set of periodic limit cycles. We show that in the particular case where only proportional control is used, any solution tends in finite time towards one of the limit cycles (whose determination depends on the initial conditions). All the cycles are orbitally unstable except one of them, the only slowly oscillating one. Finally, we provide some well-posedness and ultimate boundedness results for a time-varying perturbed version of the system under study. The given estimates show that the proportional$+$integral feedback law permits to reject various parametric perturbations.
Keywords :
Type de document :
Rapport
[Research Report] RR-3422, INRIA. 1998
Domaine :

https://hal.inria.fr/inria-00077200
Contributeur : Rapport de Recherche Inria <>
Soumis le : lundi 29 mai 2006 - 17:18:57
Dernière modification le : vendredi 25 mai 2018 - 12:02:05
Document(s) archivé(s) le : lundi 5 avril 2010 - 21:43:33

### Identifiants

• HAL Id : inria-00077200, version 1

### Citation

Marianne Akian, Pierre-Alexandre Bliman, Michel Sorine. P.I. Control of Nonlinear Oscillations for a System with Delay. [Research Report] RR-3422, INRIA. 1998. 〈inria-00077200〉

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