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inria-00423576, version 1

Implicit Euler numerical scheme and chattering-free implementation of sliding mode systems

Vincent Acary () 1, Bernard Brogliato () a, 1

Systems and Control Letters 59, 5 (2010) 284-295

Résumé : In this paper it is shown that the implicit Euler time-discretization of some classes of switching systems with sliding modes, yields a very good stabilization of the trajectory and of its derivative on the sliding surface. Therefore the spurious oscillations which are pointed out elsewhere when an explicit method is used, are avoided. Moreover the method (an event-capturing, or time-stepping algorithm) allows for multiple switching surfaces (i.e., a sliding surface of codimension ⩾2). The details of the implementation are given, and numerical examples illustrate the developments. This method may be an alternative method for chattering suppression, keeping the intrinsic discontinuous nature of the dynamics on the sliding surfaces. Links with discrete-time sliding mode controllers are studied.

  • a –  INRIA
  • 1 :  BIPOP (INRIA Grenoble Rhône-Alpes / LJK Laboratoire Jean Kuntzmann)
  • INRIA – Laboratoire Jean Kuntzmann
  • Domaine : Informatique/Modélisation et simulation
    Mathématiques/Optimisation et contrôle
  • Mots-clés : Switching systems – Filippov's differential inclusions – Complementarity problems – Backward Euler algorithm – Sliding modes – Maximal monotone mappings – Mixed linear complementarity problem – ZOH discretization
 
  • inria-00423576, version 1
  • http://hal.inria.fr/inria-00423576
  • oai:hal.inria.fr:inria-00423576
  • Contributeur : Vincent Acary <>
  • Soumis le : Lundi 12 Octobre 2009, 10:08:35
  • Dernière modification le : Dimanche 12 Mai 2013, 22:29:24