Asymptotic stabilization of passive systems without damping injection: A sampled integral technique

  • Authors:

  • Daniele Casagrande;Alessandro Astolfi;Romeo Ortega

  • Affiliations:

  • Dipartimento di Ingegneria Elettrica, Gestionale e Meccanica, Universití degli Studi di Udine, Via delle Scienze, 208-33100 Udine, Italy;Department of Electrical and Electronic Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, UK and Dipartimento di Informatica, Sistemi e Produzione, Universití degli Studi ...;Laboratoire des Signaux et Systémes, Supelec, Plateau du Moulon, 91192 Gif-sur-Yvette, France

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2011

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Abstract

Passivity in physical systems is a restatement of energy balancing, and therefore is a ubiquitous property in engineering applications. Under some weak conditions, the unique equilibrium state of passive systems is stable. However, to ensure asymptotic stability, strict output passivity and a detectability property are required. Although strict output passivity may be enforced via a damping injection that feeds back the passive output, this signal may be noisy or unmeasurable - the paradigmatic example being velocity in mechanical systems. In this paper a sampled integral stabilization (SIS) technique for the asymptotic regulation of passive systems, that requires only the knowledge of the time integral of the passive output - i.e. position in mechanical systems - is proposed. As a generalization of the previous result, it is shown that SIS is applicable to cascade connections of passive systems measuring only the storage function of the second one. Several examples, including a planar elbow manipulator and the rigid body dynamics are shown to satisfy the assumptions for the application of SIS.