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Network modelling of physical systems: a geometric approach

  • Part IV Physics In Control
  • Conference paper
  • First Online:
Advances in the control of nonlinear systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 264))

Abstract

It is discussed how network modeling of lumped-parameter physical systems naturally leads to a geometrically defined class of systems, called port-controlled Hamiltonian systems (with dissipation). The structural properties of these systems are investigated, in particular the existence of Casimir functions and their implications for stability. It is shown how the power-conserving interconnection with a controller system which is also a port-controlled Hamiltonian system defines a closed-loop port-controlled Hamiltonian system; and how this may be used for control by shaping the internal energy. Finally, extensions to implicit system descriptions (constraints, no a priori input-output structure) are discussed.

This paper is an adapted and expanded version of [33]. Part of this material can be also found in [32].

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Author information

Authors and Affiliations

  1. Fac. of Mathematical Sciences, University of Twente, Enschede, The Netherlands

    Arjan van der Schaft

  2. Laboratoire d’Automatique et de Genie des Procedes, Université Claude Bernard — Lyon 1, Villeurbanne Cedex, France

    Bernhard Maschke

  3. Lab. des Signaux et Systèmes, CNRS-Supélec, Gif-sur-Yvette, France

    Romeo Ortega

Authors
  1. Arjan van der Schaft
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  2. Bernhard Maschke
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  3. Romeo Ortega
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Editor information

Alfonso Baños PhD Françoise Lamnabhi-Lagarrigue (Docteur D’état)Francisco J. Montoya PhD

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© 2001 Springer-Verlag London Limited

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van der Schaft, A., Maschke, B., Ortega, R. (2001). Network modelling of physical systems: a geometric approach. In: Baños, A., Lamnabhi-Lagarrigue, F., Montoya, F.J. (eds) Advances in the control of nonlinear systems. Lecture Notes in Control and Information Sciences, vol 264. Springer, London. https://doi.org/10.1007/BFb0110387

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  • DOI: https://doi.org/10.1007/BFb0110387

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  • Print ISBN: 978-1-85233-378-2

  • Online ISBN: 978-1-84628-570-7

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