Network modelling of physical systems: a geometric approach

Authors

Arjan van der Schaft, Bernhard Maschke, Romeo Ortega

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.

Keywords

bond graph, dirac structure, distribute parameter system, hamiltonian system, poisson structure

Citation

• ISBN: 9781852333782
• Publisher: Springer London
• DOI: 10.1007/bfb0110387

BibTeX

@inbook{van_der_Schaft_2001,
  title={{Network modelling of physical systems: a geometric approach}},
  ISBN={9781846285707},
  ISSN={1610-7411},
  DOI={10.1007/bfb0110387},
  booktitle={{Advances in the control of nonlinear systems}},
  publisher={Springer London},
  author={van der Schaft, Arjan and Maschke, Bernhard and Ortega, Romeo},
  year={2001},
  pages={253--276}
}

Download the bib file

References

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