Port-Hamiltonian Systems: Network Modeling and Control of Nonlinear Physical Systems

Authors

A. J. Schaft

Abstract

It is shown how port-based modeling of lumped-parameter complex physical systems (multi-body systems, electrical circuits, electromechanical systems,..) naturally leads to a geometrically defined class of systems, called port-Hamiltonian systems. These are Hamiltonian systems defined with respect to a power-conserving geometric structure capturing the basic interconnection laws, and a Hamiltonian function given by the total stored energy. The structural properties of port-Hamiltonian systems are discussed, in particular the existence of Casimir functions and its implications for stability and stabilization. Furthermore it is shown how passivity-based control results from interconnecting the plant port-Hamiltonian system with a controller port-Hamiltonian system, leading to a closed-loop port-Hamiltonian system. Finally, extensions to the distributed-parameter case are provided by formulating boundary control systems as infinite-dimensional port-Hamiltonian systems.

Keywords

Hamiltonian System; Multibody System; Kinematic Constraint; Dirac Structure; Bond Graph

Citation

• ISBN: 9783211228678
• Publisher: Springer Vienna
• DOI: 10.1007/978-3-7091-2774-2_9

BibTeX

@inbook{Schaft_2004,
  title={{Port-Hamiltonian Systems: Network Modeling and Control of Nonlinear Physical Systems}},
  ISBN={9783709127742},
  DOI={10.1007/978-3-7091-2774-2_9},
  booktitle={{Advanced Dynamics and Control of Structures and Machines}},
  publisher={Springer Vienna},
  author={Schaft, A. J.},
  year={2004},
  pages={127--167}
}

Download the bib file

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