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

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Advanced Dynamics and Control of Structures and Machines

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 444))

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.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Twente, Enschede, The Netherlands

    A. J. van der Schaft

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  1. A. J. van der Schaft
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Editors and Affiliations

  1. Johannes Kepler University of Linz, Austria

    Hans Irschik  & Kurt Schlacher  & 

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van der Schaft, A.J. (2004). Port-Hamiltonian Systems: Network Modeling and Control of Nonlinear Physical Systems. In: Irschik, H., Schlacher, K. (eds) Advanced Dynamics and Control of Structures and Machines. International Centre for Mechanical Sciences, vol 444. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2774-2_9

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  • DOI: https://doi.org/10.1007/978-3-7091-2774-2_9

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-22867-8

  • Online ISBN: 978-3-7091-2774-2

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