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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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
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