Distributed PCHD-Systems, from the Lumped to the Distributed Parameter Case
The Hamiltonian approach has turned out to be an effective tool for modeling, system analysis and controller design in the lumped parameter case. There exist also several extensions to the distributed parameter case. This contribution presents a class of extended distributed parameter Hamiltonian systems, which preserves some useful properties of the well known class of Port Controlled Hamiltonian systems with Dissipation. In addition, special ports are introduced to take the boundary conditions into account. Finally, an introductory example and the example of a piezoelectric structure, a problem with two physical domains, show, how one can use the presented approach for modeling and design.
KeywordsDistributed Parameter Systems Hamiltonian Systems with Input and Dissipation
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- 2.Curtain R F, Zwart H J (1995) An Introduction to Infinite-Dimensional Linear System Theory. Springer VerlagGoogle Scholar
- 3.Ennsbrunner H (2006) Infinite Dimensional Euler-Lagrange and Port Hamiltonian Systems, PhD Thesis at the Johannes Kepler University, Linz, AustriaGoogle Scholar
- 4.Ennsbrunner H, Schlacher K (2005) On the geometrical representation and interconnection of infinite dimensional port controlled hamiltonian systems, Proceedings of 44th IEEE Conference on Decision and ControlGoogle Scholar
- 8.Nowacki W (2006) Static and Dynamic Coupled Fields in Bodies with Piezoeffects or Polarization Gradient. Springer VerlagGoogle Scholar
- 10.Schlacher K (2006) Mathematical modelling for nonlinear control-a hamiltonian approach, Proceedings of 5th Vienna Symposium on Mathematical ModellingGoogle Scholar
- 13.Zeidler E (1995) Applied Functional Analysis. Springer Verlag, New YorkGoogle Scholar