CONTROL BY INTERCONNECTION FOR DISTRIBUTED PORT HAMILTONIAN SYSTEMS

Authors

Alessandro Macchelli, Arjan van der Schaft, Claudio Melchiorri

Abstract

In this paper, new results on the control of distributed parameter systems in port Hamiltonian form are presented. The control by interconnection and energy shaping is applied to the stabilization of a distributed parameter system by means of a finite dimensional controller. The regulator acts on the system through the boundary or the distributed port. The key point is the generalization of Casimir function for systems resulting from the power conserving interconnection of an infinite and a finite dimensional part.

Keywords

Port-Hamiltonian systems; Infinite-dimensional systems; Energy-shaping

Citation

Journal: IFAC Proceedings Volumes
Year: 2005
Volume: 38
Issue: 1
Pages: 489–494
Publisher: Elsevier BV
DOI: 10.3182/20050703-6-cz-1902.00736
Note: 16th IFAC World Congress

BibTeX

@article{Macchelli_2005,
  title={{CONTROL BY INTERCONNECTION FOR DISTRIBUTED PORT HAMILTONIAN SYSTEMS}},
  volume={38},
  ISSN={1474-6670},
  DOI={10.3182/20050703-6-cz-1902.00736},
  number={1},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Macchelli, Alessandro and van der Schaft, Arjan and Melchiorri, Claudio},
  year={2005},
  pages={489--494}
}

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References

Dalsmo, On representation and integrability of mathematical structures in energy-conserving physical systems. SIAM J. Control and Optimization (1999)
Macchelli, A., van der Schaft, A. J. & Melchiorri, C. Port Hamiltonian formulation of infinite dimensional systems I. Modeling. 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) 3762-3767 Vol.4 (2004) doi:10.1109/cdc.2004.1429324 – 10.1109/cdc.2004.1429324
Macchelli, A., van der Schaft, A. J. & Melchiorri, C. Port Hamiltonian formulation of infinite dimensional systems II. Boundary control by interconnection. 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) 3768-3773 Vol.4 (2004) doi:10.1109/cdc.2004.1429325 – 10.1109/cdc.2004.1429325
Marsden, (1994)
Ortega, R., van der Schaft, A. J. & Maschke, B. M. Stabilization of port-controlled Hamiltonian systems via energy balancing. Lecture Notes in Control and Information Sciences 239–260 (1999) doi:10.1007/1-84628-577-1_13 – 10.1007/1-84628-577-1_13
Renardy, (2004)
van der Schaft, (2000)
van der Schaft, A. J. & Maschke, B. M. Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics 42, 166–194 (2002) – 10.1016/s0393-0440(01)00083-3