Interconnections of port-Hamiltonian systems: generating new passive outputs and feedback stabilization

Authors

A. Venkatraman, A.J. van der Schaft

Abstract

We consider port-Hamiltonian system models whose underlying geometric structure is the Dirac structure which consists of energy storing ports, resistive ports and external ports which are interconnected to each other by a power conserving relationship. A port-Hamiltonian system with dissipation (PHSD) is formed by the composition of a Dirac and a resistive structure. We show how the choice of a new passive output for a PHSD is reflected in a new Dirac structure. We generate a new class of passive outputs for a PHSD by changing the Hamiltonian function, interconnection and damping matrices and subsequently compute the new underlying Dirac structure. We next consider power conserving interconnections of two port-Hamiltonian systems and extend the (well known) standard feedback interconnection by considering interconnections between port-Hamiltonian systems which involve their energy storing ports, resistive ports and external ports. For port-Hamiltonian systems with dissipation, we demonstrate how these interconnections can be used for their closed-loop stabilization by the control-by-interconnection (CbI) method. Finally, we discuss the similarities between our (new) control by interconnection method and the (well-known) interconnection and damping assignment passivity-based control (IDA-PBC) method.

Citation

• Journal: IFAC Proceedings Volumes
• Year: 2010
• Volume: 43
• Issue: 14
• Pages: 605–610
• Publisher: Elsevier BV
• DOI: 10.3182/20100901-3-it-2016.00227
• Note: 8th IFAC Symposium on Nonlinear Control Systems

BibTeX

@article{Venkatraman_2010,
  title={{Interconnections of port-Hamiltonian systems: generating new passive outputs and feedback stabilization}},
  volume={43},
  ISSN={1474-6670},
  DOI={10.3182/20100901-3-it-2016.00227},
  number={14},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Venkatraman, A. and van der Schaft, A.J.},
  year={2010},
  pages={605--610}
}

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References

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