Authors

Alessandro Macchelli, Stefano Stramigioli, Arjan van der Schaft, Claudio Melchiorri

Abstract

In this paper, a passive control scheme for port Hamiltonian systems with dissipation (PHD) is presented. The control scheme is able to conserve the PHD structure of the system when constrained on a sub-manifold of the state space. The idea is to modify both the interconnection and damping structures of the system and to add a proper dynamical extension in such a way that the constraint can be related to some dynamical invariants of the resulting closed-loop system. Since part of the structure of this dynamical extension can be arbitrarily chosen, it is also possible to drive the state of the system on the constraint and to obtain the dynamical behavior defined by the constraint. For example, if a proper variable structure dynamical extension is chosen, it is possible to achieve a sliding-mode behavior that can be interpreted by means of energetic considerations.

Keywords

Hamiltonian systems; Casimir functions; constrained dynamics; sliding mode

Citation

  • Journal: IFAC Proceedings Volumes
  • Year: 2002
  • Volume: 35
  • Issue: 1
  • Pages: 13–18
  • Publisher: Elsevier BV
  • DOI: 10.3182/20020721-6-es-1901.00252
  • Note: 15th IFAC World Congress

BibTeX

@article{Macchelli_2002,
  title={{CONSIDERATIONS ON THE ZERO-DYNAMICS OF PORT HAMILTONIAN SYSTEMS AND APPLICATION TO PASSIVE IMPLEMENTATION OF SLIDING-MODE CONTROL}},
  volume={35},
  ISSN={1474-6670},
  DOI={10.3182/20020721-6-es-1901.00252},
  number={1},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Macchelli, Alessandro and Stramigioli, Stefano and Schaft, Arjan van der and Melchiorri, Claudio},
  year={2002},
  pages={13--18}
}

Download the bib file

References

  • Maschke, Port-controlled hamiltonian systems: modeling origins and system theoretic approach. Proc. 2nd IFAC NOLCOS, Bordeaux (1992)
  • Nijmeijer, (1991)
  • Ortega, Interconnection and damping assignment passivity-based control of port-controlled hamiltonian system. Automatica (2000)
  • SIRA-RAMIREZ, H. Differential geometric methods in variable-structure control. International Journal of Control 48, 1359–1390 (1988) – 10.1080/00207178808906256
  • Sira-Ramirez, A general canonical form for sliding-mode control of non-linear systems. Proc. ECC’99, Karlsruhe, Germany (1999)
  • Stramigioli, (2001)
  • van der Schaft, (1999)