Boundary Energy Shaping of Linear Distributed Port-Hamiltonian Systems

Authors

Abstract

This paper deals with the stabilization via Casimir generation and energy shaping of linear, lossless, distributed port-Hamiltonian systems. Once inputs and outputs of the distributed port-Hamiltonian system have been chosen to obtain a well-defined boundary control systems, conditions for the existence of Casimir functions in closed-loop and of the associated semigroup are given, together with a criterion to be used to check asymptotic stability. Casimir functions suggest how to select the controller Hamiltonian to introduce a minimum at the desired equilibrium, while stability is ensured if proper “pervasive” boundary damping is present. The methodology is illustrated with the help of a Timoshenko beam with full-actuation on one side.

Keywords

distributed port-Hamiltonian systems; energy shaping; Casimir functions

Citation

Journal: IFAC Proceedings Volumes
Year: 2012
Volume: 45
Issue: 19
Pages: 120–125
Publisher: Elsevier BV
DOI: 10.3182/20120829-3-it-4022.00041
Note: 4th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control

BibTeX

@article{Macchelli_2012,
  title={{Boundary Energy Shaping of Linear Distributed Port-Hamiltonian Systems}},
  volume={45},
  ISSN={1474-6670},
  DOI={10.3182/20120829-3-it-4022.00041},
  number={19},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Macchelli, Alessandro},
  year={2012},
  pages={120--125}
}

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References

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