Boundary Energy Shaping of Linear Distributed Port-Hamiltonian Systems* *This work was partially supported by the Austrian Center of Competence in Mechatronics (ACCM).

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* *This work was partially supported by the Austrian Center of Competence in Mechatronics (ACCM).}},
  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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