A port-Hamiltonian formulation of a 2D boundary controlled acoustic system

Authors

Vincent Trenchant, Yassine Fares, Hector Ramirez, Yann Le Gorrec

Abstract

This paper deals with the port Hamiltonian formulation of a 2D boundary controlled acoustic system. The system under consideration consits of an acoustic wave traveling in a tube equipped with a network of microphones/loudspeakers. The purpose of this smart skin is to damp the acoustic wave and reduce its effect at the output of the tube. It is first commented how the original 3D system can be reduced to a 2D system by considering symmetries. Then, the boundary port variables associated with the wave equation are parametrized in order to define a Dirac structure in two dimensions, compatible with the interconnection at the boundaries with the actuation system. The overall system (wave+actuators/sensors) is finally expressed as a port Hamiltonian control system and a first stabilizing distributed control law is proposed.

Keywords

Distributed Port-Hamiltonian systems; passivity based control; wave propagation

Citation

• Journal: IFAC-PapersOnLine
• Year: 2015
• Volume: 48
• Issue: 13
• Pages: 235–240
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2015.10.245
• Note: 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2015- Lyon, France, 4–7 July 2015

BibTeX

@article{Trenchant_2015,
  title={{A port-Hamiltonian formulation of a 2D boundary controlled acoustic system}},
  volume={48},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2015.10.245},
  number={13},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Trenchant, Vincent and Fares, Yassine and Ramirez, Hector and Le Gorrec, Yann},
  year={2015},
  pages={235--240}
}

Download the bib file

References

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