Coupling between hyperbolic and diffusive systems: A port-Hamiltonian formulation

Authors

Yann Le Gorrec, Denis Matignon

Abstract

The aim of this paper is to study a conservative wave equation coupled to a diffusion equation. This coupled system naturally arises in musical acoustics when viscous and thermal effects at the wall of the duct of a wind instrument are taken into account. The resulting equation, known as the Webster–Lokshin model, has variable coefficients in space, and a fractional derivative in time. This equation can be recast into the port Hamiltonian framework by using the diffusive representation of the fractional derivative in time and a multiscale state space representation. The port-Hamiltonian formalism proves adequate to reformulate this coupled system, and could enable another well-posedness analysis, using classical results from port-Hamiltonian systems theory.

Keywords

Energy storage; Port-Hamiltonian systems; Partial differential equations; Fractional derivatives; Diffusive representation

Citation

• Journal: European Journal of Control
• Year: 2013
• Volume: 19
• Issue: 6
• Pages: 505–512
• Publisher: Elsevier BV
• DOI: 10.1016/j.ejcon.2013.09.003
• Note: Lagrangian and Hamiltonian Methods for Modelling and Control

BibTeX

@article{Le_Gorrec_2013,
  title={{Coupling between hyperbolic and diffusive systems: A port-Hamiltonian formulation}},
  volume={19},
  ISSN={0947-3580},
  DOI={10.1016/j.ejcon.2013.09.003},
  number={6},
  journal={European Journal of Control},
  publisher={Elsevier BV},
  author={Le Gorrec, Yann and Matignon, Denis},
  year={2013},
  pages={505--512}
}

Download the bib file

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