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

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• 作者：Yann Le Gorrec ; Denis Matignon
• 关键词：Energy storage ; Port-Hamiltonian systems ; Partial differential equations ; Fractional derivatives ; Diffusive representation
• 刊名：European Journal of Control
• 出版年：December, 2013
• 年：2013
• 卷：19
• 期：6
• 页码：505-512
• 全文大小：280 K

文摘

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.