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Stable Realization of a Delay System Modeling a Convergent Acoustic Cone

Mignot, Rémi and Hélie, Thomas and Matignon, Denis Stable Realization of a Delay System Modeling a Convergent Acoustic Cone. (2008) In: 16th IEEE workshop on Mediterranean Control Conference, 25-27 Jun 2008, Ajaccio, France .

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Official URL: http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=4602095

Abstract

This paper deals with the physical modeling and the digital time simulation of acoustic pipes. We will study the simplified case of a single convergent cone. It is modeled by a linear system made of delays and a transfer function which represents the wave reflection at the entry of the cone. According to [1], the input/output relation of this system is causal and stable whereas the reflection function is unstable. In the continuous time-domain, a first state space representation of this delay system is done. Then, we use a change of state to separate the unobservable subspace and its orthogonal complement, which is observable. Whereas the unobservable part is unstable, it is proved that the observable part is stable, using the D-Subdivision method. Thus, isolating this latter observable subspace, to build the minimal realization, defines a stable system. Finally, a discrete-time version of this system is derived and is proved to be stable using the Jury criterion. The main contribution of this work is neither the minimal realization of the system nor the proofs of stability, but it is rather the solving of an old problem of acoustics which has heen achieved using standard tools of automatic control.

Item Type:Invited Conference
Additional Information:Thanks to IEEE editor. (c) 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. The definitive version is available at http://ieeexplore.ieee.org
Audience (conference):International conference proceedings
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Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Institut de Recherche et Coordination Acoustique/Musique - IRCAM (FRANCE)
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Deposited By: Denis Matignon
Deposited On:26 Apr 2013 11:53

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