NDLI: Stable realization of a delay system modeling a convergent acoustic cone

Content Provider	IEEE Xplore Digital Library
Author	Mignot, R. Helie, T. Matignon, D.
Copyright Year	2008
Description	Author affiliation: CNRS, IRCAM, Paris (Mignot, R.; Helie, T.)
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 been achieved using standard tools of automatic control.
Starting Page	1574
Ending Page	1579
File Size	250835
Page Count	6
File Format	PDF
ISBN	9781424425044
DOI	10.1109/MED.2008.4602095
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-06-25
Publisher Place	France
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Automation Conferences
Content Type	Text
Resource Type	Article

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