The University of Southampton
University of Southampton Institutional Repository

Finite element methods in local active control of sound

Finite element methods in local active control of sound
Finite element methods in local active control of sound
The active control of sound is analyzed in the framework of the mathematical theory of optimal control. After setting the problem in the frequency domain, we deal with the state equation, which is a Helmholtz partial differential equation. We show the existence of a unique solution and analyze a finite element approximation when the source term is a Dirac delta measure. Two optimization problems are successively considered. The first one concerns the choice of phases and amplitudes of the actuators to minimize the noise at the sensors' location. The second one consists of determining the optimal actuators' placement. Both problems are then numerically solved. Error estimates are settled and numerical results for some tests are reported.
dissipative acoustics, noise reduction, active control, optimal control problem, finite element approximation
437-465
Bermudez, A.
27183172-1114-46d3-bbd9-141879027362
Gamallo Ponte, P.
363415df-73f7-43d1-9c0c-345261281ef2
Rodriguez, E.
647a092d-014a-4b88-8d89-b050e18f5417
Bermudez, A.
27183172-1114-46d3-bbd9-141879027362
Gamallo Ponte, P.
363415df-73f7-43d1-9c0c-345261281ef2
Rodriguez, E.
647a092d-014a-4b88-8d89-b050e18f5417

Bermudez, A., Gamallo Ponte, P. and Rodriguez, E. (2004) Finite element methods in local active control of sound. SIAM Journal on Control and Optimization, 43 (2), 437-465. (doi:10.1137/S0363012903431785).

Record type: Article

Abstract

The active control of sound is analyzed in the framework of the mathematical theory of optimal control. After setting the problem in the frequency domain, we deal with the state equation, which is a Helmholtz partial differential equation. We show the existence of a unique solution and analyze a finite element approximation when the source term is a Dirac delta measure. Two optimization problems are successively considered. The first one concerns the choice of phases and amplitudes of the actuators to minimize the noise at the sensors' location. The second one consists of determining the optimal actuators' placement. Both problems are then numerically solved. Error estimates are settled and numerical results for some tests are reported.

Full text not available from this repository.

More information

Published date: 2004
Keywords: dissipative acoustics, noise reduction, active control, optimal control problem, finite element approximation

Identifiers

Local EPrints ID: 10406
URI: https://eprints.soton.ac.uk/id/eprint/10406
PURE UUID: a6db6108-4a4d-4c0d-8208-aab4142c5aaf

Catalogue record

Date deposited: 09 Jun 2005
Last modified: 17 Jul 2017 17:06

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of https://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×