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
2004
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), .
(doi:10.1137/S0363012903431785).
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.
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Published date: 2004
Keywords:
dissipative acoustics, noise reduction, active control, optimal control problem, finite element approximation
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Local EPrints ID: 10406
URI: http://eprints.soton.ac.uk/id/eprint/10406
PURE UUID: a6db6108-4a4d-4c0d-8208-aab4142c5aaf
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Date deposited: 09 Jun 2005
Last modified: 15 Mar 2024 04:59
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Author:
A. Bermudez
Author:
P. Gamallo Ponte
Author:
E. Rodriguez
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