Synchronous exploration for the control of real-time external noise suppression in a three-dimensional subdomain

V. S. Ryaben'kii

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 10, pp. 1889-1904

Résumé

A mathematical (difference) model is proposed for a real-time active shielding device that shields an acoustic field in a given subdomain from the influence of sound sources located in an additional subdomain. An algorithm for computing the current control ensuring a prescribed process is based on information produced by the author’s technique of synchronous weak noise exploration. This information can be measured in real time. Active control problems for nonstationary solutions of linear difference equations in a three-dimensional domain consisting of two subdomains are studied using the difference potential method. The shape of the domain and the boundary conditions may depend on time, while the coefficients may depend on time and spatial coordinates. If the difference problem is a mathematical model of sound propagation, the goal of control is to change the acoustic field in the given subdomains, for example, to shield the acoustic field in one subdomain from the undesirable influence (noise) of sources located in the other subdomain.

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