Analysis of the behavior of coupled loudspeakers in a MIMO ANC system in an enclosure

Abstract

In this paper the problem of coupling of acoustic sources in a confined space is treated. By considering the coupling of sources in a rectangular enclosure the set of coupled equations governing the acoustical behavior of enclosure are solved. The resulted model can be used to analyze the behavior of a multi-input multi-output (MIMO) active noise control (ANC) system in real application where coupling of sources can not be neglected. Comparison of results to the case that coupling will be ignored among loudspeakers shows that coupling will effectively change the strength of sources and hence the required voltage signals to drive the loudspeakers. The developed model gives an improved description of the acoustic environment inside the rectangular enclosure, especially in an ANC system when sources are placed in a fraction of wavelength and the interaction among sources will change the radiation impedance of other sources

Modeling and analysis of secondary sources coupling for active sound field reduction in confined spaces

“…The list of all parameters in equations (9) to (11) along with their definitions are presented in Table 1. The detailed derivation of equations (9) to (11) is presented in [16] and to avoid duplication it is not repeated here. The most important indication of relation (9), is that the volume velocity ) (ω i U is determined as a result of the voltage applied to the terminals of the loudspeaker and the acoustic pressure on the surface of the loudspeaker as a result of coupling with other loudspeakers through acoustic modes of the enclosure.…”

“…. These results for two loudspeakers are presented in reference [16]. However, for the sake of clarity on how to derive the results for L loudspeakers, it is repeated here for a single loudspeaker.…”

“…Proof: to be able to find the inverse in the left-hand side of (58), GX must be assumed to be full rank. Multiplying of both sides of equation 58 Proof: the theorem can be proved by following exactly the same steps as given by reference [16] and hence is not repeated here. In this manner, it can be shown:…”

“…However, relatively few articles to date have studied coupling of acoustic sources within a working environment [12,21] and in the context of an active control system. A preliminary investigation by the present first author on modeling coupling of a loudspeaker with the acoustic modes in an enclosed space is reported in [16] where the results for two loudspeakers when no microphone is available are presented. In this article, we extend these results to an array of L loudspeakers and M microphones, and investigate the effect of coupling of secondary sources on the overall performance of an active sound control system in a confined space.…”

Active shielding base don implicit and decentralized control

“…[18] also finds that structural modes and acoustic modes interfere each other only if they are in the same cluster. Montazeri et al coupled the acoustic environment not only with the structural, but also the loudspeakers of the active noise control [20,21]. The case of an aperture such a window is analyzed by [22].…”