Optimization of power in the problems of active control of sound
We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulation of the problem. We have also obtained optimal solutions that minimize the L-1 or L-2 norm of the control sources; the physical interpretation of the former being the overall absolute acoustic source strength. In the current paper, we minimize the power required for the operation of the active control system. It turns out that the corresponding analysis necessarily involves interaction between the sources of sound and the surrounding acoustic field, which was not the case for either L-1 or L-2. Even though it may first seem counterintuitive, one can build a control system (a particular combination of surface monopoles and dipoles) that would require no power input for operation and would even produce a net power gain while providing the exact noise cancellation. This usually comes at the expense of having the original sources of noise produce even more energy. (C) 2004 IMACS. Published by Elsevier B.V. All rights reserved.
general solution monopoles and dipoles net power gain noise cancellation active control sources volumetric and surface controls radiation of waves complex-valued quantities load on the sources by the field