Quadratic Optimization In The Problems Of Active Control Of Sound

Quadratic Optimization in the Problems of Active Control of Sound

Active Control of Noise and Vibration

This major work is the first to treat the active control of both sound and vibration in a unified way. It outlines the fundamental concepts, explains how a reliable and stable system can be designed and implemented, and details the pitfalls . It covers sound in ducts, sound radiation, sound transmission into enclosures, structural vibration and isolation, electronic control system design, and sensors and actuators.

Quadratic Optimization 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 formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).Loncaric, J. and Tsynkov, S. V. and Bushnell, Dennis M. (Technical Monitor)Langley Research CenterNOISE SPECTRA; ACOUSTIC FREQUENCIES; NOISE REDUCTION; OPTIMIZATION; ACTIVE CONTROL; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; MONOPOLES; SOUND FIELDS; SOUND GENERATORS