There are many variables associated with active noise control(ANC). The greatest noise attenuation can be achieved when these variables are optimized simultaneously with respect to a selected target function but it is generally not possible. If noise sources are excited at frequencies where the modal density is low, global control strategies are very suitable for producing noise reductions within an enclosed space. A degree of noise reductions is very sensitive to the positions of control sources and sensors. This paper deals with two objectives; One is to examine how control sources and sensors have the effects on the control performance of an ANC system for a selected noise source and the other is to estimate the averaged control performance of an ANC system when noise sources having a constant frequency and energy in an enclosed space are varied arbitrarily.
Vector concepts are used to implement these objectives. The cost function of acoustic potential energy is derived in matrix forms. Variables associated with ANC are expressed as vectors in mode axes. The Decomposition of the cost function into two orthogonal components and the eigenvalue analysis of an ANC system are theoretically studied. Through these theories, noise sources and an ANC system are expressed and analyzed in three dimensional space. To apply these theories to actual control systems, experiments on a shallow rectangular enclosure are performed.
