The behavior of a multiple channel active control system

The convergence behavior of an adaptive feedforward active control system is studied. This adjusts the outputs of a number of secondary sources to minimize a cost function comprising a combination of the sum of mean-square signals from a number of error sensors (the control error) and the sum of the mean-square signals fed to the secondary sources (the control effect). A steepest descent algorithm which performs this function is derived and analyzed. It is shown that some modes not only converge slowly but also require an excessive control effort for complete convergence. This ill-conditioned behavior can be controlled by the proper choice of the cost function minimized. Laboratory experiments using a 16-loudspeaker 32-microphone control system to control the harmonic sound in an enclosure are presented. The behavior of the practical system is accurately predicted from the theoretical analysis of the adaptive algorithm. The effect of errors in the assumed transfer matrix used by the steepest descent algorithm is briefly discussed