Minimization of the maximum error signal in active control

This paper presents a new multichannel adaptive filtering algorithm for the active control of single frequency noise in acoustic systems. Most active control systems with multiple error sensors minimize the sum of the modulus squared output of these sensors. An adaptive algorithm is presented that minimizes an alternative cost function which, in the limit, is equal to the maximum of the modulus squared values of all the error sensors. The physical consequences of minimizing the maximum modulus squared output to achieve noise reduction are investigated. An analytical framework is developed that covers the steady state performance as well as the convergence properties. By means of simulations, the proposed algorithm has been applied to a linear model of a one-dimensional (1-D) acoustic system and compared with the classical least squares solutions. The proposed algorithm is also used in simulations of the control of the pressure measured at 32 microphone positions in a room using 16 loudspeakers, when the room is excited with an 88 Hz pure tone. The results of these simulations show that the observed convergence and steady-state properties agree well with the theoretical predictions. A comparison with the least squares solutions leads to the conclusion that the proposed algorithm leads to a more uniform acoustic field in the enclosure than the classical least squares algorithm.