Fixed gain multichannel active noise control with disturbance dependent objectives and iterative solution

This paper presents a solution method for a fixed multichannel frequency domain feedforward controller, which is optimized for different sound field disturbances, each corresponding to a different control objective. A controller determined on the basis of identical control objectives for different disturbances can be solved efficiently by using the inverse of two relatively small matrices, the Hermitian square of the secondary path and the cross-spectral density matrix of all combinations between the reference signals. In contrast, the dependence between the disturbance and the control objective results in a large matrix, which may not fit in the memory of a computer. To design the controller for systems with relatively large numbers of sensors and sources, an iterative method based on the conjugate gradient technique is used. A preconditioner based on a disturbance-independent control objective is proposed. This preconditioner improves the convergence rate for some applications. A numerical example of the iterative method is given for active control of the acoustic field inside a room in which a disturbance dependent weighting function is applied to the cost function. It is shown that the iterative method efficiently finds the solution for the disturbance dependent active noise control problem.