A method for active noise control using a source-point model

In this paper, an active noise-control method is derived from a source-point model and discrete optimal control theory. A discrete state-space formulation of the model is found via a free-space Green’s function. The states of the model are pressures at past and present times on the boundary of an acoustic domain. The state-space model is used to produce a discrete single-input, single-output feedback filter that minimizes sound at selected points in the one-dimensional acoustic domain. Theoretical results are given for a single detector microphone in the acoustic domain and for full-state feedback. Both the single measurement and full-state feedback responses give satisfactory results in simulation and theory.