Polynomial approach to design of feedback virtual-microphone active noise control system

Classical active noise control systems can provide high noise attenuation at the close vicinity of the so-called error microphone. If the zone of quiet is required at a more distant location dedicated Virtual-Microphone Control systems can be applied. The aim of the paper is to present further development of this concept. However, contrary to most of the available solutions, the considered structure is not based on the Internal Model Control structure, where estimate of the output disturbance drives the control filter. Instead, estimated residual signal at the virtual microphone constitutes the controller input. This allows directly modeling the so-called difference path and taking benefits of its limited changes compared to changes of the paths from the secondary source to the real and virtual microphones. The optimal H2 controller is designed using the polynomial approach. Therefore, parametric models of the paths as well as the disturbance are necessary. The disturbance-shaping filter is split using a Diophantine equation. To cope with non-minimum phase character of the path models a transfer function is factorized into inner and outer parts. Finally causal part of the controller is extracted. An equation for the spatial attenuation gradient due to change of the virtual path is also derived. Results of experimental verification of the discussed algorithm applied to control noise in an active headrest system are presented.