Robust stability in feedback active noise control

Abstract

A major hurdle in the design of a feedback system for active noise control applications is the difficulty in guaranteeing robust stability while maintaining adequate noise reduction performance. This requirement is particularly limiting when variations in the control plant response are large, as is the case with active headrests, where head movements can drastically modify the acoustic propagation between the control sources and error sensors, which affects both the magnitude and phase of the plant transfer function. It is possible, to some degree, to design a robustly stable controller that can accommodate plant variations within a range that is determined during preliminary laboratory measurements of all expected operational configurations. The robustly stable control filter is then designed by a computationally expensive optimisation procedure based on the assumed disturbance spectrum, the nominal plant response, and its expected maximum variation. However, plant variations are in some cases so large that it is not feasible to design a controller around a nominal plant response with a pre-determined uncertainty bound, and the nominal plant response needs to be characterised at various times during controller operation. This mode of operation is made possible by the appearance of control prototyping platforms constructed around powerful DSPs and equipped with considerable memory space. Although this does not allow the expensive optimisation to be carried out by the DSP, there is great potential to make robustly stable plants that can accommodate major variations in the system and primary disturbance. This paper presents the development of a feedback controller based on the internal model control architecture and evaluates the performance of various strategies to design an adaptive, feedback control filter that is robustly stable to variations in primary disturbance spectrum and plant transfer function.