Broadband Active Noise Control Design through Nonsmooth H∞ Synthesis

This paper deals with active control of a broadband noise in a car cabin. It aims to study the achievable performance of such control in the SISO feedback case. The main limitations involved, known as waterbed effect, are critical for such problem due to the presence of non-minimum phase zeros. To evaluate the intrinsic limitations due to these non-minimum phase zeros, a multi-objective control synthesis is proposed, allowing to cope with classical speciffications (performance and robustness), without pessimism. The control synthesis is based on a H∞ criterion to be minimized under some decoupled constraints. It consists in a non-convex and non-smooth optimization problem, for which a local optimum may be efficiently obtained. A particular control structure is considered in order to reduce the number of decision variables, to set relevant bounds on these parameters and to choose appropriate initial conditions. Then the optimization problem is solved using recent results on non-smooth optimization. The whole design process is detailed, including the identiffication of the synthesis model. The control strategy is then applied to an instrumented cavity, which shares most of the acoustic characteristics of a car cabin. Finally, the analysis of the results gives clear conclusions on SISO feedback possibilities, and paves the way for an efficient multivariable design case.