Effects of imperfect secondary path modeling on adaptive active noise control systems

Implementation of adaptive active noise control (ANC) systems requires an estimate model of the secondary path to be uploaded onto digital control hardware. In practice, this model is not necessarily perfect; however, to avoid mathematical difficulties, theoretical analysis of these systems is usually conducted for a perfect secondary path model. This paper conducts a stochastic analysis on performance of Filtered-x LMS (FxLMS)-based ANC systems when the actual secondary path and its model are not identical. This analysis results in a number of mathematical expressions, describing effects of a general secondary path model on stability, steady-state performance and convergence speed of FxLMS-based ANC systems. As a surprising result, it is found that intentional misadjustment of secondary path models can enhance performance of ANC systems in practice. Theoretical results are found to be in a good agreement with the results obtained from numerical analysis. Also, experimental results confirm the validity and accuracy of the theoretical results.