A Novel Narrowband Active Noise Control System with Online Secondary Path Modeling Based on Factor Decomposition and Application in Open Space

Due to the complexity of the coupling between the active noise control (ANC) controller and secondary path estimator, performance analysis of the system becomes particularly difficult. At present, the performance analysis of the system is often based on the fact that the secondary path tends to be stable, and the secondary path fitting error is minimal. However, in the early stage of system operation, or when the secondary path changes suddenly, the secondary path fitting error is significant, which easily causes divergence of the system control. It is still unable to guarantee the step-size bounds of convergence stability. Therefore, factor decomposition was used to analyze the mean weight behavior in this study. This strategy emphasizes the influence of secondary path modeling (SPM) error. The mean square behavior was evaluated using the energy conservation relationship. According to the established theoretical model, the convergence condition of the system was derived and the upper bound of step size suitable for all stages of system operation was obtained. The simulation and experimental results show that the ANC system is quite stable and robust under extreme conditions and has an obvious noise reduction effect in a specific range of open space, which can reach about 20 dB noise reduction.