Study on Active Noise Control of Sinusoidal Noise. Robustness for Modeling Error.

Abstract

We describe a design method of evaluating robust stability of a filtered-x type adaptive notch filter which can be executed by performing only a few calculations for periodic noise such as engine noise. The algorithm needs to obtain the identification model of the acoustic transfer function by using different notch filter for each control frequency. However. a modeling error increases in the frequency range where both gain and phase of the acoustic transfer function varies largely, so that leads to an instability. For the purpose of maintaining stability, we propose a method that classifies a modeling error into gain error and phase error and stabilizes the system by evaluating allowable limit for each error in all control frequency range. Theoretical analyses and computer simulations based on introduced equations reveal the following. Even if gain error exists. the system can be stabilized by adjustment of the step size parameter. On the other hand. even if phase error exists, the system can be controlled in a stable manner by obtaining all identification models at frequency intervals where phase deviati on is less than 90 degrees. Moreover, the design method of guaranteeing robust stability can be developed clearly in the paper.