Root locus analysis and design of the adaptation process in active noise control

This paper applies root locus theory to develop a graphical tool for the analysis and design of adaptive active noise control systems. It is shown that the poles of the adaptation process performed in these systems move on typical trajectories in the z-plane as the adaptation step-size varies. Based on this finding, the dominant root of the adaptation process and its trajectory can be determined. The first contribution of this paper is formulating parameters of the adaptation process root locus. The next contribution is introducing a mechanism for modifying the trajectory of the dominant root in the root locus. This mechanism creates a single open loop zero in the original root locus. It is shown that appropriate localization of this zero can cause the dominant root of the locus to be pushed toward the origin, and thereby the adaptation process becomes faster. The validity of the theoretical findings is confirmed in an experimental setup which is implemented using real-time multi-threading and multi-core processing techniques.