A State-Space Modeling of One-Dimensional Active Noise Control Systems

Abstract

A state-space representation of a dynamic system for one-dimensional sound reflection and transmission is developed. The state-space modeling is the first step for future development of an active noise control system using modern control synthesis tools. In contrast to a classical frequency-domain description, the state model allows direct computation of the system’s time response and provides a forum for modern control synthesis, which leads to an optimal control algorithm. Based on the governing wave equation, the state model is derived using a finite difference technique combined with analytical expressions. Numerical simulation of the dynamic system model is presented, which shows a good agreement with the frequency-domain solutions. Discretization errors are investigated and improved by using nonuniform grids.