A STATE-SPACE MODELING OF ONE-DIMENSIONAL ACTIVE NOISE-CONTROL SYSTEMS

A state-space representation of a dynamic system for one-dimensional s ound reflection and transmission is developed. The state-space modelin g is the first step for future development of an active noise control system using modern control synthesis tools. In contrast to a classica l frequency-domain description, the state model allows direct computat ion of the system's time response and provides a forum for modern cont rol synthesis, which leads to an optimal control algorithm. Based on t he governing wave equation, the stare model is derived using a finite difference technique combined with analytical expressions. Numerical s imulation 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.