Optimal location of sensors and actuators for an active noise control problem

Abstract

We consider the problem of optimal location of actuators and sensors for optimizing their performance in reducing the noise field in a cavity. The control strategy is based on a static output feedback control, and the optimization problem is formulated as minimizing the quadratic cost function which is averaged over the random initial conditions. The solution of the optimization problem requires solving a matrix Riccati equation and a Lyapunov equation. We demonstrate the effectiveness of the control strategy and its dependence on location of the sensors and actuators in several numerical examples.