Adaptive design of robust feedback controllers for active noise control

Abstract

We introduce a design method for adaptive feedback controllers in active noise control, which can be realised using a modified frequency domain LMS algorithm. The controller is made adaptive to changes in the disturbance, while maintaining robust stability and other design constraints which were found useful for active control. The controller design problem is described in the frequency domain using an H/sub 2/ performance objective of disturbance rejection, an H/sub /spl infin// constraint corresponding to robust stability for multiplicative plant uncertainty, an H/sub /spl infin// constraint corresponding to limits on disturbance enhancement, and an H/sub 2/ constraint corresponding to limit on the control output power. The design problem is first formulated as a convex optimisation problem using an internal model controller with an FIR Q-parameter, and then reformulated as an unconstrained problem using penalty or barrier functions, where the steepest descent method is used to search for the optimal controller. We show that this approach can be realised using a frequency domain LMS algorithm, without significantly increasing its computation complexity.