Adaptive design of robust feedback controllers for active noise control

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 H₂ performance objective of disturbance rejection, an H_∞ constraint corresponding to robust stability for multiplicative plant uncertainty, an H_∞ constraint corresponding to limits on disturbance enhancement, and an H₂ 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