Experimental implementation of fixed-gain and adaptive disturbance rejection controllers.

Abstract

Although active noise control has been a subject of interest for over fifty years, it has become feasible only with recent technological advances. This thesis formulates the problem of noise control in a one-dimensional acoustic duct in a form that lends itself to the application of feedback control theory. Controllers are designed using precompensated LQG synthesis and are experimentally verified. With the success of feedforward techniques for active noise control, feedback control researchers have begun to explore the relationship between these two control paradigms. This dissertation further investigates this relationship by means of the classical Bode integral constraint on achievable performance. This constraint provides insight into the phenomenon of spillover which we define as disturbance amplification by the closed-loop system relative to the open-loop transfer function gain. Specifically, it is shown that a particular feedforward controller called the zero spillover controller avoids spillover by producing perfect disturbance cancellation at every frequency. The analysis suggests that spillover can be avoided only if the control speaker and the disturbance source are noncolocated and the performance microphone and the measurement microphone are noncolocated. For realizability, we derive the approximate zero spillover controller which is shown to be an optimal feedback controller for an LQG problem with suitable cross weighting. The results are illustrated by means of structural and acoustic examples. To overcome modeling error and/or plant uncertainties, we develop a direct adaptive control algorithm for an $\eta $th-order linear systems. The stability of the adaptive controller is proved using Lyapunov arguments. The controller is designed to provide robust adaptive stabilization and constant disturbance rejection. This problem is then applied to the problem of step command following. The results are applied to nonlinear systems using numerical simulations and they are experimentally implemented on an electromagnetically controlled oscillator.