Retrospective Cost Adaptive Control for Feedback and Feedforward Noise Control

Abstract

This dissertation concerns the development of retrospective cost adaptive control (RCAC) and the application of RCAC to the active noise control (ANC) problem. We further the development of RCAC by presenting an alternative interpretation the retrospective performance variable. The retrospective performance decomposition is derived which separates the retrospective performance into the sum of a pseudo-performance term and a model-matching error term. We demonstrate an experimental application of RCAC by applying it to the broadband feedback road noise suppression problem in a vehicle. We show that RCAC is able to suppress the primary modes of the road noise at the performance microphone location. However, qualitative evaluation of the noise at the location of the driver was poor. This leads to the question, if you suppress the noise at the performance microphone, what is effect at the actual ear of the driver where you may not be able to place a sensor. The concept of spatial spillover is explored, where we develop an operator that relates relative suppression at the performance microphone to relative suppression at the evaluation microphone, which we denote as the spatial spillover function. The properties of the spatial spillover function are then validated numerically and experimentally. Finally, the framework of RCAC is extended to the feedforward control problem. Comparisons of RCAC feedforward control are made to linear-quadratic-Gaussian (LQG) control. It is shown that under certain conditions, RCAC is able to match the performance of LQG. Furthermore, we compare RCAC to the filtered-x/filtered-u least-mean-square (Fx/FuLMS) and the filtered-x/filtered-u recursive-least-square (Fx/FuRLS) algorithms and demonstrate numerically that RCAC is able to achieve better asymptotic performance that FuRLS. The RCAC feedforward control algorithm is demonstrated in an acoustic experiment. We demonstrate experimentally that if the ideal feedforward controller is implementable, the RCAC controller is able to recover the frequency response of the ideal controller.