Retrospective cost adaptive harmonic disturbance rejection using dereverberated target models

Abstract

This paper focuses on adaptive feedback disturbance rejection for lightly damped structures using retrospective cost adaptive control (RCAC). RCAC uses a target model of the closed-loop dynamics in order to enable controller adaptation. The target model captures specific features of the dynamics of the structure; in the SISO case, this information consists of the sign of the leading numerator coefficient, relative degree, and nonminimum-phase zeros of the discretized dynamics. The present paper investigates the feasibility of using a dereverberated transfer function (DTF) as the target model for harmonic disturbance rejection with unknown disturbances. In particular, the dereverberated target model (DTM) obtained by magnitude and phase averaging captures the magnitude and phase trend of the structure but ignores resonances and anti-resonances, thus providing a low-order target model for controller adaptation. The robustness of RCAC is investigated with the target model given by a DTF based on a nominal model with erroneous damping ratio. The technique is implemented experimentally on an acoustic noise control setup.