ADAPTIVE BAND-LIMITED DISTURBANCE REJECTION IN LINEAR DISCRETE-TIME-SYSTEMS

The problem of adaptively rejecting a disturbance consisting of a line ar combination of sinusoids with unknown and/or time varying frequenci es for SISO LTI discrete-time systems is considered. The rejection of the disturbance input is achieved by constructing the set of stabilizi ng controllers using the Youla parametrization and adjusting the Youla parameter to achieve asymptotic disturbance rejection. The first main result in this paper concerns off-line controller design where a cont roller that achieves regulation is numerically designed off-line based on the assumption that only the sequence of discrete disturbance inpu t values (as opposed to a model of the disturbance) is available. A le ast squares based optimization algorithm is used in the controller des ign. As expected, it is shown, under some mild assumptions, that if th e off-line designed controller achieves regulation, then it must inclu de a model of the disturbance input. The second main result concerns o n-line controller design where recursive versions of the off-line algo rithm used above for controller design are presented and their converg ence properties analyzed. Conditions under which the on-line algorithm s yield an asymptotic controller that achieves regulation are presente d. Conditions both for the case where the disturbance input properties are constant but unknown and for the case where they are unknown and time-varying are given. The on-line controller construction amounts to an adaptive implementation of the Internal Model Principle. The perfo rmance robustness of the off-line designed controller in the face of p lant model uncertainties is investigated. It is shown, under some mild assumptions, that performance robustness is realized provided interna l stability is maintained. The performance of the adaptation algorithm s is illustrated through a simulation example.