Frequency Domain Aspects of Modeling and Control in Adaptive Systems
Abstract: In this thesis various aspects of modeling and control in adaptive systems are presented from a frequency domain viewpoint.The thesis consists of three parts, where the first part contains a general introduction and background information concerning the problems that will be treated. In the second part some recursive identification algorithms are studied with respect to their ability to track time-varying systems and their disturbance sensitivity. Simple and illustrative frequency domain expressions that describe these properties are derived using asymptotic methods. The algorithms that are treated are the constant gain gradient (LMS) algorithm, the recursive least squares algorithm with constant forgetting factor and the Kalman filter respectively. The behavior of these methods when applied to FIR and ARX systems are studied. In the third part of the thesis adaptive control based on low order models is studied. The adaptive control algorithm that is investigated is the recursive least squares algorithm combined with pole placement regulator design. Starting from frequency domain expressions, that describe how a low order model obtained by system identification approximates a higher order system, the consequences for adaptive control are investigated. It is shown how a proper use of filtering in the identification part of the adaptive regulator can improve the robustness properties of the adaptive regulator with respect to unmodelled dynamics.
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