Repetitive control is employed in numerous industrial applications to allow systems to track or reject unknown periodic signals of a known period. This thesis takes a novel approach to the design and analysis of such systems, by introducing a useful performance measure, referred to as the induced power-norm. This measure represents the maximum power-norm of the steady-state error vector in the system, for all periodic inputs of unit power-norm. The approach taken here is also new in that it is a sampled-data formulation. Hence, the intersample behavior is directly taken into account.
First, a methodology is developed for designing optimal sampled-data repetitive controllers, based on minimizing the power-norm of the steady-state error vector for a given periodic input. It is shown that such an optimal controller always exists. This methodology is then generalized to the case of an unknown periodic input by minimizing the induced power-norm. Fast discretization is verified to be a useful computational tool for obtaining suboptimal controllers in both methodologies. To demonstrate these methodologies, active suppression of fan noise present in an acoustic duct is discussed with promising results.
Also formulated and analyzed in this thesis is a robust tracking problem for sampled-data repetitive control systems in the presence of structured linear periodically time-varying perturbations. Specifically, we investigate whether the induced power-norm of the closed-loop system remains below a given bound for a class of such perturbations. The result is stated in terms of a necessary and sufficient condition that involves Dullerud's generalized notion of structured singular values for operators. Computational aspects are addressed with a numerical example.
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