This paper concerns matching a system with time-delayed feedback to a rational transfer function model and its application to repetitive controller design. Necessary and sufficient conditions on the order of the plant, reference model, and controller are obtained for the existence of causal and stabilizing exact model matching solutions. The results are applied to robust repetitive controller design, in which a delayed feedback is introduced in the repetitive controller for rejecting periodic disturbances while simultaneously achieving input-output model matching. Furthermore, the 2-D model matching method also renders computationally efficient solutions. Also addressed are some subtle points on the selection of a low-pass filter required for robust stability. Finally, the approach is experimentally applied for turning noncircular shapes.

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