This paper converts the design of robust repetitive controller into a standard problem. In order to handle the large delay in the internal model structure of repetitive controller, a new framework, which utilizes Structured Singular Values method (μ synthesis) for solution, is proposed. It is shown that the μ value of the new framework is a tight upper bound of the μ value of the standard problem. Under this framework, the conditions of robust stability and robust performance can be incorporated and analyzed. The designed repetitive controller preserves a special low-order filter structure for efficient real-time implementation. The robust performance can be achieved not only to the periodic signals of the fundamental frequency and its harmonics as the existing repetitive controller did, but also to asynchronous periodic and non-periodic signals by choosing appropriate performance weighting function. The design procedure is more systematic and less conservative than conventional methods. A robust repetitive controller designed using this method is implemented on a hydraulic servo for noncircular cutting. Experimental results are presented to illustrate the control system synthesis procedure and performance.

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