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Improving Robustness Filter Bandwidth in Repetitive Control by Considering Model Mismatch

Repetitive control (RC) is used to track and reject periodic signals by including a model of a periodic signal in the feedback path. The performance of RC can be improved by including an inverse plant response filter, but due to modeling uncertainty at high frequencies, a low‐pass robustness filter is also required to limit the bandwidth of the signal model and ensure stability. The design of robustness filters is presently ad‐hoc, which may result in excessively conservative performance. This article proposes a new automatic method for designing the robustness filter based on convex optimization and an uncertainty model. Experimental results on a nanopositioning system demonstrate that the proposed method outperforms the traditional brick‐wall filter approach.