This paper investigates the robust repetitive controller design with improved tracking performance for nano-manipulating systems with time delay. In order to handle the time delay caused by the analog-to-digital (A/D) conversion of the capacitive sensors with ultra high precision, we modify the conventional repetitive control structure where the design of low pass filter is formulated as an H optimization problem. For the purpose of tracking performance improvement, we further modify the structure of the low pass filter by shaping the sensitivity functions of the closed-loop system. With consideration of the existing of model uncertainties, the design of the modified low pass filter is also formulated as an H optimization of infinite dimensional systems. The effectiveness of the proposed repetitive control architecture is further verified by real time experiments on a piezo driven nano-stage, where significant tracking performance improvements are demonstrated comparing with the traditional repetitive controller.

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