Subject to stability constraints, tracking performance of a plug-in type repetitive control system with periodic inputs is explored in this note. An upper bound for the square integral of the tracking error over one time period of periodic input signals is derived based on Fourier analysis. The magnitude and the decay rate of the tracking error can be estimated using the harmonics of the input signal within the designed bandwidth. Both computer simulations and experimental results are presented to illustrate the effectiveness of the proposed method. It is also shown that the tracking error can decay significantly in the first two time periods in the proposed repetitive control system if the required bandwidth conditions are satisfied.
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Yao et al. (2005) studied this question.
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