Discrete-time repetitive control with model-less FIR filter inversion for high performance nanopositioning

Repetitive control (RC) is used to track and reject periodic exogenous signals. RC achieves tracking by incorporating a model of a periodic signal in the feedback path, which provides infinite loop-gain at the harmonic frequencies of the periodic signal. To improve robustness, the periodic signal model is bandwidth limited, and to improve the performance, an inverse plant response filter is used. This filter can either be an infinite impulse response (IIR) filter or a finite impulse response (FIR) filter. The accuracy of the filter typically determines the allowable bandwidth of the periodic signal model, and it is therefore desirable to obtain the most accurate inverse possible. In this paper a model-less method for synthesizing an FIR filter for the inverse response is presented, and it is compared to the common approach of using an inverse model-based IIR filter. An experimental comparison of the two approaches is presented, and it is demonstrated that the two methods produce identical results, but where the model-less FIR filter approach has the added benefit of avoiding the modeling effort needed to obtain the IIR filter.