A time-varying Q-filter design for iterative learning control with application to an ultra-precision dual-stage actuated wafer stage

Iterative learning control is known as an effective technique for improving the performance of systems that require repetitive work. In general, a linear time-invariant low-pass Q-filter is employed to provide robustness to modeling errors and model uncertainties, as well as to suppress the noise transmission in the learning process. A lower bandwidth of Q-filter results in less noise amplification but at the cost of decreasing the learning performance. The filter’s bandwidth thus forms a fixed trade-off between attenuation of repetitive errors and amplification of noise. Although linear time-varying Q-filter in finite impulse response type has been proposed, the performance is still unsatisfactory for the filter of this type has a low attenuation rate in high frequency and is unable to obtain a low bandwidth as well. Therefore, in this article, a linear time-varying Q-filter in infinite impulse response type is put forward, providing a better means to deal with the trade-off. To demonstrate that, experiments have been conducted on the developed dual-stage actuated wafer stage, which consists of a short-stroke stage for accurate positioning and a long-stroke stage for coarse positioning. The results illustrate that the proposed method results in a significant improvement in tracking performance, which includes lower converged error and decreased settling time.