Robust Repetitive Control of Nanopositioning Stages Using the Spectrum-Selection Filter With Narrow Passbands

Abstract

The repetitive control (RC) is a promising control technique to achieve the high-speed periodic operation of nanopositioning stages. However, the conventional RC is fairly sensitive to the period-time uncertainty of the reference input and tends to amplify the tracking error at nonperiodic frequencies. To overcome these two limitations simultaneously, a robust RC (RRC) is proposed by integrating a band-stop filter into the spectrum-selection filter scheme in this article. With a developed general structure of the band-stop filter, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${H_\infty }$</tex-math></inline-formula> optimization problem is modeled to determine the filter parameter. Comparative experiments are conducted on a commercial nanopositioning stage to validate the superiorities of the proposed RRC. The experimental results show that the proposed RRC scheme significantly improves the robustness against the period-time uncertainty of the reference input while keeping an excellent tracking performance.