Aliasing of Resonance Phenomena in Sampled-Data Feedback Control Design: Hazards, Modeling, and a Solution

Abstract

High-performance control design for electromechanical sampled-data systems with aliased plant dynamics is investigated. Though from a theoretical viewpoint the aliasing phenomenon is automatically handled by direct sampled-data control, such an approach cannot be used in conjunction with models derived through system identification. From a practical viewpoint, aliasing is often considered as an undesirable phenomenon and a typical remedy is the increase of the sampling frequency. However, the sampling frequency is upper bounded due to physical and economical constraints and aliasing may be inevitable. Control design for plants with aliased dynamics has not received explicit attention in the literature and it is not clear how to handle this situation. In this paper, it is shown that aliased resonance phenomena can effectively be suppressed in sampled-data feedback control design without the need for increasing the sampling frequency. Furthermore, it is shown experimentally on an industrial wafer stage that ignoring aliasing during control design can have a disastrous effect on closed-loop performance. Additionally, a novel, practically feasible procedure for identification of (possibly aliased) resonance phenomena based on multirate system theory is proposed.