Local Rational Modeling for Identification Beyond the Nyquist Frequency: Applied to a Prototype Wafer Stage

Fast-rate models are essential for control design, specifically to address intersample behavior. The aim of this article is to develop a frequency-domain nonparametric identification technique to estimate fast-rate models of systems that have relevant dynamics and allow for actuation above the Nyquist frequency of a slow-rate output. Examples of such systems include vision-in-the-loop systems. Through local rational models over multiple frequency bands, aliased components are effectively disentangled, particularly for lightly damped systems. The developed technique accurately determines nonparametric fast-rate models of systems with slow-rate outputs, all within a single identification experiment. Finally, the effectiveness of the technique is demonstrated through experiments conducted on a prototype wafer stage used for semiconductor manufacturing.