System identification beyond the Nyquist frequency
A kernel-regularized approach
Max Van Haren (Eindhoven University of Technology)
R. S. Smith (ETH Zürich)
T.A.E. Oomen (Eindhoven University of Technology, TU Delft - Team Jan-Willem van Wingerden)
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Abstract
Models that contain intersample behavior are important for control design of systems with slow-rate outputs. The aim of this paper is to develop a system identification technique for fast-rate models of systems where only slow-rate output measurements are available, e.g., vision-in-the-loop systems. In this paper, the intersample response is estimated by identifying fast-rate models through least-squares criteria, and the limitations of these models are determined. In addition, a method is developed that surpasses these limitations and is capable of estimating unique fast-rate models of arbitrary order by regularizing the least-squares estimate. The developed method utilizes fast-rate inputs and slow-rate output measurements and identifies fast-rate models accurately in a single identification experiment. Finally, both simulation and experimental validation on a prototype wafer stage demonstrate the effectiveness of the framework.
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