System Identification Beyond the Nyquist Frequency: A Kernel-Regularized Approach

TL;DR

This paper introduces a kernel-regularized system identification method that accurately estimates fast-rate models from slow-rate output data, surpassing traditional limitations and validated through simulations and experiments.

Contribution

It develops a novel regularization-based approach to identify high-frequency system models from low-frequency measurements, enabling single-experiment fast-rate modeling.

Findings

Effective estimation of fast-rate models from slow-rate data

Surpasses limitations of traditional least-squares methods

Validated on simulation and real-world wafer stage system

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 outputs 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.