Finite-Time Learning Control Using Frequency Response Data With Application to a Nanopositioning Stage

Learning control enables significant performance improvement for systems that perform repeating tasks. Achieving high tracking performance by utilizing past error data typically requires noncausal learning that is based on a parametric model of the process. Such model-based approaches impose significant requirements on modeling and filter design. The aim of this paper is to reduce these requirements by developing a learning control framework that enables performance improvement through noncausal learning without relying on a parametric model. This is achieved by explicitly using the discrete Fourier transform to enable learning by using a nonparametric frequency response function model of the process. The effectiveness of the developed method is illustrated by application to a nanopositioning stage.