A control scheme called repetitive control is proposed, in which the controlled variables follow periodic reference commands. A high-accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period L into the closed-loop system. Sufficient conditions for the stability of repetitive control systems and modified repetitive control systems are derived by applying the small-gain theorem and the stability theorem for time-lag systems. Synthesis algorithms are presented by both the state-space approach and the factorization approach. In the former approach, the technique of the Kalman filter and perfect regulation is utilized, while coprime factorization over the matrix ring of proper stable rational functions and the solution of the Hankel norm approximation are used in the latter one. >

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Repetitive control system: a new type servo system for periodic exogenous signals

This paper discusses linear iterative learning and repetitive control, presenting general purpose control laws with only a few parameters to tune The method of tuning them is straightforward, maki

http://www.dct.tue.nl/New/Steinbuch/ILC/longman_paper.pdf

Iterative learning control and repetitive control for engineering practice

Survey on iterative learning control, repetitive control, and run-to-run control

Control can enable high-bandwidth nanopositioning needed to increase the operating speed of scanning probe microscopes (SPMs). High-speed SPMs can substantially impact the throughput of a wide range of emerging nanosciences and nanotechnologies. In particular, inversion-based control can find the feedforward input needed to account for the positioning dynamics and, thus, achieve the required precision and bandwidth. This article reviews inversion-based feedforward approaches used for high-speed SPMs such as optimal inversion that accounts for model uncertainty and inversion-based iterative control for repetitive applications. The article establishes connections to other existing methods such as zero-phase-error-tracking feedforward and robust feedforward. Additionally the article reviews the use of feedforward in emerging applications such as SPM-based nanoscale combinatorial-science studies, image-based control for subnanometer-scale studies, and imaging of large soft biosamples with SPMs.

https://faculty.washington.edu/devasia/Research/Papers/2009_Feedforward_review_paper.pdf

A review of feedforward control approaches in nanopositioning for high-speed spm

Tracking errors in disk drive systems have a significant repetitive component that is not explicitly taken into account in conventional servo controllers. A modified prototype repetitive controller is applied as a plug-in module to a Winchester disk drive with a preexisting analog feedback controller to demonstrate its efficacy in the reduction of this periodic component. A review of the Winchester disk drive system is included. >

T. Kubo

Papers

High Accuracy Control of a Proton Synchrotron Magnet Power Supply