Dissertation/Thesis Abstract

Design enhancements in repetitive and interative learning control
by Bao, Jiangcheng, Ph.D., Columbia University, 2010, 157; 3420866
Abstract (Summary)

Both Repetitive Control (RC) and Iterative Learning Control (ILC) aim to eliminate tracking errors in feedback control systems that perform repetitive tasks, or experience periodic disturbances, or both. Several enhancements to the performance of RC and ILC are developed here. First, it is observed that an image of a startup jump can exist in the RC command for many periods. RC systems usually eliminate this jump discontinuity slowly due to its high frequency content. The nature of this startup jump image is studied, and various methods are developed to prevent or reduce such discontinuities. Due to modeling error, a low pass filter is usually required to cut off the learning process above some frequency to produce stability robustness. This study shows that peaks in the passband of the cutoff filter force one to use a lower cutoff frequency than one could use otherwise. The second topic therefore develops improvements to the zero-phase low-pass filters used. The improved filter designs use quadratic programming with inequality constraints to improve filter performance and therefore allows a higher cutoff. This filter design can also function as an effective anti-aliasing filter. The third topic considers situations in which the period of the disturbance is not an integer number of time steps, which would normally require interpolation. However, interpolation usually results in substantial error remaining after convergence. Various enhancements to the cutoff filter allow the filter to perform the extra function of adjusting for a fractional time step shift in the disturbance period. Finally, it is shown that various ILC law families can be unified by considering each as a special case of a quadratic cost ILC law with appropriately chosen weight matrices. The stability robustness to magnitude and phase errors in the model is studied for these ILC laws. With this knowledge and the model uncertainty as a function of frequency, one can design a more sophisticated ILC law by adjusting the learning rate in the ILC law associated with each singular value of the system in order to maximize the robustness where needed.

Indexing (document details)
Advisor: Longman, Richard W.
School: Columbia University
School Location: United States -- New York
Source: DAI-B 71/09, Dissertation Abstracts International
Subjects: Mechanical engineering
Keywords: Filter design, Interative learning control, Periodic disturbances, Quadratic programming, Repetitive control, Tracking errors
Publication Number: 3420866
ISBN: 978-1-124-18563-7
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