To deal with an iterative learning control (ILC) system with plant uncertainty, a set of new terms related with robust convergence is first defined. This paper proposes a sufficient condition for not only robust convergence but also robust stability of ILC for uncertain linear systems, including plant uncertainty. Thus, to find a new condition unrelated to the uncertainty, we first separate it into a known part and uncertainty one using linear fractional transformations (LFTs). Then, robust convergence and robust stability of an ILC system is determined by structured singular value (μ) of only the known part. Based on the novel condition, a learning controller and a feedback controller are developed at the same time to ensure robust convergence and robust stability of the ILC system under plant uncertainty. Lastly, the feasibility of the proposed convergence condition and design method are confirmed through computer simulation on an one-link flexible arm.
An Iterative Learning Control for Uncertain Systems Using Structured Singular Value
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Doh, T., Moon, J., and Chung, M. J. (December 1, 1999). "An Iterative Learning Control for Uncertain Systems Using Structured Singular Value." ASME. J. Dyn. Sys., Meas., Control. December 1999; 121(4): 660–667. https://doi.org/10.1115/1.2802532
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