This paper presents a frequency domain analysis toward the robustness, convergence speed, and steady-state error for general linear time invariant (LTI) iterative learning control (ILC) for single-input-single-output (SISO) LTI systems and demonstrates the optimality of norm-optimal iterative learning control (NO-ILC) in terms of balancing the tradeoff between robustness, convergence speed, and steady-state error. The key part of designing LTI ILC updating laws is to choose the Q-filter and learning gain to achieve the desired robustness and performance, i.e., convergence speed and steady-state error. An analytical equation that characterizes these three terms for NO-ILC has been previously presented in the literature. For general LTI ILC updating laws, however, this relationship is still unknown. Adopting a frequency domain analysis approach, this paper characterizes this relationship for LTI ILC updating laws and, subsequently, demonstrates the optimality of NO-ILC in terms of balancing the tradeoff between robustness, convergence speed, and steady-state error.
Optimality of Norm-Optimal Iterative Learning Control Among Linear Time Invariant Iterative Learning Control Laws in Terms of Balancing Robustness and Performance
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received November 6, 2017; final manuscript received November 21, 2018; published online December 19, 2018. Assoc. Editor: Soo Jeon.
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Ge, X., Stein, J. L., and Ersal, T. (December 19, 2018). "Optimality of Norm-Optimal Iterative Learning Control Among Linear Time Invariant Iterative Learning Control Laws in Terms of Balancing Robustness and Performance." ASME. J. Dyn. Sys., Meas., Control. April 2019; 141(4): 044502. https://doi.org/10.1115/1.4042091
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