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Technical Brief

Optimality of Norm-Optimal Iterative Learning Control Among Linear Time Invariant Iterative Learning Control Laws in Terms of Balancing Robustness and Performance

[+] Author and Article Information
Xinyi Ge

Mechanical Engineering,
University of Michigan,
Ann Arbor , MI 48109,
e-mail: gexinyi@umich.edu

Jeffrey L. Stein

Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109,
e-mail: stein@umich.edu

Tulga Ersal

Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109,
e-mail: tersal@umich.edu

1Corresponding author.

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.

J. Dyn. Sys., Meas., Control 141(4), 044502 (Dec 19, 2018) (5 pages) Paper No: DS-17-1555; doi: 10.1115/1.4042091 History: Received November 06, 2017; Revised November 21, 2018

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.

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Figures

Grahic Jump Location
Fig. 2

Optimality of NO-ILC in the tradeoff between robustness and convergence speed when Q-filter is disabled

Grahic Jump Location
Fig. 1

Illustration of allowable model uncertainties and the vector Go(ejθ)L(ejθ) on the complex plane at a particular frequency θ

Grahic Jump Location
Fig. 3

Optimality of NO-ILC in tradeoff between robustness, convergence speed, and steady-state error [13]

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