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Research Papers

A Frequency-Dependent Filter Design Approach for Norm-Optimal Iterative Learning Control and Its Fundamental Trade-Off Between Robustness, Convergence Speed, and Steady-State Error

[+] Author and Article Information
Xinyi Ge

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

Jeffrey L. Stein

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

Tulga Ersal

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

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 17, 2017; final manuscript received June 14, 2017; published online September 20, 2017. Assoc. Editor: Douglas Bristow.

J. Dyn. Sys., Meas., Control 140(2), 021004 (Sep 20, 2017) (10 pages) Paper No: DS-17-1032; doi: 10.1115/1.4037271 History: Received January 17, 2017; Revised June 14, 2017

This paper focuses on norm-optimal iterative learning control (NO-ILC) for single-input-single-output (SISO) linear time invariant (LTI) systems and presents an infinite time horizon approach for a frequency-dependent design of NO-ILC weighting filters. Because NO-ILC is a model-based learning algorithm, model uncertainty can degrade its performance; hence, ensuring robust monotonic convergence (RMC) against model uncertainty is important. This robustness, however, must be balanced against convergence speed (CS) and steady-state error (SSE). The weighting filter design approaches for NO-ILC in the literature provide limited design freedom to adjust this trade-off. Moreover, even though qualitative guidelines to adjust the trade-off exist, a quantitative characterization of the trade-off is not yet available. To address these two gaps, a frequency-dependent weighting filter design is proposed in this paper and the robustness, convergence speed, and steady-state error are analyzed in the frequency domain. An analytical expression characterizing the fundamental trade-off of NO-ILC with respect to robustness, convergence speed, and steady-state error at each frequency is presented. Compared to the state of the art, a frequency-dependent filter design gives increased freedom to adjust the trade-off between robustness, convergence speed, and steady-state error because it allows the design to meet different performance requirements at different frequencies. Simulation examples are given to confirm the analysis and demonstrate the utility of the developed filter design technique.

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References

Figures

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Fig. 1

Graphical interpretation of Eq. (11)

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Fig. 2

RMC region example for (a) W3(e) = 0, and (b) W3(e) ≠ 0

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Fig. 3

Illustration of how the RMC region changes with respect to W1(ejθ), W2(ejθ), and W3(ejθ)

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Fig. 4

Achieving RMC for the example modeling uncertainty region: (a) at ω1 and (b) at ω2

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Fig. 5

Illustration of the trade-off between (a) convergence speed and robustness and (b) steady-state tracking error and robustness

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Fig. 6

Performance surface for NO-ILC

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Fig. 7

Bode plot of system model and uncertainty

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Fig. 8

RMC disk for Example 1 at different frequencies: (a) 3.72 rad/s and (b) 16.63 rad/s

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Fig. 9

Monotonic convergence of tracking error and input difference in the iteration domain for Example 1

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Fig. 10

Bode plot of system model and uncertainty range for Example 2

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Fig. 11

RMC disk for Example 2 at different frequencies: (a) 7.90 rad/s and (b) 31.51 rad/s

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Fig. 12

Tracking error and input difference in iteration domain for Example 2

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Fig. 13

(a) Robustness at different frequency for W2,Ex1(z) and W2,Ex3(z) and (b) two-norm of tracking error in iteration domain

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Fig. 14

(a) Robustness at different frequencies for W3,Ex2(z) and W3,Ex3(z) and (b) two-norm of tracking error in iteration domain for Example 3

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Fig. 15

Comparison of the tracking error for the second plant in Example 3 with different W3(z) designs at 27.48 rad/s after tenth iteration

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