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TECHNICAL PAPERS

Noise Tolerant Iterative Learning Control and Identification for Continuous-Time Systems With Unknown Bounded Input Disturbances

[+] Author and Article Information
Tae-Hyoung Kim, Xiaoguang Zheng

Department of Systems Science,  Kyoto University, Uji, Kyoto 611-0011, Japan

Toshiharu Sugie1

Department of Systems Science,  Kyoto University, Uji, Kyoto 611-0011, Japansugie@i.kyoto-u.ac.jp

1

Corresponding author.

J. Dyn. Sys., Meas., Control 129(6), 825-836 (Mar 16, 2007) (12 pages) doi:10.1115/1.2789474 History: Received April 12, 2006; Revised March 16, 2007

This paper considers the problems of both noise tolerant iterative learning control (ILC) and iterative identification for a class of continuous-time systems with unknown bounded input disturbance and measurement noise. To this aim, we first propose a formulation of an extended ILC scheme using sampled input∕output (I∕O) data. The proposed ILC method has distinctive features as follows. Its learning law works in a prescribed finite-dimensional parameter space and employs I∕O data of all past trials efficiently. Also, the time derivative of tracking error is not required. Then, it is presented how the uncertain parameters can be identified by using the proposed ILC algorithm and how robust it is against measurement noise through a numerical example. Furthermore, its experimental evaluation is performed to demonstrate the effectiveness of the proposed identification scheme.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

ILC configuration. (a) Scheme of ILC. (b) Parameter update law given by Eqs. 17,18.

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Figure 2

Impulse response contaminated by noise

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Figure 3

Measured behavior of ỹk(t) at the kth iteration (k=5,10,60)

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Figure 4

Norm of tracking error, ∥ek∥, to show the convergence

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Figure 5

Measured behavior of ỹk(t) at k=20

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Figure 6

E(∥ΔαFik∥) with respect to cond(LFi)E(∥ΔαF1k∥): ∗, E(∥ΔαF2k∥): 엯, and E(∥ΔαF3k∥): ◻)

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Figure 7

Time plot of maximum-length sequence

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Figure 8

Measured behavior of ỹk(t) at the kth iteration (k=5,13,70)

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Figure 9

Identified system parameters αik(i=1,2,3,4)

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Figure 10

Identified coefficients d0, d1, and d2 in d(t)

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Figure 11

Bode diagrams of the estimated system with αk at k=1,50

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Figure 12

Euclidean norm of parameter identification error: ∥α*−αk∥

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Figure 13

Hankel norm of error system: ∥G−Ĝk∥H

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Figure 14

Identified system parameters αik(i=1,2,3,4) obtained when the initial condition (Eq. 35) is used

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Figure 15

Identified coefficients d0, d1, and d2 in d(t) obtained when the initial condition (Eq. 35) is used

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Figure 16

Bode diagrams of the estimated system with αk at k=1,40

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Figure 17

ILC configuration

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Figure 18

Impulse response contaminated by noise

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Figure 19

Time plot of maximum-length sequence

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Figure 20

Control ub(t) and output ỹb(t) corrupted with noise

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Figure 21

Measured behavior of ν̃k(t) at the kth iteration (k=5,10,100)

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Figure 22

Identified system parameters αik(i=1,2,3,4)

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Figure 23

Euclidean norm of parameter identification error: ∥α*−αk∥

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Figure 24

Bode diagrams of the estimated system with αk at k=1,40

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Figure 25

Hankel norm of error system: ∥G−Ĝk∥H

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Figure 26

Identified system parameters αik(i=1,2,3,4) obtained when the initial condition (Eq. 35) is used

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Figure 27

Bode diagrams of the estimated system with αk at k=1,20

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Figure 28

Two-mass resonant system configuration

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Figure 29

Impulse response of the plant

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Figure 30

Measured behavior of ν̃k(t) at the kth iteration (k=1,2,…,23)

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Figure 31

Identified system parameter αik(i=1,2,3) and K

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Figure 32

Comparison of the model simulation response using αk and χk with the experimental response ỹk(t)−ỹb(t), where k=20

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