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Research Papers

Iterative Learning Identification/Iterative Learning Control for Linear Time-Varying Systems

[+] Author and Article Information
Nanjun Liu

Ford Research and Innovation Center,
Dearborn, MI 48124
e-mail: liu98@illinois.edu

Andrew Alleyne

Mechanical Science and Engineering,
University of Illinois,
Urbana, IL 61801
e-mail: alleyne@illinois.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 3, 2015; final manuscript received May 8, 2016; published online June 15, 2016. Assoc. Editor: Zongxuan Sun.

J. Dyn. Sys., Meas., Control 138(10), 101005 (Jun 15, 2016) (9 pages) Paper No: DS-15-1365; doi: 10.1115/1.4033630 History: Received August 03, 2015; Revised May 08, 2016

This paper integrates a previously developed iterative learning identification (ILI) (Liu, N., and Alleyne, A. G., 2016, “Iterative Learning Identification for Linear Time-Varying Systems,” IEEE Trans. Control Syst. Technol., 24(1), pp. 310–317) and iterative learning control (ILC) algorithms (Bristow, D. A., Tharayil, M., and Alleyne, A. G., 2006, “A Survey of Iterative Learning Control,” IEEE Control Syst. Mag., 26(3), pp. 96–114), into a single norm-optimal framework. Similar to the classical separation principle in linear systems, this work provides conditions under which the identification and control can be combined and guaranteed to converge. The algorithm is applicable to a class of linear time-varying (LTV) systems with parameters that vary rapidly and analysis provides a sufficient condition for algorithm convergence. The benefit of the integrated ILI/ILC algorithm is a faster tracking error convergence in the iteration domain when compared with an ILC using fixed parameter estimates. A simple example is introduced to illustrate the primary benefits. Simulations and experiments are consistent and demonstrate the convergence speed benefit.

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References

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Figures

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Fig. 1

Integrated ILI and ILC design

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Fig. 2

One DOF pick and place robot arm

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Fig. 3

PD closed-loop control of the pick and place robot with ILC

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Fig. 4

Experimental closed loop tracking result with a PD feedback controller (no ILC)

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Fig. 5

Simulated parameter identification results at iteration 10

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Fig. 6

Simulated root-mean-square (RMS) parameter estimation error in the iteration domain

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Fig. 7

Simulated RMS tracking error convergence in iteration domain

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Fig. 8

Experimental parameter identification results at iteration 10

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Fig. 9

Experimental RMS parameter estimation error

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Fig. 10

Experimental RMS tracking error

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Fig. 11

Tracking result with ILC controllers

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Fig. 12

Simulated RMS parameter estimation error in the iteration domain. (a) Experimental tracking error at iteration 3 and (b) experimental tracking error at iteration 10.

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