This paper considers iterative learning control law design using the theory of linear repetitive processes. This setting enables trial-to-trial error convergence and along-the-trial performance to be considered simultaneously in the design. It is also shown that this design extends naturally to include robustness to unmodeled plant dynamics. The results from experimental application of these laws to a gantry robot performing a pick and place operation are given, together with a discussion of the positioning of this approach relative to alternatives and possible further research.
Issue Section:
Research Papers
References
1.
Arimoto
, S.
, Kawamura
, S.
, and Miyazaki
, F.
, 1984, “Bettering Operations of Robots by Learning
,” J. Rob. Syst.
, 1
(2
), pp. 123
–140
.2.
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
.3.
Ahn
, H.-S.
, Chen
, Y.
, and Moore
, K. L.
, 2007, “Iterative Learning Control: Brief Survey and Categorization
,” IEEE Trans. Syst., Man, Cybern., Part C
, 37
(6
), pp. 1109
–1121
.4.
Rogers
, E.
, Galkowski
, K.
, and Owens
, D. H.
, 2007, Control Systems Theory and Applications for Linear Repetitive Processes
(Lecture Notes in Control and Information Sciences), Springer-Verlag
, Berlin
, Vol. 349
.5.
Roesser
, R. P.
, 1975, “A Discrete State Space Model for Linear Image Processing
,” IEEE Trans. Autom. Control
, 20
, pp. 1
–10
.6.
Fornasini
, E.
, and Marchesini
, G.
, 1978, “Doubly-Indexed Dynamical Systems: State Space Models and Structural Properties
,” Math. Syst. Theory
, 12
, pp. 59
–72
.7.
Kurek
, J. E.
, and Zaremba
, M. B.
, 1993, “Iterative Learning Control Synthesis Based on 2-D System Theory
,” IEEE Trans. Autom. Control
, 38
(1
), pp. 121
–125
.8.
Hladowski
, L.
, Galkowski
, K.
, Cai
, Z.
, Rogers
, E.
, Freeman
, C. T.
, and Lewin
, P. L.
, 2010, “Experimentally Supported 2D Systems Based Iterative Learning Control Law Design for Error Convergence and Performance
,” Control Eng. Pract.
, 18
(4
), pp. 339
–348
.9.
Arimoto
, S.
, Miyazaki
, F.
, Kawamura
, S.
, and Tamaki
, S.
, 1985, “Learning Control Theory for Dynamical Systems
,” Proceedings of the 24th IEEE Conference on Decision and Control
, Fort Lauderdale, FL, pp. 1375
–1380
.10.
Arimoto
, S.
, Miyazaki
, F.
, and Kawamura
, S.
, 1984, “Bettering Operation of Dynamical Systems by Learning: A New Control Theory for Servomechanism or Mechatronics Systems
,” Proceedings of the 23rd IEEE Conference on Decision and Control
, Las Vegas, NV, pp. 1064
–1069
.11.
Wang
, D.
, 1999, “On Anticipatory Iterative Learning Control Designs for Continuous Time Nonlinear Dynamic Systems
,” Proceedings of the 38th IEEE Conference on Decision and Control
, Phoenix, AZ, pp. 1605
–1610
.12.
Wang
, Y.
, and Longman
, R. W.
, 1996, “Use of Non-Causal Digital Signal Processing in Learning and Repetitive Control
,” Adv. Astronaut. Sci.
, 90
(1
), pp. 649
–668
.13.
Freeman
, C.
, Lewin
, P. L.
, and Rogers
, E.
, 2007, “Further Results on the Experimental Evaluation of Iterative Learning Control Algorithms for Non-Minimum Phase Plants
,” Int. J. Control
, 80
(4
), pp. 569
–582
.14.
Wallen
, J.
, Norrlof
, M.
, and Gunnarsson
, S.
, 2008, “Arm-side Evaluation of ILC Applied to a Six-Degrees-of-Freedom Industrial Robot
,” Proceedings of 17th IFAC World Congress 2008
, Seoul, Korea, pp. 13450
–13455
.15.
Chen
, Y. Q.
, Wen
, C. Y.
, and Sun
, M. X.
, 2007, “A Robust High-Order p-Type Learning Controller Using Current Iteration Tracking Error
,” Int. J. Control
, 68
(2
), pp. 331
–342
.16.
Norrlof
, M.
, and Gunnarsson
, S.
, 1999, “A Frequency Domain Analysis of a Second Order Iterative Learning Control Algorithm
,” Proceedings of the 38th Conference on Decision and Control
, Phoenix, AZ, pp. 1587
–1592
.17.
Ratcliffe
, J. D.
, Hatonen
, J. J.
, Lewin
, P. L.
, Rogers
, E.
, Harte
, T. J.
, and Owens
, D. H.
, 2005, “P-Type Iterative Learning Control for Systems that Contain Resonance
,” Int. J. Adapt. Control Signal Process.
, 19
(10
), pp. 769
–796
.18.
El
Ghaoui
, L.
, Nikoukhah
, R.
, and Delebecque
, F.
, 1995, “LMITOOL: A Package for LMI Optimization
,” IEEE Conference on Decision and Control
, Vol. 3
, pp. 3096
–3101
.19.
Zhang
, B.
, Wang
, D.
, Zhou
, K. K.
, Ye
, Y.
, and Wang
, Y.
, 2008, “Pseudo-Downsampled Iterative Learning Control
,” Int. J. Robust Nonlinear Control
, 18
(10
), pp. 1072
–1088
.20.
Zhang
, B.
, Wang
, D.
, Zhou
, K. K.
, Ye
, Y.
, and Wang
, Y.
, 2008, “Cyclic Pseudo-Downsampled Iterative Learning Control for High Performance Tracking
,” Control Eng. Pract.
, 17
(8
), pp. 957
–965
.21.
Longman
, R. W.
, 2000, “Iterative Learning Control and Repetitive Control for Engineering Practice
,” Int. J. Control
, 73
, pp. 930
–954
.22.
van de Wijdeven
, J.
, Donkers
, T.
, and Bosgra
, O. H.
, 2009, “Iterative Learning Control for Uncertain Systems: Robust Monotonic Convergence Analysis
,” Automatica
, 45
(10
), pp. 2383
–2391
.23.
Xu
, J.-X.
, Chen
, Y.
, Lee
, T. H.
, and Yamamoto
, S.
, 1999, “Terminal ILC With an Application to RTPCVD Thickness Control
,” Automatica
, 35
(9
), pp. 1535
–1542
.Copyright © 2012
by American Society of Mechanical Engineers
You do not currently have access to this content.