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.

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
.
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