Phase lead is introduced to iterative learning control systems. The best phase lead is the one that can exactly compensate the phase lag of a system. A zero phase learning control using reversed time input runs is proposed based on the analysis in frequency domain utilizing a simple phase lead generation method. The plant itself or a nominal model is used to obtain the desired phase lead to ensure the monotonic convergence of tracking errors. The learning controller is robust to large inaccuracies of system models.
1.
Arimoto
, S.
, Kawamura
, S.
, and Miyazaki
, F.
, 1984
, “Bettering Operation of Robots by Learning
,” J. Rob. Syst.
, 1
(2
), pp. 123
–140
.2.
Casalino, G., and Bartolini, G., 1984, “A Learning Procedure for the Control of Movements of Robotic Manipulators,” Proc. of 4th IASTED Symposium on Robotics and Automation, Amsterdam, Netherlands, pp. 108–111.
3.
Craig, J. J., 1984, “Adaptive Control of Manipulator Through Repeated Trials,” Proc. of American Control Conference, pp. 1566–1573.
4.
Arimoto
, S.
, 1990
, “Learning Control Theory for Robotic Motion
,” Int. J. Adapt. Control Signal Process.
, 4
(6
), pp. 543
–564
.5.
Chien
, C. J.
, and Liu
, J. S.
, 1996
, “A P-Type Iterative Controller for Robust Output Tracking of Nonlinear Time-Varying Systems
,” Int. J. Control
, 64
(2
), pp. 319
–334
.6.
Kuc
, T.-Y.
, Lee
, J. S.
, and Nam
, K.
, 1992
, “An Iterative Learning Control Theory for a Class of Nonlinear Dynamic Systems
,” Automatica
, 28
(6
), pp. 1215
–1221
.7.
Saab
, S. S.
, 1994
, “On the P-Type Learning Control
,” IEEE Trans. Autom. Control
, 39
(11
), pp. 2298
–2302
.8.
Heinzinger
, G.
, Fenwick
, D.
, Paden
, B.
, and Miyazaki
, F.
, 1992
, “Stability of Learning Control With Disturbance and Uncertain Initial Conditions
,” IEEE Trans. Autom. Control
, 37
(1
), pp. 110
–114
.9.
Bien
, Z.
, and Huh
, K. M.
, 1989
, “Higher-Order Iterative Learning Control Algorithm
,” IEE Proc.-D: Control Theory Appl.
, 136
(3
), pp. 105
–112
.10.
Amann
, N.
, Ownes
, D. H.
, and Rogers
, E.
, 1996
, “Iterative Learning Control Using Optimal Feedback and Feedforward Action
,” Int. J. Control
, 65
(2
), pp. 277
–293
.11.
Frueh
, J. A.
, and Phan
, M. Q.
, 2000
, “Linear Quadratic Optimal Control (LQL)
,” Int. J. Control
, 73
(10
), pp. 832
–839
.12.
Imamoto, H., and Shin, S., 1994, “Model Reference Learning Control With Function Approximation,” Proc. of 1st Asian Control Conference, Tokyo, Japan, pp. 269–272.
13.
Lee
, J. S.
, Park
, B. H.
, and Kuc
, T.-Y.
, 1996
, “Adaptive Learning Control of Uncertain Robotic Systems
,” Int. J. Control
, 65
(5
), pp. 725
–744
.14.
Choi, J. Y., and Park, H. J., 1995, “Adaptive Learning Control of Affine Nonlinear Systems Using Piecewise Linearly Trained Networks,” Proc. of IEEE International Conference on Neural Networks, Perth, Australia, pp. 2338–2341.
15.
Xu, J. X., and Xu, J., 2001, “A New Fuzzy Logic Learning Control Approach for Repetitive Trajectory Tracking Problems,” Proc. of American Control Conference, Arlington, VA, pp. 3878–3883.
16.
Phan
, M. Q.
, and Juang
, J. N.
, 1996
, “Design of Learning Controllers Based on an Auto-Regressive Representation of a Linear System
,” AIAA J. Guidance, Control, Dyna.
, 19
(2
), pp. 355
–362
.17.
Phan, M. Q., and Frueh, J. A., 1996, “Learning Control for Trajectory Tracking Using Basis Function,” Proc. of 35th Conference on Decision and Control, Kobe, Japan, pp. 2490–2492.
18.
Lee
, J. W.
, Lee
, H. S.
, and Bien
, Z.
, 1993
, “Iterative Learning Control With Feedback Using Fourier Series With Application to Robot Trajectory Tracking
,” Robotica
, 11
, pp. 291
–298
.19.
Wang
, D.
, 2000
, “On D-Type and P-Type ILC Designs and Anticipatory Approach
,” Int. J. Control
, 73
(10
), pp. 890
–901
.20.
Longman
, R. W.
, and Songchon
, T.
, 1999
, “Trade-Offs in Designing Learning/Repetitive Controller Using Zero-Phase Filter for Long Term Stabilization
,” Adv. Astronaut. Sci.
, 99
, pp. 673
–692
.21.
Elci, H., Longman, R. W., Phan, M., Juang, J.-N., and Ugoletti, R., 1994, “Automated Learning Control Through Model Updating for Precision Motion Control,” ASME Adaptive Structures and Composite Materials: Analysis and Application, AD-Vol. 45/MD-Vol. 54, pp. 299–314.
22.
De Luca
, A.
, Paesano
, G.
, and Ulivi
, G.
, 1992
, “A Frequency-Domain Approach to Learning Control: Implementation for a Robot Manipulator
,” IEEE Trans. Ind. Electron.
, 39
(1
), pp. 1
–10
.23.
Goh
, C. J.
, 1994
, “A Frequency Domain Analysis of Learning Control
,” ASME J. Dyn. Syst., Meas., Control
, 116
(4
), pp. 781
–786
.24.
Kavli
, T.
, 1992
, “Frequency Domain Synthesis of Trajectory Learning Controllers for Robot Manipulators
,” J. Rob. Syst.
, 9
(5
), pp. 663
–680
.25.
Longman
, R. W.
, 2000
, “Iterative Learning Control and Repetitive Control for Engineering Practice
,” Int. J. Control
, 73
(10
), pp. 930
–954
.26.
Moore, K. L., 1993, Iterative Learning Control for Deterministic System, Springer-Verlag, London.
27.
Longman, R. W., 2000, “Practical Design Methods for Iterative Learning Control and Repetitive Control,” Tutorial Notes of 6th International Conference on Control, Automation, Robotics and Vision, Singapore.
28.
Ambardar, A., 1999, Analog and Digital Signal Processing, Brooks/Cole, Pacific Grove, CA.
29.
Yamakita
, M.
, and Furuta
, K.
, 1991
, “Iterative Generation of Virtual Reference for a Manipulator
,” Robotica
, 9
, pp. 71
–80
.30.
Kinoshita
, K.
, Sogo
, T.
, and Adachi
, N.
, 2002
, “Iterative Learning Control Using Adjoint Systems and Stable Inversion
,” Asian J. Control
,4
(1
), pp. 60
–67
.31.
Ghosh, J., and Paden, B., 1999, “Iterative Learning Control for Nonlinear Nonminimum Phase Plants With Input Disturbance,” Proc. of American Control Conference, San Diego, CA, pp. 2584–2589.
32.
Le Page, W. R., 1980, Complex Variables and the Laplace Transform for Engineers, Dover Publications, New York.
33.
Ye, Y., and Wang, D., 2003, “Better Robot Tracking Accuracy With Phase Lead Compensated ILC,” Proc. of IEEE International Conference on Robotics and Automation, Taipei, pp. 4380–4385.
34.
Elci, H., Longman, R. W., Phan, M., Juang, J.-N., and Ugoletti, R., 1994, “Discrete Frequency Based Learning Control for Precision Motion Control,” Proc. of IEEE International Conference on Systems, Man, and Cybernetics, San Antonio, TX, 3, pp. 2767–2773.
35.
Jang, H. S., and Longman, R. W., 1994, “A New Learning Control Law With Monotonic Decay of Tracking Error Norm,” Proc. 32nd Allerton Conference on Communication, Control, and Computing, University of Illinois, Urbana, pp. 314–323.
36.
Jang
, H. S.
, and Longman
, R. W.
, 1996
, “An Update on a Monotonic Learning Control Law and Some Fuzzy Logic Learning Gain Adjustment Techniques
,” Adv. Astronaut. Sci.
, 90
, pp. 301
–318
.37.
Lee-Glauser
, G.
, Juang
, J.-N.
, and Longman
, R. W.
, 1996
, “Comparison and Combination of Learning Controllers: Computational Enhancement and Experiments
,” AIAA J. Guidance, Control Dyn.
, 19
(5
), pp. 1116
–1123
.38.
Markusson, O., Hjalmarsson, H., and Norrlo¨f, M., 2001, “Iterative Learning Control of Nonlinear Non-Minimum Phase Systems and Its Application to System and Model Inversion,” Proc. of 40th IEEE Conference on Decision and Control, Orlando, FL, pp. 4481–4482.
39.
Longman, R. W., 1998, “Designing Iterative Learning and Repetitive Controllers,” Iterative Learning Control: Analysis, Design, Integration and Applications, edited by Z. Bien and J. Xu, Kluwer Academic Publishers, Boston, pp. 107–146.
40.
Ye, Y., and Wang, D., 2002, “Multi-Channel Design for ILC With Robot Experiments,” Proc. of the 7th International Conference on Control, Automation, Robotics and Vision, Singapore, pp. 1066–1070.
Copyright © 2005
by ASME
You do not currently have access to this content.
