Fractional uncertainties are involved in many practical systems. Currently, there is a lack of research results about such general class of nonlinear systems in the context of learning control. This paper presents a Lyapunov-synthesis approach to repetitive learning control (RLC) being unified due to the use of the direct parametrization and adaptive bounding techniques. To effectively handle fractional uncertainties, the estimation method for such uncertainties is elaborated to facilitate the controller design and convergence analysis. Its novelty lies in the less requirement for the knowledge about the system undertaken. Unsaturated- and saturated-learning algorithms are, respectively, characterized by which both the boundedness of the variables in the closed-loop system undertaken and the asymptotical convergence of the tracking error are established. Experimental results are provided to verify the effectiveness of the presented learning control.
Issue Section:
Research Papers
References
1.
Tomizuka
, M.
, Tsao
, T.-C.
, and Chew
, K.-K.
, 1989
, “Analysis and Synthesis of Discrete-Time Repetitive Controllers
,” ASME J. Dyn. Syst. Meas. Control
, 111
(3
), pp. 353
–358
.2.
Arimoto
, S.
, 1990
, “Learning Control Theory for Robotic Motion
,” Int. J. Adapt. Control Signal Process.
, 4
(6
), pp. 543
–564
.3.
Longman
, R. W.
, 2000
, “Iterative Learning Control and Repetitive Control for Engineering Practice
,” Int. J. Control
, 73
(10
), pp. 930
–954
.4.
Bristow
, D. A.
, Tharayil
, M.
, and Alleyne
, A. G.
, 2006
, “A Survey of Iterative Learning Control
,” IEEE Trans. Control Syst. Mag.
, 26
(3
), pp. 96
–114
.5.
Wang
, D.
, Ye
, Y.
, and Zhang
, B.
, 2014
, Practical Iterative Learning Control With Frequency Domain Design and Sampled Data Implementation
, Springer
, Singapore
.6.
Pipeleers
, G.
, and Moore
, K. L.
, 2014
, “Unified Analysis of Iterative Learning and Repetitive Controllers in Trial Domain
,” IEEE Trans. Autom. Control
, 59
(4
), pp. 953
–965
.7.
Sadegh
, N.
, Horowitz
, R.
, Kao
, W.
, and Tomizuka
, M.
, 1990
, “A Unified Approach to Design of Adaptive and Repetitive Controllers for Robotic Manipulators
,” ASME J. Dyn. Syst. Meas. Control
, 112
(4
), pp. 618
–629
.8.
Kuc
, T.-Y.
, Kwanghee
, N.
, and Lee
, J.
, 1991
, “An Iterative Learning Control of Robot Manipulators
,” IEEE Trans. Rob. Autom.
, 7
(6
), pp. 853
–842
.9.
Qu
, Z.
, Dorsey
, J.
, Dawson
, D.
, and Johnson
, R.
, 1993
, “Linear Learning Control of Robot Motion
,” J. Rob. Syst.
, 10
(1
), pp. 123
–140
.10.
Park
, B.
, Kuc
, T.
, and Lee
, J.
, 1996
, “Adaptive Learning Control of Uncertain Robotic Systems
,” Int. J. Control
, 65
(5
), pp. 725
–744
.11.
Qu
, Z.
, and Xu
, J. X.
, 2002
, “Model Based Learning Control and Their Comparisons Using Lyapunov Direct Method
,” Asian J. Control
, 4
(1
), pp. 99
–110
.12.
Xu
, J. X.
, 2011
, “A Survey on Iterative Learning Control for Nonlinear Systems
,” Int. J. Control
, 84
(7
), pp. 1275
–1294
.13.
French
, M.
, and Rogers
, E.
, 2000
, “Non-Linear Iterative Learning by an Adaptive Lyapunov Technique
,” Int. J. Control
, 73
(10
), pp. 840
–850
.14.
Sun
, D.
, and Mills
, J. K.
, 1999
, “Performance Improvement of Industrial Robot Trajectory Tracking Using Adaptive-Learning Scheme
,” ASME J. Dyn. Syst. Meas. Control
, 121
(2
), pp. 285
–292
.15.
Xu
, L.
, and Yao
, B.
, 2001
, “Adaptive Robust Repetitive Control of a Class of Nonlinear Systems in Normal Form With Applications to Motion Control of Linear Motors
,” IEEE/ASME International Conference on Advanced Intelligent Mechantronics (AIM
), Como, Italy, July 8–12, pp. 527
–532
.16.
Xu
, J. X.
, and Tan
, Y.
, 2002
, “A Composite Energy Function-Based Learning Control Approach for Nonlinear Systems With Time-Varying Parametric Uncertainties
,” IEEE Trans. Autom. Control
, 47
(11
), pp. 1940
–1945
.17.
Dixon
, W. E.
, Zergeroglu
, E.
, Dawson
, D. M.
, and Costic
, B. T.
, 2002
, “Repetitive Learning Control: A Lyapunov-Based Approach
,” IEEE Trans. Syst. Man Cybern., Part B
, 32
(4
), pp. 538
–545
.18.
Sun
, M.
, and Ge
, S. S.
, 2006
, “Adaptive Repetitive Control for a Class of Nonlinearly Parametrized Systems
,” IEEE Trans. Autom. Control
, 51
(10
), pp. 1684
–1688
.19.
Tan
, Y. H. H.
, Dai
, D. H.
, and Xu
, J. X.
, 2012
, “Unified Iterative Learning Control Schemes for Nonlinear Dynamic Systems With Nonlinear Input Uncertainties
,” Automatica
, 48
(12
), pp. 3173
–3182
.20.
Tayebi
, A.
, and Chien
, C. J.
, 2007
, “A Unified Adaptive Iterative Learning Control Framework for Uncertain Nonlinear Systems
,” IEEE Trans. Autom. Control
, 52
(10
), pp. 1907
–1913
.21.
Qu
, Z.
, and Xu
, J. X.
, 2002
, “Asymptotic Learning Control for a Class of Cascaded Nonlinear Uncertain Systems
,” IEEE Trans. Autom. Control
, 47
(8
), pp. 1369
–1376
.22.
Chien
, C. J.
, 2008
, “A Combined Adaptive Law for Fuzzy Iterative Learning Control of Nonlinear Systems With Varying Control Tasks
,” IEEE Trans. Fuzzy Syst.
, 16
(1
), pp. 40
–51
.23.
Quan
, Q.
, and Cai
, K. Y.
, 2011
, “A Filtered Repetitive Controller for a Class of Nonlinear Systems
,” IEEE Trans. Autom. Control
, 56
(2
), pp. 399
–405
.24.
Qu
, Z.
, 1998
, Robust Control of Nonlinear Uncertain Systems
, Wiley
, New York
.25.
Tian
, Y.
, and Yu
, X.
, 2003
, “Robust Learning Control for a Class of Nonlinear Systems With Periodic and a Periodic Uncertainties
,” Automatica
, 39
(11
), pp. 1957
–1966
.26.
Chen
, W.
, and Jiao
, L.
, 2010
, “Adaptive Tracking for Periodically Time-Varying and Nonlinearly Parameterized Systems Using Multilayer Neural Network
,” IEEE Trans. Neural Networks
, 21
(2
), pp. 345
–351
.27.
Li
, X.
, Huang
, D.
, Chu
, B.
, and Xu
, J. X.
, 2016
, “Robust Iterative Learning Control for Systems With Norm-Bounded Uncertainties
,” Int. J. Robust Nonlinear Control
, 26
(4
), pp. 697
–718
.28.
Marino
, R.
, and Tomei
, P.
, 2009
, “An Iterative Learning Control for a Class of Partially Feedback Linearizable Systems
,” IEEE Trans. Autom. Control
, 54
(8
), pp. 1991
–1996
.29.
Sun
, M.
, 2009
, “A Barbalat-Like Lemma With Its Application to Learning Control
,” IEEE Trans. Autom. Control
, 54
(9
), pp. 2222
–2225
.30.
Yang
, Z.
, Yam
, S. C. P.
, Li
, L. K.
, and Wang
, Y.
, 2010
, “Universal Repetitive Learning Control for Nonparametric Uncertainty and Unknown Control Gain Matrix
,” IEEE Trans. Autom. Control
, 55
(7
), pp. 1710
–1715
.31.
Jin
, X.
, Huang
, D.
, and Xu
, J.-X.
, 2012
, “Iterative Learning Control for Systems With Nonparametric Uncertainties Under Alignment Condition
,” 51st IEEE Conference on Decision and Control (CDC
), Maui, HI, Dec. 10–13, pp. 3942
–3947
.32.
Huang
, D.
, Xu
, J.-X.
, Yang
, S.
, and Jin
, X.
, 2015
, “Observer Based Repetitive Learning Control for a Class of Nonlinear Systems With Non-Parametric Uncertainties
,” Int. J. Robust Nonlinear Control
, 25
(8
), pp. 1214
–1229
.33.
Sun
, M.
, Wang
, Y.
, and Wang
, D.
, 2005
, “Variable-Structure Repetitive Control: A Discrete-Time Strategy
,” IEEE Trans. Ind. Electron.
, 52
(2
), pp. 610
–616
.Copyright © 2018 by ASME
You do not currently have access to this content.
