This paper presents some new results on synthesis and stability analysis of a class of repetitive controllers for discrete-time multi-input multi-output (MIMO) linear time-invariant (LTI) systems. In particular, the necessary and sufficient conditions for exponential stability of the resulting closed-loop systems are derived. A simulation case study featuring a flexible mechanical system is also presented.
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Technical Briefs
1.
Arimoto, S., 1986, “Mathematical Theory of Learning with Applications to Robot Control,” Adaptive and Learning Systems, K. S. Narendra, ed., Plenum Publishing.
2.
Chew
K-K.
Tomizuka
M.
1990
, “Digital Control of Repetitive Errors in Disk Drive Systems
,” IEEE Control System Magazine
, Vol. 10
, No. 1
, pp. 16
–20
.3.
Desoer, C. A., Vidyasagar, M., 1975, Feedback Systems: Input-Output Properties, Academic Press.
4.
Francis
B. A.
Woham
W. M.
1975
, “The Internal Model Principle for Linear Multivariable Regulators
,” Appl. Math. Opt.
, Vol. 2
, pp. 170
–194
.5.
Hara
S.
Yamamoto
Y.
Omata
T.
Nakano
M.
1988
, “Repetitive Control System: A New Type Servo System for Periodic Exogenous Signals
,” IEEE Trans Automat. Contr.
, Vol. 33
, No. 7
, pp. 659
–667
.6.
Horowitz, R., Kao, W-W., Boals, M., and Sadegh, N., 1989, “Digital Implementation of Repetitive Controllers for Robotic Manipulators,” Proc. 1989 IEEE Int. Conf. on Robotics and Automation, Scottsdale, AR, May 1989.
7.
Hu, J., and Tomizuka, M., 1991, “A New Plug-In Adaptive Controller for Rejection of Periodic Disturbances,” Presented at the 1991 ASME Winter Annual Meeting, DSC-Vol. 33, Dec. 1–6, 1991, Atlanta, GA.
8.
Inoue, T., Nakano, M., and Iwai, S., 1981a, “High Accuracy Control of Servomechanism for Repeated Contouring,” Proc. 10th Annual Symp. Incremental Motion Contr. Syst. and Devices, pp. 258–292.
9.
Inoue, T., Nakano, M., and Iwai, S., 1981b, “High Accuracy Control of a Proton Synchrotran Magnet Power Supply,” Proc. 8th World Congress of IFAC, 1981, Vol. XX, pp. 216–221.
10.
Jeon, D., and Tomizuka, M., 1991, “Repetitive Contact Force Control,” Presented at the 1991 ASME Winter Annual Meeting, DSC-Vol. 33, December 1–6, 1991, Atlanta, GA.
11.
Kato, T., 1984, Perturbation Theory for Linear Operators, Springer-Verlag, 1984, 2/ed.
12.
Kawamura, S., Miyazaki, F., and Arimoto, S., 1988, “Realization of Robot Motion Based on a Learning Method,” IEEE Trans. System, Man, Machine, Cybernetics.
13.
Narendra, K. S., and Annaswamy, A. M., 1989, Stable Adaptive Systems, Prentice Hall.
14.
Omata
T.
Hara
S.
Nakano
M.
1987
, “Nonlinear Repetitive Control with Application to Trajectory Control of Manipulators
,” J. Robotic Syst.
, Vol. 4
, pp. 631
–652
.15.
Sadegh, N., 1991, “Synthesis and Stability Analysis of Repetitive Control Systems,” Proceedings of the 1991 American Control Conference, Vol. 3, pp. 2634–2639.
16.
Sadegh
N.
Horowitz
R.
Kao
W.-W.
Tomizuka
M.
1990
, “A Unified Approach to the Design of Adaptive and Repetitive Controllers for Robotic Manipulators
,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol. 112
, Dec, pp. 618
–629
.17.
Sadegh
N.
Guglielmo
K.
1991
, “A New Repetitive Controller for Mechanical Manipulators
,” Journal of Robotic Systems
, Vol. 8
(4
), pp. 507
–522
.18.
Tomizuka
M.
Tsao
T-C.
Chew
K-K.
1989
, “Analysis and Synthesis of discrete-time repetitive controllers
,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol. 11
, No. 3
, pp. 353
–358
.19.
Yamamoto, Y., and Hara, S., 1987, “Relationships Between Internal and External Stability of Infinite Dimensional Systems with Applications to a Servo Problem,” Proc. 26th Conf. on Decision and Control, pp. 1558–1563.
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