Upper bounds on transient response magnitudes for a SISO continuous-time repetitive control system are derived. Limiting the size of these transients is shown to be related to limiting the ∞-norm of a transfer function product of filters used in the repetitive controller. The decay rate of the transients is related to the peak of a function of frequency called the regeneration spectrum, which has previously been shown in the literature to be a measure of the relative stability of the system. Bounds derived here, although conservative, can be useful in the design of the repetitive controller, as illustrated by means of an example.

1.
Chew
K. K.
, and
Tomizuka
M.
,
1990
, “
Digital Control of Repetitive Errors in Disk Drive Systems
,”
IEEE Control Systems Magazine
, Vol.
10
, No.
1
, Jan., pp.
16
20
.
2.
Churchill, R. V., 1972, Operational Mathematics, McGraw-Hill, New York.
3.
Doyle, J. C., Francis, B. A., and Tannenbaum, A. R., 1992, Feedback Control Theory, Macmillan, New York.
4.
Garimella, S. S., 1994, “Application of Repetitive Control and Iterative Learning Control to Cold Rolling Processes,” Ph.D. dissertation. Department of Mechanical Engineering, The Ohio State University, Columbus, Ohio.
5.
Garimella, S. S., and Srinivasan, K., 1994, “Application of Repetitive Control to Eccentricity Compensation in Rolling,” Proceedings of the American Control Conference, Baltimore, June, pp. 2904–2908.
6.
Hara, S., Omata, T., and Nakano, M., 1985, “Synthesis of Repetitive Control Systems and Its Application,” Proceedings of the 24th IEEE Conference on Decision and Control, Ft. Lauderdale, Florida, Dec. pp. 1387–1392.
7.
Hara
S.
,
Yamamoto
Y.
,
Omata
T.
, and
Nakano
M.
,
1988
, “
Repetitive Control System: A New Type Servo System for Periodic Exogenous Signals
,”
IEEE Transactions on Automatic Control
, Vol.
33
, No.
7
, July, pp.
659
667
.
8.
Srinivasan
K.
, and
Shaw
F.-R.
,
1991
, “
Analysis and Design of Repetitive Control Systems Using the Regeneration Spectrum
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
113
, pp.
216
222
.
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