Repetitive control schemes for asymptotic tracking and disturbance rejection of periodic signals with an unknown period are presented. A sampled data recursive scheme for identifying the period of a periodic signal with a resolution finer than the sampling interval is presented. Discrete-time self-tuning repetitive controllers, which adapt both the periodic signal period and sampling interval, are proposed based on the period identification scheme. The fine adaptation of the controller sampling interval makes the identified signal period an exact integer multiples of the controller sampling interval and renders a superior tracking performance than that of the conventional fixed sampling interval repetitive controllers. Experimental results on a linear motion system are presented to demonstrate the effectiveness of the proposed control schemes. [S0022-0434(00)01402-7]

Issue Section:
Technical Briefs
Keywords:
time-varying systems, periodic control, tracking, uncertain systems, stability, sampled data systems, recursive estimation, discrete time systems, adaptive control, self-adjusting systems
Topics:
Control equipment, Signals, Stability
1.
Hara
,
S.
,
Yomamoto
,
Y.
,
Omata
,
T.
, and
Nakano
,
M.
,
1988
, “
Repetitive Control System: A New Type Servo System for Periodic Exogenous Signals
,”
IEEE Trans. Autom. Control.
,
33
, No.
7
, p.
659
659
.
2.
Tomizuka
,
M.
,
Tsao
,
T-C.
, and
Chew
,
K. K.
,
1989
, “
Discrete-Time Domain Analysis and Synthesis of Repetitive Controllers
,”
ASME J. Dyn. Syst., Meas., Control
,
111
, No.
3
, pp.
353
–
358
.
3.
Tsao, T-C., and Tomizuka, M., 1988, “Adaptive and Repetitive Digital Control Algorithms for Noncircular Machining,” Proceedings ACC, Atlanta, GA., June, pp. 115–120.
4.
Omata
,
T.
et al.,
1987
, “
Nonlinear Repetitive Control with Application to Trajectory Control of Manipulators
,”
J. Robot. Syst.
,
4
, No.
5
, pp.
631
–
652
.
5.
Tasi, M., Anwar, G., and Tomizuka, M., 1988, “Discrete Time Repetitive Control for Robot Manipulator,” Proc. of IEEE Int. Conf. on Robotics and Automation, p. 1341.
6.
Chew
,
K. K.
, and
Tomizuka
,
M.
,
1990
, “
Digital Control of Repetitive Errors in Disk Drive Systems
,”
IEEE Control Syst. Mag.
,
10
, p.
16
16
.
7.
Higuchi, T., Otsuka, M., Mizuno, T., and Ide, T., 1990, “Application of Periodic Learning Control with Inverse Transfer Function Compensation in Totally Active Magnetic Bearings,” Proc. 2nd. Int. Symp. on Magnetic Bearings, p. 257.
8.
Tsao
,
T.
,
Burke
,
J. B.
, and
Ferreira
,
P. M.
,
1989
, “
Control of Radial Runout in Face Milling
,” Symposium on Control Issues in Manufacturing Processes
ASME DSC-
,
18
, p.
99
99
.
9.
Tsao
,
T. C.
, and
Pong
,
K.
, 1991, “
Control of Radial Runout in Multi-Tooth Face Milling
,”
Tran. of NAMRI/SME
, Vol.
19
, p.
183
183
.
10.
Kobayashi et al., 1990, “Reduction of Motor Speed Fluctuation Using the Repetitive Control,” Proc. 29th CDC, Hawaii, pp. 1697–1702.
11.
Tsao
,
T.-C.
, and
Pong
,
K.-C.
, 1992, “
Spindle Speed Regulation and Tracking in Interrupted Cutting
,”
Tran. of NAMRI/SME
, Vol.
20
, p.
235
235
.
12.
Tsao, T-C., and Nemani, M., 1992, “Asymptotic Rejection of Periodic Disturbances with Uncertain Period,” Proc. American Control Conference, Chicago, IL, June, pp. 2696–2699.
13.
Hu, J-S., 1992, “Variable Structure Digital Repetitive Controller,” Proc. American Control Conference, Chicago, IL, June, pp. 2686–2690.
14.
Desoer, C. A., and Vidyasagar, M., 1975, Feedback Systems: Input-Output Properties, Academic Press, New York.
15.
Manayathara
,
T. J.
,
Tsao
,
T. C.
, and
Bentsman
,
J.
,
1996
, “
Rejection of Unknown Periodic Load Disturbances in Continuous Steel Casting Process Using Learning Repetitive Approach
,”
IEEE Trans. Control Systems Technol.
,
4
, No.
3
, p.
265
265
.
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