A method for designing repetitive feedback controllers using nonparametric frequency response plant models is developed. In comparison to the zero-phase-error (ZPE) controller (ASME J. Dyn. Syst. Meas. Control, 111, pp. 353–358), this method has the added benefit of providing improved transient performance when the plant inverse is unstable. In this controller design process, a connection is made between model uncertainty and the desired frequency response of the so-called q filter. Also, it will be shown that an optimal equiripple filter is useful when designing high-order q filters. The entire process was experimentally verified on an engine control application. A repetitive controller was used to determine the dynamic fueling requirements of a fuel injected, spark-ignition engine subjected to periodic changes in the throttle position. This fueling information is necessary when designing feedforward fueling algorithms.

Keywords:
control system synthesis, fuel optimal control, closed loop systems, robust control, internal combustion engines, fuel systems, uncertain systems, feedforward, frequency response, feedback
Topics:
Control equipment, Design, Errors, Feedback, Filters, Frequency response, Fuels, Transients (Dynamics), Stability, Engines, Feedforward control, Control systems
1.
Kempf, C., Messner, W., Tomizuka, M., and Horowitz, R., 1992, “A Comparison of Four Discrete-Time Repetitive Control Algorithms,” Proceedings of the American Control Conference, pp. 2700–2704.
2.
Inoue, T., Nakano, M., and Iwai, S., 1981, “High Accuracy Control of a Proton Synchrotron Magnet Power Supply,” Proceedings of the 8th Triennial IFAC World Congress, Vol. 6, pp. 3137–3142.
3.
Inoue, T., 1990, “Practical Repetitive Control System Design,” Proceedings of the 29th IEEE Conference on Decision and Control, Honolulu, Hawaii, Vol. 3, pp. 1673–1678.
4.
Ko¨rogˇlu, H., and Morgu¨l, O., 1999, “Discrete-Time LQ Optimal Repetitive Control,” Proceedings of the American Control Conference, San Diego, California, Vol. 5, pp. 3287–3291.
5.
Peery, T., and O¨zbay, H., 1993, “On H∞ Optimal Repetitive Controllers,” Proceedings of the 32nd IEEE Conference on Decision and Control, San Antonio, Texas, Vol. 2, pp. 1146–1151.
6.
Hara
,
S.
,
Yamamoto
,
Y.
,
Omata
,
T.
, and
Nakano
,
M.
,
1988
, “
Repetitive Control System: A New Type Servo System for Periodic Exogenous Signals
,”
IEEE Trans. Autom. Control
,
33
, pp.
659
–
668
.
7.
Li, J., and Tsao, T. C., 1998, “A Two Parameter Robust Repetitive Control Design Using Structured Singular Values,” Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, Florida, Vol. 2, pp. 1230–1235.
8.
Tomizuka
,
M.
,
Tsao
,
T. C.
, and
Chew
,
K. K.
,
1989
, “
Analysis and Synthesis of Discrete-Time Repetitive Controllers
,”
ASME, J. Dyn. Syst. Meas.
,
111
, pp.
353
–
358
.
9.
Tomizuka
,
M.
,
1987
, “
Zero Phase Error Tracking Algorithm for Digital Control
,”
ASME J. Dyn. Syst., Meas., Control
,
190
, pp.
65
–
68
.
10.
Yamada, M., Riadh, Z., and Funahashi, Y., 1999, “Design of Discrete-Time Repetitive Control System for Pole Placement and Application,” IEEE/ASME Transactions on Mechatronics, Vol. 4, pp. 110–118.
11.
Guo, L., 1997, “Reducing the Manufactureing Costs Associated With Hard Disk Drives—A New Disturbance Rejection Control Scheme,” IEEE/ASME Transactions on Mechatronics, Vol. 2, pp. 77–85.
12.
Smith, C., and Tomizuka, M., 2000, “A Cost Effective Repetitive Controller,” Proceedings of the American Control Conference, Chicago, Illinois, Vol. 2, pp. 1169–1174.
13.
Bendat, J. S., and Piersol, A. G., 1986, Random Data: Analysis and Measurement Procedures, 2nd Edition, John Wiley & Sons, New York.
14.
Zhou, K., and Doyle, J. C., 1998, Essentials of Robust Control, Prentice–Hall, Upper Saddle River, NJ.
15.
Proakis, J. G., and Manolakis, D. G., 1996, Digital Signal Processing: Prin-ciples, Algorithms, and Applications, 3rd ed., Prentice–Hall, Upper Saddle River, NJ.
16.
Oppenheim, A. V., and Schafer, R. W., 1998, Discrete-Time Signal Processing, 2nd ed., Prentice–Hall, Upper Saddle River, NJ.
17.
Ljung, L., 1999, System Identification: Theory for the User, 2nd ed., Prentice–Hall, Upper Saddle River, NJ.
18.
Clarkson, P. M., 1993, Optimal and Adaptive Signal Processing, CRC Press, Boca Raton, FL.
Copyright © 2004
 by ASME
You do not currently have access to this content.