A disturbance cancellation extension by means of Youla parametrization to a stabilizing nominal controller is investigated. In the case of a known disturbance model, disturbance frequencies or period time, it may be implemented directly as an add-on device to the existing control system. The nominal control system may be designed without consideration of the deterministic disturbances. This way it may suffice with a PID controller. It may also be a more complex one e.g., designed to obtain certain robustness properties. For known relation between the disturbance frequencies (one or more periodic signals) but unknown fundamental frequency, a frequency shaped disturbance model estimation scheme is utilized. This makes it possible to e.g., adapt the disturbance model to minimize the error directly with respect to the output. For periodic disturbances the scheme implements a self-tuning discrete time repetitive controller. To illustrate the feasibility of the approach taken it is used for rejecting a periodic disturbance acting on a nonminimum-phase plant.

1.
A˚stro¨m
K.
,
Hagander
P.
, and
Sternby
J.
,
1984
. “
Zeros of Sampled Systems
,”
Automatica
20
(
1
),
31
38
.
2.
A˚stro¨m, K., and B. Wittenmark, 1984, Computer controlled system, Prentice-Hall.
3.
Hara, S., and Y. Yamamoto, 1985, “Stability of Repetitive Control Systems,” Proceedings of the 25th Conference on Decision and Control.
4.
Hillerstro¨m, G., 1992, “Rejection of Periodic Disturbances,” Licentiate Thesis 1992:21L Lulea˚ University of Technology.
5.
Hillerstro¨m, G., 1994, “On Repetitive Control,” Doctoral thesis 1994:155D Lulea˚ University of Technology.
6.
Hillerstro¨m, G. and J. Sternby, 1994a, “Application of repetitive control to a peristaltic pump,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL 116 (4).
7.
Hillerstro¨m, G. and J. Sternby, 1994b, “Rejection of Periodic Disturbances with Unknown Period—A Frequency Domain Approach,” Proceedings of the American Control Conference. 1626–1631 Baltimore.
8.
Hillerstro¨m, G. and J. Sternby, 1994c, “Repetitive Control Using Low Order Models.” Proceedings of the American Control Conference. 1873–1878 Baltimore.
9.
Inoue, T., M. Nakano and S. Iwai, 1981, “High Accuracy Control of Servo-mechanism for Repeated Contouring,” 10th Annual Symposium on Incremental Motion Control Systems and Devices. 285–292, Chicago.
10.
Langari, A. and B. Francis, 1994a, “Sampled-data Repetitive Control Systems,” Research Report No. 9403 Systems Control Group, University of Toronto.
11.
Langari, A. and B. A. Francis, 1994b, “Sampled-data Repetitive Control Systems,” Proceedings of the American Control Conference. 3234–3235 Baltimore.
12.
Medvedev, A. and G. Hillerstro¨m, 1993, “On Perfect Disturbance Rejection.” Proceedings of the 32nd Conference on Decision and Control, 1324–1329 San Antonio, Texas.
13.
Medvedev, A. and G. Hillerstro¨m, 1994, “External Model Control of a Peristaltic Pump,” Preprints of the IFAC Symposium on Advanced Control of Chemical Processes. 519–524 Kyoto, Japan.
14.
Middleton
R.
,
Goodwin
G. C.
and
Longman
R. W.
,
1989
, “
A Method for Improving the Dynamic Accuracy of a Robot Performing a Repetitive Task
,”
The International Journal of Robotics Research
8
(
5
),
67
74
.
15.
Ro¨nnba¨ck, S., G. Hillerstro¨m and J. Sternby, 1993, “Periodic-disturbance Rejection and Setpoint Tracking with Application to a Peristaltic Pump,” Proceedings of the European Control Conference, 202–208 Groningen, The Netherlands.
16.
Sadegh
N.
,
Horowitz
R.
,
Kao
W.-W.
and
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
,
112
,
618
629
.
17.
Tomizuka
M.
,
Chew
K.-K.
and
Tsao
T.-C
,
1989
, “
Analysis and Synthesis of Discrete-time Repetitive Controllers
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
111
,
353
358
.
18.
Tomizuka
M.
,
Chew
K.-K.
and
Yang
W.-C.
,
1990
, “
Disturbance Rejection Through an External Model
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
112
,
559
564
.
19.
Tomizuka
M.
,
1993
, “
On the Design of Digital Tracking Controllers
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
115
(
2B
),
412
418
.
20.
Tsao, T. and M. Tomizuka, 1988, “Adaptive and Repetitive Digital Control Algorithms for Noncircular Machining. Proceedings of the American Control Conference. 115–120.
21.
Tsao, T.-C. and M. Nemani, 1992, “Asymptotic Rejection of Periodic Disturbances with Uncertain Period,” Proceedings of the American Control Conference. 2696–2699.
22.
Tsao, T.-C. and Y.-X. Qian, 1993, “An Adaptive Repetitive Control Scheme for Tracking Periodic Signals with Unknown Period,” Proceedings of the American Control Conference. 1736–1740 San Francisco.
23.
Tsypkin, Y., 1991, “Robust Adaptive Control of Systems Under Bounded Uncertainty,” IFAC Symposium on Identification and System Parameter Estimation. 205–208 Budapest, Hungary.
24.
Walgama, K., 1991, “On the Control of Systems with Input Saturation or Periodic Disturbances,” Doctoral thesis 1991:093D Lulea˚ University of Technology.
25.
Wolfram, S., 1991. Mathematica—A System for Doing Mathematics by Computer, second edition. Addison Wesley.
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