An adaptive regulation approach against disturbances consisting of linear combinations of sinusoids with unknown and/or time varying amplitudes, frequencies, and phases for SISO LTI discrete-time systems is considered. The new regulation approach proposed is based on constructing a set of stabilizing controllers using the Youla parametrization of stabilizing controllers and adjusting the Youla parameter to achieve asymptotic disturbance rejection. Three adaptive regulator design algorithms are presented and their convergence properties analyzed. Conditions under which the on-line algorithms yield an asymptotic controller that achieves regulation are presented. Conditions both for the case where the disturbance input properties are constant but unknown and for the case where they are unknown and time varying are given. In the case of error feedback, the on-line controller construction amounts to an adaptive implementation of the Internal Model Principle. The performance of the adaptation algorithms is illustrated through a simulation example. A companion paper [4] describes the implementation and evaluation of the algorithms for the problem of noise cancellation in an acoustic duct.
Issue Section:
Technical Papers
1.
K. J. Astrom and B. Wittenmark, Adaptive Control, Addison-Wesley, 1995.
2.
F. Ben Amara, “Adaptive Sinusoidal Disturbance Rejection in Linear Systems With Application To Noise Cancellation,” Ph.D. thesis, The University of Michigan, 1996.
3.
Ben Amara
F.
Kabamba
P. T.
Ulsoy
A. G.
Adaptive Band-Limited Disturbance Rejection in Linear Discrete-Time Systems
,” Mathematical Problems in Engineering
, Vol. 1
, No. 2
, pp. 139
–177
, 1995
.4.
F. Ben Amara, P. T. Kabamba, and A. G. Ulsoy, “Adaptive Algorithms for Sinusoidal Disturbance Rejection—Part II; Experiments,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT AND CONTROL, published in this issue pp. 655–659.
5.
M. Bodson, “Adaptive Algorithms for the Rejection of Sinusoidal Disturbances with Unknown Frequency,” Proceeding of the 13th IFAC Triennial World Congress, San Francisco, CA, Vol. K, pp. 229–234, 1996.
6.
Canetti
R. M.
Espana
M. D.
Convergence Analysis of the Least-Squares Identification Algorithm with a Variable Forgetting Factor for Time-Varying Linear Systems
,” Automatica
, Vol. 25
, pp. 609
–612
, 1989
.7.
G. Celantano and R. Setola, “A Technique for Narrow-Band Persistent-Disturbance Attenuation,” Proceedings of the 1996 IFAC World Congress, San Francisco, CA, 1996.
8.
C. K. Chak and G. Feng, “Adaptive Control with External Model for Periodic Disturbance Rejection,” International Journal of Systems Sciences, pp. 1965–1976, 1994.
9.
C. Corduneanu, Almost Periodic Functions, Wiley, NY, 1961.
10.
H. Elliott and G. C. Goodwin, “Adaptive Implementation of the Internal Model Principle,” Proceedings of the 23rd Conference on Decision and Control, pp. 1292–1297, 1984.
11.
G. Feng, “Robust Adaptive Rejection of Unknown Deterministic Disturbances,” Proceedings of the American Control Conference, pp. 1624–1625, 1994.
12.
Feng
G.
Palaniswami
M.
A Stable Adaptive Implementation of the Internal Model Principle
,” IEEE Transactions on Automatic Control
, Vol. 37
, pp. 1120
–1225
, 1992
.13.
B. A. Francis, A Course in H∞ Control Theory, Springer-Verlag, New York, 1987.
14.
G. Hillerstrom and J. Sternby, “Rejection of Periodic Disturbances with Unknown Period—A Frequency Domain Approach,” Proceedings of the American Control Conference, pp. 1626–1631, 1994.
15.
Johnson
C. D.
A Discrete-Time Disturbance-Accomodating Control Theory for Digital Control of Dynamic System
,” Control of Dynamic Systems
, Vol. 18
, pp. 223
–315
, 1982
.16.
S. Y. Liang and S. A. Perry, “In-Process Compensation for Milling Cutter Runout Via Chip Load Manipulation,” ASME Journal of Engineering for Industry, Vol. 116, 1994.
17.
R. Lozano. “Identification of Time-Varying Linear Models,” Proceedings of the IEEE Conference on Decision and Control, pp. 604–606, 1983.
18.
J. M. Maciejowski, Multivariable Feedback Design, Addison-Wesley, 1989.
19.
T. J. Manayathara, T.-C. Tsao, J. Bentsman, and D. Ross, “Rejection of Unknown Periodic Load Disturbances in Continuous Steel Casting Process Using Learning Repetitive Control Approach,” IEEE Transactions on Control Systems Technology, pp. 259–265, 1996.
20.
W. Messner and M. Bodson, “Design of Adaptive Feedforward Algorithms Using Internal Model Equivalence,” International Journal of Adaptive Control and Signal Processing, pp. 199–212, 1995.
21.
Nakano
M.
She
J.-H.
Mastuo
Y.
Hino
T.
Elimination of Position-Dependent Disturbances in Constant-Speed-Rotation Control Systems
,” Control Engineering Practice
, Vol. 4
, pp. 1241
–1248
, 1996
.22.
V. O. Nikiforov, “Adaptive Servocompensation of Input Disturbances,” Proceedings of the 13th IFAC Triennial World Congress, San Francisco, CA, Vol. K, pp. 175–180, 1996.
23.
Palaniswami
M.
Adaptive Internal Model for Disturbance Rejection and Control
,” IEE Proceedings-D
, Vol. 140
, pp. 51
–59
, 1993
.24.
H. L. Royden, Real Analysis, Macmillan, 1988.
25.
Sacks
A.
Bodson
M.
Khosla
P.
Experimental Results of Adaptive Periodic Disturbance Cancellation in a High Performance Magnetic Disk Drive
,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol. 118
, pp. 416
–424
, 1996
.26.
Stevens
A. J.
Steven
S. Y.
Runout Rejection in End Milling Through Two-Dimensional Repetitive Force Control
,” Mechatronics
, Vol. 5
, pp. 1
–13
, 1995
.27.
Tay
T. T.
Moore
J. B.
Enhancement of Fixed Controllers Via Adaptive—Q Disturbance Estimate Feedback
,” Automatica
, Vol. 27
, pp. 39
–53
, 1991
.28.
Tomizuka
M.
Tsao
T. C.
Chew
K. K.
Discrete Time Domain Analysis and Synthesis of Repetitive Controllers
,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol. 111
, pp. 353
–358
, 1989
.29.
T. C. Tsao and M. Nemani, “Asymptotic Rejection of Periodic Disturbances With Uncertain Period,” Proceedings of the American Control Conference, pp. 2696–2699, 1992.
30.
T. C. Tsao and Y. X. Qian, “An Adaptive Repetitive Control Scheme for Tracking Periodic Signals with Unknown Period,” Proceedings of the American Control Conference, pp. 1726–1730, 1993.
31.
Tung
E. D.
Anwar
G.
Tomizuka
M.
Low Velocity Friction Compensation and Feedforward Solution Based on Repetitive Control
,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol. 115
, pp. 279
–284
, 1993
.32.
M. Vidyasagar, Control System Synthesis: A Factorization Approach, M.I.T. Press, MA, 1985.
33.
Z. Wang, I. M. Y. Mareels, and J. B. Moore, “Adaptive Disturbance Rejection,” Proceedings of the IEEE Conference on Decision and Control, pp. 2836–2841, 1991.
34.
B. Wie and M. Gonzalez, “Control Synthesis for Flexible Space Structures Excited by Persistent Disturbances,” Journal of Guidance, Control, and Dynamics, 1992.
35.
Yang
W. C.
Tomizuka
M.
Disturbance Rejection Through an External Model for Non-Minimum Phase Systems
,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol. 116
, pp. 39
–44
, 1994
.36.
Youla
D. C.
Jabr
H. A.
Bongiorno
J. J.
Modern Wiener-Hopf Design of Optimal Controllers—Part II: The Multivariable Case
,” IEEE Transactions on Automatic Control
, Vol. 21
, pp. 319
–338
, 1976
.
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