A new and simple robust repetitive controller design procedure in controller parameter space is presented here. The structure of the repetitive controller filters are fixed, thus, simplifying the design procedure to tuning of the fixed structure filters’ parameters. This approach results in simple and physically meaningful robust controllers that are easily implementable. The design method is based on mapping frequency domain performance specifications into a chosen controller parameter plane. Weighted sensitivity (nominal performance) and weighted complementary sensitivity (robust stability) function magnitude bounds are chosen as the frequency domain specifications to be mapped into controller parameter space here. The design method is illustrated numerically in the context of a servohydraulic material testing machine application available in the literature.
Issue Section:
Technical Briefs
1.
Inoue
, T.
, Nakano
, M.
, and Iwai
, S.
, 1981, “High Accuracy Control of a Proton Synchrotron Magnet Power Supply
,” Proceedings of 8th World Congress of IFAC
, Kyoto
, Pergamon Press
, Oxford
, pp. 258
–292
.2.
Omata
, T.
, Hara
, S.
, and Nakano
, M.
, 1987, “Nonlinear Repetitive Control With Application to Trajectory Control of Manipulators
,” J. Rob. Syst.
0741-2223, 4
(5
), pp. 631
–652
.3.
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 J. Dyn. Syst., Meas., Control
0022-0434, 112
, pp. 618
–629
.4.
Kobayashi
, F.
, Hara
, S.
, Tanaka
, H.
, 1990, “Reduction of Motor Speed Fluctuation Using Repetitive Control
,” 29th IEEE Conference on Decision and Control
, Hawaii, pp. 1697
–1702
.5.
Tung
, E.
, Anwar
, G.
, and Tomizuka
, M.
, 1991, “Low Velocity Friction Compensation and Feedforward Solution Based on Repetitive Control
,” American Control Conference
, Boston, pp. 2615
–2620
.6.
Jolly
, T.
, Tsao
, T. C.
, and Bentsman
, J.
, 1993, “Rejection of Unknown Periodic Load Disturbances in Continuous Steel Casting Processes Using Learning Repetitive Control Approach
,” IEEE Symposium on Intelligent Control Systems
.7.
Shaw
, F. R.
, and Srinivasan
, K.
, 1993, “Discrete-Time Repetitive Control System Design Using the Regeneration Spectrum
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 115
, pp. 228
–237
.8.
Tsao
, T. C.
, and Tomizuka
, M.
, 1994, “Robust Adaptive and Repetitive Digital Tracking Control and Application to a Hydraulic Servo for Noncircular Machining
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 116
, pp. 24
–32
.9.
Garimella
, S. S.
, and Srinivasan
, K.
, 1996, “Application of Repetitive Control to Eccentricity Compensation in Rolling
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 118
, pp. 657
–664
.10.
Moon
, J. H.
, Lee
, M. N.
, and Chung
, M.
, 1998, “Repetitive Control for the Track-Following Servo System of an Optical Disk Drive
,” IEEE Trans. Control Syst. Technol.
1063-6536, 6
(5
), pp. 663
–670
.11.
Lee
, R. C. H.
, and Smith
, M. C.
, 1998, “Repetitive Control Experiments for a CD Player
,” American Control Conference
, pp. 2682
–2684
.12.
Prell
, A. P.
, Tsao
, T. C.
, and Bergman
, L. A.
, 1999, “Application of Repetitive Control to Vibration Attenuation in Certain Engineering Structures
,” J. Vib. Control
1077-5463, 5
, pp. 741
–760
.13.
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
0018-9286, 33
, pp. 657
–667
.14.
Srinivasan
, K.
, and Shaw
, F. R.
, 1991, “Analysis and Design of Repetitive Control Systems Using the Regeneration Spectrum
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 113
, pp. 216
–222
.15.
Tomizuka
, M.
, Tsao
, T. C.
, and Chew
, K. K.
, 1989, “Analysis and Synthesis of Discrete-Time Repetitive Controllers
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 111
, pp. 353
–358
.16.
Srinivasan
, K.
, Özbay
, H.
, and Jung
, I. S.
, 1995, “A Design Procedure for Repetitive Control Systems
,” ASME IMECE, Proceedings of ASME Dynamic Systems and Control Division
, San Francisco, Nov., ASME
, New York
, DSC Vol. 57-1
, pp. 581
–593
.17.
Özbay
, H.
, 1993, “H∞ Optimal Controller Design for a Class of Distributed Parameter Systems
,” Int. J. Control
0020-7179, 58
, pp. 739
–782
.18.
Peery
, T.
, and Özbay
, H.
, 1997, “H∞ Optimal Repetitive Controller Design for Stable Plants
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 119
, pp. 541
–547
.19.
Roh
, C. L.
, and Chung
, M. J.
, 1995, “Design of Repetitive Control System for an Uncertain Plant
,” Electron. Lett.
0013-5194, 31
(22
), pp. 1959
–1960
.20.
Weiss
, G.
, and Häfele
, M.
, 1999, “Repetitive Control of MIMO Systems Using H∞ Design
,” Automatica
0005-1098, 35
, pp. 1185
–1199
.21.
Güvenç
, L.
, 1996, “Stability and Performance Robustness Analysis of Repetitive Control Systems Using Structured Singular Values
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 117
, pp. 593
–597
.22.
Li
, J.
, and Tsao
, T. C.
, 1998, “Robust Performance Repetitive Control Design Using Structured Singular Values and Its Implementation
,” ASME International Mechanical Engineer’s Congress and Exposition
, Nov.23.
Güvenç
, L.
, 2003, “Repetitive Controller Design in Parameter Space
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 125
, pp. 134
–138
.24.
Ackermann
, J.
, Blue
, P.
, Bünte
, T.
, Güvenç
, L.
, Kaesbauer
, D.
, Kordt
, M.
, Muhler
, M.
, and Odenthal
, D.
, 2002, Robust Control: The Parameter Space Approach
, Springer-Verlag
, Berlin
.25.
Weiss
, G.
, 1997, “Repetitive Control Systems: Old and New Ideas
,” Systems and Control in the 21st Century
, C.
Byrnes
, B.
Datta
, D.
Gilliam
, and C.
Martin
, eds., PSCT
, Birkhäuser, Boston
, Vol. 22
, pp. 389
–404
.26.
Doyle
, J. C.
, Francis
, B. A.
, and Tannenbaum
, A. R.
, 1992, Feedback Control Theory
, Macmillan
, New York
.27.
Djaferis
, T. E.
, 1991, “Representations of Controllers That Achieve Robust Performance for Systems With Real Parameter Uncertainty
,” Syst. Control Lett.
0167-6911, 16
, pp. 329
–339
.28.
Saeki
, M.
, and Hirayama
, D.
, 1996, “Parameter Space Design Method of PID Controller for Robust Sensitivity Minimization Problem
,” Trans. Soc. Instrum. Control Eng.
, 32
(12
), pp. 1612
–1619
.29.
Saeki
, M.
, and Kimura
, J.
, 1997, “Design Method of Robust PID Controller and CAD System
,” 11th IFAC Symposium on System Identification
, pp. 1587
–1593
.30.
Güvenç
, L.
, and Ackermann
, J.
, 2001, “Links Between the Parameter Space and Frequency Domain Methods of Robust Control
,” Int. J. Robust Nonlinear Control
1049-8923, 11
(15
), pp. 1435
–1453
.31.
Odenthal
, D.
, and Blue
, P.
, 2000, “Mapping of H-infinity Design Specifications Into Parameter Space
,” Proc. of 3rd IFAC Symposium on Robust Control Design
, Prague.32.
Besson
, V.
, and Shenton
, A. T.
, 1997, “Interactive Control System Design by a Mixed H∞ -Parameter Space Method
,” IEEE Trans. Autom. Control
0018-9286, 42
, pp. 946
–955
.Copyright © 2006
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