Robust Discrete-Time Variable Structure Control Methods

[+] Author and Article Information
Jung-ho Kim, Seung-Hyun Oh, Dong-il “Dan” Cho

School of Electrical Engineering and Computer Science, Seoul National University, San 56-1, Shinlim-dong, Kwanak-ku, Seoul 151-742, Korea

J. Karl Hedrick

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

J. Dyn. Sys., Meas., Control 122(4), 766-775 (Feb 04, 2000) (10 pages) doi:10.1115/1.1320448 History: Received February 04, 2000
Copyright © 2000 by ASME
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Kaynak,  O., and Denker,  A., 1993, “Discrete-time Sliding Mode Control in the Presence of System Uncertainty,” Int. J. Control, 57, No. 5, pp. 1177–1189.
Su, W.-C., Drakunov, S. V., and Özgüner, Ü., 1993, “Sliding Mode Control in Discrete Time Linear Systems,” Proc. IFAC 12th World Congress, Vol. 2, pp. 267–270.
Gao,  W., Wang,  Y., and Homaifa,  A., 1995, “Discrete-time Variable Structure Control Systems,” IEEE Trans. Ind. Electron., 42, No. 2, pp. 117–122.
Corradini,  M. L., and Orlando,  G., 1998, “Variable structure control of discretized continuous-time systems,” IEEE Trans. Autom. Control, 43, No. 9, pp. 1329–1334.
Eun,  Y., Kim,  J., Kim,  K., and Cho,  D., 1999, “Discrete-time Variable Structure Controller with a Decoupled Disturbance Compensator and Its Application to a CNC Servomechanism,” IEEE Trans. Control Syst. Technol., 7, No. 4, pp. 414–423.
Kim, J., and Cho, D., 2000, “Discrete-time Variable Structure Control Using Recursive Switching Function,” Proc. American Control Conference, pp. 1113–1117.
Draženović,  B., 1969, “The Invariance Conditions in Variable Structure Systems,” Automatica, 5, pp. 287–295.
Young,  K. D., Utkin,  V. I., and Özgüner,  Ü., 1999, “A Control Engineer’s Guide to Sliding Mode Control,” IEEE Trans. Control Syst. Technol., 7, No. 3, pp. 328–342.
Slotine,  J.-J. E., and Sastry,  S. S., 1983, “Tracking Control of Nonlinear Systems Using Sliding Surfaces with Applications to Robot Manipulators,” Int. J. Control, 38, No. 2, pp. 465–492.
Burton,  J. A., and Zinober,  A. S. I., 1986, “Continuous Approximation of Variable Structure Control,” Int. J. Syst. Sci., 17, No. 6, pp. 875–885.
Utkin,  V. I., 1977, “Variable Structure Systems with Sliding Modes,” IEEE Trans. Autom. Control, 22, No. 2, pp. 212–222.
Utkin,  V. I., 1984, “Variable Structure Systems: Present and Future,” Autom. Remote Control (Engl. Transl.), 4, No. 9, pp. 1105–1120.
DeCarlo,  R. A., Żak,  S. H., and Mathews,  G. P., 1988, “Variable Structure Control of Nonlinear Multivariable Systems: A Tutorial,” Proc. IEEE, 76, No. 3, pp. 212–232.
Hung,  J. Y., Gao,  W. B., and Hung,  J. C., 1993, “Variable Structure Control: A Survey,” IEEE Trans. Ind. Electron., 40, No. 1, pp. 2–22.
Milosavljević,  Č., 1985, “General Conditions for the Existence of a Quasisliding Mode on the Switching Hyperplane in Discrete Variable Structure Systems,” Autom. Remote Control (Engl. Transl.), 46, No. 3, pp. 307–314.
Sarpturk,  S. Z., Istefanopulos,  Y., and Kaynak,  O., 1987, “On the stability of Discrete-time Sliding Mode Control Systems,” IEEE Trans. Autom. Control, 32, No. 10, pp. 930–932.
Furuta,  K., 1990, “Sliding Mode Control of a Discrete System,” Syst. Control Lett., 14, pp. 145–152.
Sira-Ramı́rez,  H., 1991, “Non-linear Discrete Variable Structure Systems in Quasi-sliding Mode,” Int. J. Control, 54, No. 5, pp. 1171–1187.
Drakunov,  S., and Utkin,  V. I., 1992, “Sliding Mode Control in Dynamic Systems,” Int. J. Control, 55, No. 4, pp. 1029–1037.
Yu, X. H., 1993, “Conditions for the Existence of Discrete-time Sliding Mode,” Proc. IFAC 12th World Congress, Vol. 2, pp. 215–218.
Su, W.-C., Drakunov, S. V., and Özgüner, Ü., 1996, “Implementation of Variable Structure Control for Sampled-data Systems,” Robust Control via Variable Structure and Lyapunov Techniques, F. Garofalo and L. Glielmo, eds., Vol. 217 of Lecture Notes in Control and Information Sciences, Springer-Verlag, pp. 87–106.
Young,  K. D., and Özgüner  Ü., 1996, “Co-states for Sliding Mode Design in Linear Systems,” Syst. Control Lett., 27, No. 4, pp. 233–242.
Chen,  X., and Fukuda,  T., 1997, “Computer-controlled Continuous-time Variable Structure Systems with Sliding Modes,” Int. J. Control, 67, No. 4, pp. 619–639.
Wang,  W.-J., Wu,  G.-H., and Yang,  D.-C., 1994, “Variable Structure Control Design for Uncertain Discrete-time Systems,” IEEE Trans. Autom. Control, 39, No. 1, pp. 99–102.
Pan,  Y., and Furuta,  K., 1997, “Discrete-time VSS Controller Design,” Int. J. Robust and Nonlinear Control, 7, No. 4, pp. 373–386.
Chan,  C. Y., 1991, “Servo-systems with Discrete-variable Structure Control,” Syst. Control Lett., 17, No. 4, pp. 321–325.
Pan,  Y., and Furuta,  K., 1994, “VSS Controller Design for Discrete-time Systems,” Control-Theory and Advanced Technology, 10, No. 4, pp. 669–687.
Pieper,  J. K., and Surgenor,  B. W., 1993, “Discrete Sliding Control of a Coupled-drives Apparatus with Optimal Sliding Surface and Switching Gain,” IEE Proc.-D: Control Theory Appl., 140, No. 2, pp. 70–78.
Furuta, K., and Pan, Y., 1995, “A New Approach to Design a Sliding Sector for VSS Controller,” Proc. American Control Conference, pp. 1304–1308.
Won, M., 1994, Multiple Surface Sliding Control with Application to Engine Control, Ph.D. thesis, Mechanical Engineering, University of California at Berkeley.
Eun,  Y., and Cho,  D., 1999, “Robustness of Multivariable Discrete-time Variable Structure Control,” Int. J. Control, 72, No. 12, pp. 1106–1115.
Misawa,  E. A., 1997, “Discrete-time Sliding Mode Control: The Linear Case,” ASME J. Dyn. Syst., Meas., Control, 119, No. 4, pp. 819–821.
Cho,  D., Kato,  Y., and Spilman,  D., 1993, “Sliding Mode and Classical Controllers in Magnetic Levitation Systems,” IEEE Control Syst. Mag., 13, No. 1, pp. 42–48.
Choi, B.-K., 1999, A Study on High Precision Contouring Control for CNC Machining Center, Ph.D. thesis, School of Electrical Engineering, Seoul National University. (in Korean).
Na, I. J., Choi, C. H., Jang, T. J., Choi, B.-K., and Song, O. S., 1996, “Contour Error Analysis and Gain Tuning for CNC Machining Center,” Proc. 4th International Workshop on Advanced Motion Control, Vol. 1, pp. 197–202.


Grahic Jump Location
Difference of Bs in phase plane
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Switching criteria in phase plane
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TNV-40 machining center
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Experimental hardware setup
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Implementation schematic for x-axis
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Circular motion: air cutting
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Circular motion: milling with spindle motor at 900 rpm
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Circular motion: milling with spindle motor at 1200 rpm
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Circular motion: milling with spindle motor at 1500 rpm




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