This paper presents a state feedback discrete variable structure controller for robust tracking of linear multivariable systems with unmatched, additive uncertainties. Extension of the controller to output feedback using a prediction observer with bias estimation is also given. It is shown that the state feedback controller guarantees attractiveness and invariance of a boundary layer, while the output feedback controller does so after a transient. Unlike existing schemes, the controllers utilize a single sliding hyperplane regardless of the number of inputs. This attribute enables the development of a procedure that admits, under minor restrictions, direct application of well-established linear control strategies in the design of tracking error dynamics. A numerical example is used to illustrate the proposed controllers. [S0022-0434(00)01904-3]
Issue Section:
Technical Papers
1.
Utkin
, V. I.
, 1977
, “Variable Structure Systems with Sliding Mode
,” IEEE Trans. Autom. Control
, 22
, No. 2
, pp. 212
–222
.2.
DeCarlo
, R. A.
, Z˙ak
, S. H.
, and Matthews
, G. P.
, 1988
, “Variable Structure Control of Nonlinear Multivariable Systems: A Tutorial
,” Proc. IEEE
, 76
, pp. 212
–232
.3.
Milosavljevic
, C.
, 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
.4.
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
.5.
Furuta
, K.
, 1990
, “Sliding Mode Control of a Discrete System
,” Syst. Contr. Lett.
, 14
, pp. 145
–152
.6.
Yu, X., 1994, “Digital Variable Structure Control with Pseudo-Sliding Modes,” A. S. I. Zinober, ed., Variable Structure and Lyapunov Control, Springer-Verlag, London, pp. 133–155.
7.
Pan
, Y.
, and Furuta
, K.
, 1994
, “VSS Controller Design for Discrete-Time Systems
,” Contr.-Theor. Adv. Tech.
, 10
, No. 4
, pp. 669
–687
.8.
Gao
, W.
, Wang
, Y.
, and Homaifa
, A.
, 1995
, “Discrete-Time Variable Structure Control Systems
,” IEEE Trans. Ind. Electron.
, 42
, No. 2
, pp. 117
–122
.9.
Lee
, R.-C.
, and Wang
, W.-J.
, 1995
, “Robust Variable Structure Control Synthesis in Discrete-Time Uncertain Systems
,” Contr.-Theory Adv. Tech.
, 10
, No. 4
, pp. 1785
–1796
.10.
Corradini, M. L., and Orlando, G., 1996, “Variable Structure Control for Uncertain Sampled Data Systems,” Proc. Int. Workshop on Variable Structure Syst., Tokyo, Japan, pp. 117–121.
11.
Misawa
, E. A.
, 1997
, “Discrete-Time Sliding Mode Control: The Linear Case
,” ASME J. Dyn. Syst. Meas. Contr.
, 119
, No. 4
, pp. 819
–821
.12.
Su, W.-C., Drakunov, S. V., and O¨zgu¨ner, U¨., 1993, “Sliding Mode Control in Discrete-Time Linear Systems,” Proc. IFAC World Congress, Sydney, Australia, pp. 297–300.
13.
Chan
, C. Y.
, 1994
, “Robust Discrete-Time Sliding Mode Controller
,” Syst. Control Lett.
, 23
, pp. 371
–374
.14.
Fujisaki, Y., Togawa, K., and Hirai, K., 1994, “Sliding Mode Control for Multi-Input Discrete Time Systems,” Proc. IEEE Conf. Decision Contr., Lake Buena Vista, FL, pp. 1937–1935.
15.
Utkin, V. I., 1994, “Sliding Mode Control in Discrete-Time and Difference Systems,” A. S. I. Zinober, ed., Variable Structure and Lyapunov Control, Springer-Verlag, London, pp. 87–107.
16.
Yu, F. Chang, Z. X., and Shi, Y. W., 1996, “Variable Structure Control of Discrete-Time Systems and Their Quality,” Proc. IEEE Int. Conf. Indust. Tech., Shanghai, China, pp. 816–820.
17.
Koshkouei, A. J., and Zinober, A. S. I., 1996, “Sliding Lattice Design for Discrete-Time Linear Multivariable Systems,” in Proc. IEEE Conf. Decision Contr., Kobe, Japan, pp. 1497–1502.
18.
Wang
, W.-J.
, Lee
, R.-C.
, and Yang
, D.-C.
, 1996
, “Sliding Mode Control Design in Multi-Input Perturbed Discrete-Time Systems
,” ASME J. Dyn. Syst. Meas. Contr.
, 118
, No. 1
, pp. 322
–327
.19.
Tang, C. Y., and Misawa, E. A., 1999, “On Discrete Variable Structure Control with Switching Sector,” K. D. Young and U¨. O¨zgu¨ner, eds., Variable Structure Systems, Sliding Mode and Nonlinear Control, Springer-Verlag, London, pp. 27–41.
20.
Sira-Ramirez
, H.
, 1991
, “Nonlinear Discrete Variable Structure Systems in Quasi-Sliding Mode
,” Int. J. Control
, 54
, No. 5
, pp. 1171
–1187
.21.
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
.22.
Furuta, K., 1990, “VSS-Type Self-Tuning Control-β Equivalent Control Approach,” Proc. Amer. Contr. Conf., San Francisco, CA, pp. 980–984.
23.
Pieper, J. K., and Goheen, K. R., 1993, “Discrete Time Sliding Mode Control via Input-Output Models,” Proc. Amer. Contr. Conf., San Francisco, CA, pp. 964–965.
24.
Su, W.-C., Drakunov, S. V, O¨zgu¨ner, U¨, and Young, K. D., 1993, “Sliding Mode with Chattering Reduction in Sampled Data Systems,” Proc. IEEE Conf. Decision Contr., San Antonio, TX, pp. 2452–2457.
25.
Misawa, E. A., 1995, “Observer-Based Discrete-Time Sliding Mode Control with Computational Time Delay: The Linear Case,” Proc. Amer. Contr. Conf., Seattle, WA, pp. 1323–1327.
26.
Suzuki, T., and Furuta, K., 1996, “Discrete-Time VSS represented by Input-Output Relation,” Proc. Int. Workshop on Variable Structure Syst., Tokyo, Japan, pp. 122–126.
27.
Zhou, K., Doyle, J. C., and Glover, K., 1996, Robust and Optimal Control, Prentice-Hall, Upper Saddle River, NJ.
28.
Spurgeon
, S. K.
, 1992
, “Hyperplane Design Techniques for Discrete-Time Variable Structure Control Systems
,” Int. J. Control
, 55
, No. 2
, pp. 445
–456
.29.
Franklin, G., Powell, J., and Workman, M., 1990, Digital Control of Dynamic Systems, Addison-Wesley, Reading, MA, 2nd Ed.
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