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Robust discrete-time chattering free sliding mode control. (English) Zbl 0985.93007
Summary: A new control algorithm based on discrete-time variable structure systems theory is proposed. The basic feature of this algorithm is that trajectories reach the sliding manifold in finite time, without chattering. Apart from stability, the robustness of the algorithm with respect to parameter uncertainties, as well as external disturbances, is considered. It is demonstrated that the robustness is improved by decreasing the sampling period. The theory is illustrated on a DC servo-position system.

93B12 Variable structure systems
93D21 Adaptive or robust stabilization
93C55 Discrete-time control/observation systems
Full Text: DOI
[1] Bartolini, G.; Ferrara, A.; Utkin, V.I., Adaptive sliding mode control in discrete-time systems, Automatica, 31, 769-773, (1995) · Zbl 0825.93097
[2] De Carlo, R.; Zak, S.H.; Matthews, G.O., Variable structure control of nonlinear multivariable systems: a tutorial, Proc. IEEE, 76, 212-232, (1988)
[3] Draženović, B., The invariance conditions in variable structure systems, Automatica, 5, 287-295, (1969) · Zbl 0182.48302
[4] Elaydi, S.N., An introduction to difference equations, (1996), Springer Berlin · Zbl 0840.39002
[5] Furuta, K., Sliding mode of a discrete system, Systems & control lett., 14, 145-152, (1990) · Zbl 0692.93043
[6] Gao, W.; Wang, Y.; Homaifa, A., Discrete-time variable structure control systems, IEEE trans., IE-42, 117-122, (1995)
[7] Gao, W.; Hung, J.C., Variable structure control of nonlinear systems: a new approach, IEEE trans., IE-40, 45-55, (1993)
[8] Golo, G.; Milosavljević, Č., Two-phase triangular wave oscillator based on discrete-time sliding mode control, Electron. lett., 33, 1838-1839, (1997)
[9] H. Hashimoto, Robust digital sliding mode control applied to motion control systems, Japan/USA Symposium on Flexible Automation 1, ASME, 1992.
[10] Milosavljević, Č., General conditions for the existence of a quasi-sliding mode on the switching hyperplane in discrete variable structure systems, Automatic remote control, 46, 307-314, (1985) · Zbl 0583.93043
[11] Potts, R.B.; Yu, X., Discrete variable structure system with pseudo-sliding mode, J. Australia. math. soc. B, 32, 365-376, (1991) · Zbl 0733.34021
[12] Sira-Ramirez, H., Non-linear variable structure systems in quasi-sliding mode, Int. J. control, 54, 1171-1187, (1991) · Zbl 0738.93049
[13] Spurgeon, S.K., Hyperplane design techniques for discrete-time variable structure systems, Int. J. control, 55, 445-456, (1992) · Zbl 0748.93014
[14] Utkin, V., Sliding modes in control and optimization, (1992), Springer Berlin · Zbl 0748.93044
[15] Wang, W.J.; Wu, G.H., Variable structure control design on discrete-time systems from another viewpoint, Control theory adv. technol., 8, 1-16, (1992)
[16] K.D. Young, V. Utkin, Ü. Özguner, A control engineer’s guide to sliding mode control, Proceedings of VSS ’96, Tokyo, pp. 1-14.
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