On sampled data variable structure control systems

It is shown that the motion of sampled-data variable structure control systems can be divided into three phases, namely reaching phase, switching phase and chattering phase. The definitions of the three phases are given and the characteristics of the three phases are described. It is shown that in the reaching phase the switching function decreases monotonically, and in the switching phase the switching function stops decreasing but the magnitude of position error decreases monotonically, while in the chattering phase all variables stop decreasing and the chattering is dominated by the velocity. The bound or limit values of corresponding variables are given.

[1]  H. Sira-Ramírez.  Non-linear discrete variable structure systems in quasi-sliding mode , 1991 .

[2]  Sergey V. Drakunov,et al.  Sliding-mode control in discrete-state and hybrid systems , 1996, IEEE Trans. Autom. Control..

[3]  K. Furuta.  Sliding mode control of a discrete system , 1990 .

[4]  Vadim I. Utkin,et al.  Adaptive sliding mode control in discrete-time systems , 1995, Autom..

[5]  B. R. Menezes,et al.  A geometric approach to sampled data quasi-sliding modes analysis , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[6]  Xinghuo Yu,et al.  Analysis of discrete variable structure systems with pseudo-sliding modes , 1992 .

[7]  John Y. Hung,et al.  Variable structure control: a survey , 1993, IEEE Trans. Ind. Electron..

[8]  Wu-Chung Su,et al.  Implementation of variable structure control for sampled-data systems , 1996 .

[9]  S. Spurgeon.  Choice of discontinuous control component for robust sliding mode performance , 1991 .

[10]  R. Decarlo,et al.  Variable structure control of nonlinear multivariable systems: a tutorial , 1988, Proc. IEEE.

[11]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[12]  O. Kaynak,et al.  On the stability of discrete-time sliding mode control systems , 1987 .

[13]  F. Zheng,et al.  Variable structure control of discrete-time stochastic systems , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[14]  Okyay Kaynak,et al.  Discrete-time sliding mode control in the presence of system uncertainty , 1993 .

[15]  Andrzej Bartoszewicz,et al.  Discrete-time quasi-sliding-mode control strategies , 1998, IEEE Trans. Ind. Electron..

[16]  Ülle Kotta,et al.  Comments on "On the stability of discrete-time sliding mode control systems" [with reply] , 1989 .

[17]  Weibing Gao,et al.  Discrete-time variable structure control systems , 1995, IEEE Trans. Ind. Electron..

[18]  V. I. Utkin,et al.  Discontinuous Control Systems: State of Art in Theory and Applications , 1987 .

[19]  Toshio Fukuda,et al.  Computer-controlled continuous-time variable structure systems with sliding modes , 1997 .

[20]  Xinghuo Yu,et al.  Bifurcation and Chaotic Behaviors in a Discrete Variable Structure System with Unbounded Control Magnitude , 1997 .