Discrete-time Variable Structure Control

This chapter presents some discrete-time variable structure (VS) control design algorithms with sliding sectors and then proposes a discrete-time VS controller with an invariant sliding sector. The invariant sliding sector is an invariant subset of the state space determined by a linear and a quadratic functions on the state variable. To ensure the invariance, a VS control law is implemented. Inside the sector with the VS control law, a Lyapunov function keeps decreasing. If the state is inside the subset in some time instance, then the VS control input will let the state remain inside. A discrete-time VS controller with the invariant sliding sector for discrete-time systems is designed such that the state is moved into the sector in finite steps and stays there from then on. The resultant VS control system is quadratically stable as there exists a Lyapunov function which decreases in the state space. Simulation results are given to show the efficiency of the proposed design algorithm of the discrete-time VS controller.

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

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

[3]  Vadim I. Utkin,et al.  On Discrete-Time Sliding Modes , 1989 .

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

[5]  R. B. Potts,et al.  A class of discrete variable structure systems , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

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

[7]  Vadim I. Utkin,et al.  Design of discrete-time adaptive sliding mode control , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[8]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[9]  Katsuhisa Furuta.  VSS-Type Self-Tuning Control-ß Equivalent Control Approach , 1993, 1993 American Control Conference.

[10]  Katsuhisa Furuta,et al.  Discrete-time adaptive VSS control system using transfer function , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[11]  Katsuhisa Furuta,et al.  VSS type self-tuning control , 1993, IEEE Trans. Ind. Electron..

[12]  Wen-June Wang,et al.  Variable structure control design for uncertain discrete-time systems , 1994, IEEE Trans. Autom. Control..

[13]  E. A. Misawa.  Observer-based discrete-time sliding mode control with computational time delay: the linear case , 1995, Proceedings of 1995 American Control Conference - ACC'95.

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

[15]  Alan S. I. Zinober,et al.  Discrete-Time Sliding Mode Control Design , 1996 .

[16]  E. A. Misawa,et al.  Discrete-Time Sliding Mode Control: The Linear Case , 1997 .

[17]  Vadim I. Utkin,et al.  Variable structure control for uncertain sampled data systems , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[18]  Giorgio Bartolini,et al.  Digital second order sliding mode control of SISO uncertain nonlinear systems , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[19]  K. Furuta,et al.  Discrete-time VS controller design based on input-output model , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[20]  Katsuhisa Furuta,et al.  Invariant sliding sector for variable structure control , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[21]  Katsuhisa Furuta,et al.  Discrete-time Variable Structure Control for Descriptor System , 2000 .

[22]  Wu-Chung Su,et al.  An O(T2) boundary layer in sliding mode for sampled-data systems , 2000, IEEE Trans. Autom. Control..

[23]  G. Golo,et al.  Robust discrete-time chattering free sliding mode control , 2000 .

[24]  A. Jafari Koshkouei,et al.  Sliding Mode Control of Discrete-Time Systems , 2000 .

[25]  Xinghuo Yu,et al.  Discrete Sliding Mode Control Design With Invariant Sliding Sectors , 2000 .

[26]  Chun-Yi Su,et al.  Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis , 2000, IEEE Trans. Autom. Control..

[27]  Yaodong Pan,et al.  Variable structure control with sliding sector , 2000, Autom..