Adaptive switching gain for a discrete-time sliding mode controller

Sliding mode control is a well-known technique capable of making the closed loop system robust with respect to certain kinds of parameter variations and unmodelled dynamics. The sliding mode control law consists of a continuous component which is based on the model knowledge and discontinuous component which is based on the model uncertainty. This paper extends two known adaption laws for the switching gain for continuous-time sliding mode controllers to the multiple input case. Because these adaption laws have some fundamental problems in discrete-time, we introduce a new adaption law specifically designed for discrete-time sliding mode controllers.

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

[2]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[3]  Chun-Yi Su,et al.  An adaptive variable structure model following control design for robot manipulators , 1991 .

[4]  Chun-Yi Su,et al.  Adaptive sliding mode control of constrained robot manipulators , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

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

[6]  Wen-June Wang,et al.  Output feedback in variable structure systems with a simple adaption law , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

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

[8]  H. Sira-Ramirez,et al.  Adaptive dynamical sliding mode control via backstepping , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[9]  T. Hesketh,et al.  Adaptive learning control of robot manipulators in task space , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[10]  Jeff K. Pieper,et al.  Linear-quadratic optimal model-following control of a helicopter in hover , 1994, Proceedings of 1994 American Control Conference - ACC '94.

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

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

[13]  C. M. Kwan.  Hybrid force/position control for manipulators with motor dynamics using a sliding-adaptive approach , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[14]  Yuqiang Wu,et al.  A design scheme of variable structure adaptive control for uncertain dynamic systems , 1996, Autom..

[15]  Young-Uk Park,et al.  Discrete-time adaptive sliding mode power system stabilizer with only input/output measurements , 1996 .

[16]  K. R. Goheen,et al.  Linear quadratic optimal model‐following control of a helicopter in hover , 1996 .

[17]  Andrzej Bartoszewicz,et al.  Remarks on Discrete-time Variable Structure Control Systems , 1996 .

[18]  C.Y. Chan.  Discrete adaptive sliding-mode tracking controller , 1997, Autom..

[19]  Antonella Ferrara,et al.  A simplified adaptive control scheme based on a combined backstepping/second order sliding mode algorithm , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

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

[21]  Yury Stepanenko,et al.  A Sliding Mode Controller with Improved Adaptation Laws for the Upper Bounds on the Norm of Uncertainties , 1998, Autom..

[22]  Henning Lenz,et al.  Adaptive Sliding-Mode Control of the Absolute Gain , 1998 .

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

[24]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[25]  V. Utkin.  Adaptive discrete-time sliding mode control of infinite-dimensional systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[26]  U. Ozguner,et al.  Sliding mode: control engineering in practice , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[27]  C. Y. Chan.  Discrete adaptive sliding-mode control of a class of stochastic systems , 1999, Autom..

[28]  A. Jafari Koshkouei,et al.  Adaptive Sliding Backstepping Control of Nonlinear Semi-Strict Feedback Form Systems , 1999 .

[29]  S. Sankaranarayanan,et al.  Adaptive variable structure control of a class of nonlinear systems with nonvanishing perturbations via backstepping , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[30]  Young-Hoon Roh,et al.  Sliding mode control with uncertainty adaptation for uncertain input-delay systems , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[31]  G. Monsees,et al.  Adaptive switching gain for a discrete-time sliding mode controller , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[32]  Michael Trentini,et al.  Mixed Norm Control of a Helicopter , 2001 .