Derivative and integral terminal sliding mode control for a class of MIMO nonlinear systems

This paper presents derivative and integral terminal sliding mode control (TSMC) for a class of MIMO nonlinear systems in a unified viewpoint. First, integral TSMC is developed for robust output tracking of uncertain relative-degree-one systems by introducing sign and fractional integral terminal sliding modes. Next, by combining derivative and integral terminal sliding modes in a recursive structure, two derivative-integral terminal sliding mode control (DI-TMSC) methods are proposed to achieve exact or approximate finite-time convergence for the output tracking of higher order nonlinear systems. Different from traditional TSMC, this paper accomplishes finite convergence time for more general high-order MIMO systems and avoids the singular problem in the controller design. Furthermore, the control system is forced to start on the terminal sliding hyperplane, so that the reaching time of the sliding modes is eliminated. In other words, the transient response is improved under more relaxed stability conditions. Finally, several numerical simulations and experiments show the expected control performance.

[1]  Leonid M. Fridman,et al.  Optimal Lyapunov function selection for reaching time estimation of Super Twisting algorithm , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[2]  Vadim I. Utkin,et al.  On multi-input chattering-free second-order sliding mode control , 2000, IEEE Trans. Autom. Control..

[3]  Zheng Zhang,et al.  Sliding-Mode Sensorless Control of Direct-Drive PM Synchronous Motors for Washing Machine Applications , 2009, IEEE Transactions on Industry Applications.

[4]  S. Gulati,et al.  Control of Nonlinear Systems Using Terminal Sliding Modes , 1992, 1992 American Control Conference.

[5]  Xu Zibin,et al.  Backstepping control for a class of uncertain systems based on non-singular terminal sliding mode , 2009, 2009 International Conference on Industrial Mechatronics and Automation.

[6]  Li-Chen Fu,et al.  SMOOTH SLIDING MODE CONTROL FOR CONSTRAINED MANIPULATOR WITH JOINT FLEXIBILITY , 2005 .

[7]  Wei Lin,et al.  Global finite-time stabilization of a class of uncertain nonlinear systems , 2005, Autom..

[8]  J. Mahdavi,et al.  Application of state space averaging method to sliding mode control of PWM DC/DC converters , 1997, IAS '97. Conference Record of the 1997 IEEE Industry Applications Conference Thirty-Second IAS Annual Meeting.

[9]  Alexander S. Poznyak,et al.  Reaching Time Estimation for “Super-Twisting” Second Order Sliding Mode Controller via Lyapunov Function Designing , 2009, IEEE Transactions on Automatic Control.

[10]  V. C Onclusions,et al.  Fast Terminal Sliding-Mode Control Design for Nonlinear , 2002 .

[11]  Zhihong Man,et al.  Non-singular terminal sliding mode control of rigid manipulators , 2002, Autom..

[12]  Tzuu-Hseng S. Li,et al.  Fuzzy terminal sliding-mode controller for robotic manipulators , 2005, IEEE International Conference on Mechatronics, 2005. ICM '05..

[13]  Chin-Wang Tao,et al.  Adaptive fuzzy terminal sliding mode controller for linear systems with mismatched time-varying uncertainties , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[14]  Xinghuo Yu,et al.  Model reference adaptive control systems with terminal sliding modes , 1996 .

[15]  Xinghuo Yu,et al.  On singularity free recursive fast terminal sliding mode control , 2008, 2008 International Workshop on Variable Structure Systems.

[16]  G. Hirzinger,et al.  Finite-time tracking for robot manipulators with singularity-free continuous control: a passivity-based approach , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[17]  L. Xie,et al.  Integral terminal sliding mode cooperative control of multi-robot networks , 2009, 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics.

[18]  Xinghuo Yu,et al.  Terminal sliding mode control of MIMO linear systems , 1997 .

[19]  Jian Chen,et al.  A continuous asymptotic tracking control strategy for uncertain nonlinear systems , 2004, IEEE Transactions on Automatic Control.

[20]  O. Barambones,et al.  Energy-based approach to sliding composite adaptive control for rigid robots with finite error convergence time , 2002 .

[21]  Xinghuo Yu,et al.  Fast terminal sliding-mode control design for nonlinear dynamical systems , 2002 .

[22]  Yunhui Liu,et al.  Dynamic sliding PID control for tracking of robot manipulators: theory and experiments , 2003, IEEE Trans. Robotics Autom..

[23]  Zhihong Man,et al.  Fast finite-time consensus of a class of high-order uncertain nonlinear systems , 2010, 2010 5th IEEE Conference on Industrial Electronics and Applications.

[24]  Jiann-Fuh Chen,et al.  Real-time implementation of grey fuzzy terminal sliding mode control for PWM DC-AC converters , 2008 .

[25]  C.-S. Chiu.  Mixed Feedforward/Feedback Based Adaptive Fuzzy Control for a Class of MIMO Nonlinear Systems , 2006, IEEE Transactions on Fuzzy Systems.

[26]  Lei Guo,et al.  Composite disturbance-observer-based control and terminal sliding mode control for uncertain structural systems , 2009, Int. J. Syst. Sci..

[27]  Michael Defoort,et al.  A Third-Order Sliding-Mode Controller for a Stepper Motor , 2009, IEEE Transactions on Industrial Electronics.

[28]  Shaoyuan Li,et al.  A New Terminal Sliding Mode Control for Robotic Manipulators , 2008 .