Second-order sliding mode control applied to inverted pendulum

Sliding mode control (SMC) has been considered as an effective tool in different studies for control systems. The robustness of SMC against the disturbances and model uncertainties makes the system stable. However, the chattering phenomenon degrades the system performances, it may even lead to instability. This paper deals with the second order sliding mode the twisting and super-twisting algorithm to solve the tracking control of underactuated manipulators. Further, comparison between controllers has been done. Simulation results are given to demonstrate the effectiveness of the proposed approaches.

[1]  Giuseppe Oriolo,et al.  Comments on "Adaptive variable structure set-point control of underactuated robots" , 2001, IEEE Trans. Autom. Control..

[2]  Chun-Yi Su,et al.  Adaptive variable structure set-point control of underactuated robots , 1999, IEEE Trans. Autom. Control..

[3]  Reza Olfati-Saber,et al.  Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicles , 2001 .

[4]  G. Bartolini,et al.  Chattering avoidance by second-order sliding mode control , 1998, IEEE Trans. Autom. Control..

[5]  Jun Zhao,et al.  Hybrid control for global stabilization of the cart-pendulum system , 2001, Autom..

[6]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

[7]  Leonid M. Fridman,et al.  Analysis of second-order sliding-mode algorithms in the frequency domain , 2004, IEEE Transactions on Automatic Control.

[8]  Jean-Pierre Barbot,et al.  Sliding Mode Control In Engineering , 2002 .

[9]  N. Derbel,et al.  A sliding mode control applied to whirling pendulum , 2008, 2008 2nd International Conference on Signals, Circuits and Systems.

[10]  Y. Soh,et al.  Robust observer with sliding mode estimation for nonlinear uncertain systems , 2007 .

[11]  J. L. Bogdanoff,et al.  On the stabilization of the inverted pendulum. , 1967 .

[12]  Giorgio Bartolini,et al.  2-Sliding Mode with Adaptation * , 1999 .

[13]  Vadim I. Utkin,et al.  Chattering suppression methods in sliding mode control systems , 2007, Annu. Rev. Control..

[14]  S. V. Emel'yanov,et al.  High-order sliding modes in control systems , 1996 .

[15]  Arie Levant,et al.  Chattering Analysis , 2007, IEEE Transactions on Automatic Control.

[16]  Antonella Ferrara,et al.  Chattering avoidance by second-order sliding mode control , 1998, IEEE Transactions on Automatic Control.

[17]  A. Levant.  Sliding order and sliding accuracy in sliding mode control , 1993 .

[18]  L. Fridman,et al.  Parameter tuning of second-order sliding mode controllers for linear plants with dynamic actuators , 2006, Autom..

[19]  R. M. Hirschorn,et al.  Stabilization of single‐input nonlinear systems using higher‐order term compensating sliding mode control , 2008 .

[20]  Rogelio Lozano,et al.  Non-linear Control for Underactuated Mechanical Systems , 2001 .

[21]  Vadim I. Utkin,et al.  Sliding Modes and their Application in Variable Structure Systems , 1978 .

[22]  Rey-Chue Hwang,et al.  A self-tuning PID control for a class of nonlinear systems based on the Lyapunov approach , 2002 .

[23]  Christopher Edwards,et al.  Advances in variable structure and sliding mode control , 2006 .

[24]  A. Zinober,et al.  Continuous approximation of variable structure control , 1986 .

[25]  Nahum Shimkin,et al.  Nonlinear Control Systems , 2008 .

[26]  Jaime A. Moreno,et al.  Strict Lyapunov Functions for the Super-Twisting Algorithm , 2012, IEEE Transactions on Automatic Control.

[27]  Rogelio Lozano,et al.  The cart-pole system , 2002 .

[28]  Leonid Fridman.  Chattering analysis in sliding mode systems with inertial sensors , 2003 .

[29]  Chun-Yi Su,et al.  Variable structure control of robotic manipulator with PID sliding surfaces , 1998 .