Fast Terminal Sliding-Mode Control With an Integral Filter Applied to a Van Der Pol Oscillator

This paper proposes a procedure for designing a fast terminal sliding-mode control involving an integral filter that guarantees a finite time of convergence to zero dynamics, robustness against polynomial bounded uncertainties, and external disturbances. It reduces the chattering effect by employing a state-dependent gain and adds an integral filter to smooth the input control signal. We suggest a simplified algorithm to design the controller. To test the performance of the algorithm, we use a Van der Pol chaotic oscillator synchronization with perturbations in the states. Finally, we compare the performance of the method by using the proposed controller with the filter turned-on and turned-off.

[2]  Sundarapandian Vaidyanathan,et al.  Global Chaos Synchronization of the Forced Van der Pol Chaotic Oscillators via Adaptive Control Method , 2015 .

[3]  M. Basin,et al.  Super-twisting observer design for systems of dimension more than one , 2015, 2015 International Workshop on Recent Advances in Sliding Modes (RASM).

[4]  G. Bartolini,et al.  Regularization of Second Order Sliding Mode Control Systems , 2008 .

[5]  Jinkun Liu,et al.  Advanced Sliding Mode Control for Mechanical Systems , 2011 .

[6]  Eckehard Schöll,et al.  Handbook of Chaos Control , 2007 .

[7]  Avrie Levent,et al.  Robust exact differentiation via sliding mode technique , 1998, Autom..

[8]  Lakshmanan,et al.  Transmission of signals by synchronization in a chaotic Van der Pol-Duffing oscillator. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  Vadim I. Utkin,et al.  On Convergence Time and Disturbance Rejection of Super-Twisting Control , 2013, IEEE Transactions on Automatic Control.

[10]  Leonid M. Fridman,et al.  Fast second-order Sliding Mode Control design based on Lyapunov function , 2013, 52nd IEEE Conference on Decision and Control.

[11]  M. Shinriki,et al.  Multimode oscillations in a modified Van Der Pol oscillator containing a positive nonlinear conductance , 1981, Proceedings of the IEEE.

[12]  Rafael Martínez-Guerra,et al.  Secure communications via synchronization of Liouvillian chaotic systems , 2016, J. Frankl. Inst..

[13]  Xinghuo Yu,et al.  Terminal sliding mode control design for uncertain dynamic systems , 1998 .

[14]  Jaime A. Moreno,et al.  A Lyapunov approach to second-order sliding mode controllers and observers , 2008, 2008 47th IEEE Conference on Decision and Control.

[15]  R. Martínez-Guerra,et al.  Generalized Synchronization in chaotic Liouvillian fractional systems , 2016, ACC.

[16]  Yuri B. Shtessel,et al.  Continuous Finite-Time Higher Order Output Regulators for Systems With Unmatched Unbounded Disturbances , 2016, IEEE Transactions on Industrial Electronics.

[17]  Pavol Brunovský,et al.  A classification of linear controllable systems , 1970, Kybernetika.

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

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

[20]  Balth. van der Pol Jun..  LXXXVIII. On “relaxation-oscillations” , 1926 .

[21]  Andrzej Bartoszewicz,et al.  Sliding Mode Control , 2007 .

[22]  A. N. Njah,et al.  Synchronization via active control of parametrically and externally excited Φ6 Van der Pol and Duffing oscillators and application to secure communications , 2011 .

[23]  Alexander S. Poznyak,et al.  Designing a terminal optimal control with an integral sliding mode component using a saddle point method approach: a Cartesian 3D-crane application , 2016 .

[24]  Vadim I. Utkin,et al.  Sliding mode control in electromechanical systems , 1999 .