Robust stabilization of underactuated nonlinear systems: A fast terminal sliding mode approach.

This paper presents a fast terminal sliding mode based control design strategy for a class of uncertain underactuated nonlinear systems. Strategically, this development encompasses those electro-mechanical underactuated systems which can be transformed into the so-called regular form. The novelty of the proposed technique lies in the hierarchical development of a fast terminal sliding attractor design for the considered class. Having established sliding mode along the designed manifold, the close loop dynamics become finite time stable which, consequently, result in high precision. In addition, the adverse effects of the chattering phenomenon are reduced via strong reachability condition and the robustness of the system against uncertainties is confirmed theoretically. A simulation as well as experimental study of an inverted pendulum is presented to demonstrate the applicability of the proposed technique.

[1]  Thierry Floquet,et al.  Second‐order sliding mode control of underactuated mechanical systems I: Local stabilization with application to an inverted pendulum , 2008 .

[2]  K Furuta,et al.  Swing-up Control of Inverted Pendulum Using Pseudo-State Feedback , 1992 .

[3]  Toshiharu Sugie,et al.  Passivity based control of a class of Hamiltonian systems with nonholonomic constraints , 2012, Autom..

[4]  Danijel Pavković,et al.  Modeling and control of a pneumatically actuated inverted pendulum. , 2009, ISA transactions.

[5]  Rogelio Lozano,et al.  Energy based control of the Pendubot , 2000, IEEE Trans. Autom. Control..

[6]  Qudrat Khan,et al.  Robust Dynamic Integral Sliding Mode for MIMO Nonlinear Systems Operating Under Matched and Unmatched Uncertainties , 2014 .

[7]  Ümit Özgüner,et al.  Sliding mode control of a class of underactuated systems , 2008, Autom..

[8]  Jung-Shan Lin,et al.  Nonlinear control design for a class of underactuated systems , 2010, 2010 IEEE International Conference on Control Applications.

[9]  Akira Inoue,et al.  Stabilization controller for a cart-type inverted pendulum via a partial linearization method , 2010, Proceedings of the 2010 International Conference on Modelling, Identification and Control.

[10]  Romeo Ortega,et al.  Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment , 2002, IEEE Trans. Autom. Control..

[11]  Dongya Zhao,et al.  Output Feedback Terminal Sliding Mode Control for a Class of Second Order Nonlinear Systems , 2013 .

[12]  Suying Zhang,et al.  A New Type of Adaptive Neural Network Fuzzy Controller in the Double Inverted Pendulum System , 2011, AICI.

[13]  A. Isidori.  Nonlinear Control Systems , 1985 .

[14]  Zhihong Man,et al.  Continuous finite-time control for robotic manipulators with terminal sliding mode , 2003, Autom..

[15]  Dongkyoung Chwa,et al.  Swing-Up and Stabilization Control of Inverted-Pendulum Systems via Coupled Sliding-Mode Control Method , 2009, IEEE Transactions on Industrial Electronics.

[16]  Jin Bae Park,et al.  Finite time control of nonlinear underactuated systems using terminal sliding surface , 2009, 2009 IEEE International Symposium on Industrial Electronics.

[17]  Xin Xin,et al.  Energy-Based Swing-Up Control for a Remotely Driven Acrobot: Theoretical and Experimental Results , 2012, IEEE Transactions on Control Systems Technology.

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

[19]  Arun D. Mahindrakar,et al.  Control of a Class of Underactuated Mechanical Systems Using Sliding Modes , 2009, IEEE Transactions on Robotics.

[20]  Chitralekha Mahanta,et al.  Integral backstepping sliding mode control for underactuated systems: swing-up and stabilization of the Cart-Pendulum System. , 2013, ISA transactions.

[21]  Hongxing Li,et al.  Finite-time control for nonlinear spacecraft attitude based on terminal sliding mode technique. , 2014, ISA transactions.

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

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

[24]  Lixia Deng,et al.  The design for the controller of the linear inverted pendulum based on backstepping , 2011, Proceedings of 2011 International Conference on Electronic & Mechanical Engineering and Information Technology.

[25]  Nabil Derbel,et al.  Second-order sliding mode approaches for the control of a class of underactuated systems , 2015, Int. J. Autom. Comput..

[26]  Mingjun Zhang,et al.  Hybrid control of the Pendubot , 2002 .

[27]  Ronald S. Fearing,et al.  Tracking fast inverted trajectories of the underactuated Acrobot , 1999, IEEE Trans. Robotics Autom..