Stabilization of an Underactuated Ball-and-Beam System Using a Second-Order Sliding Mode Control
Jie Yang*, Qinglin Wang*, Yuan Li*,
and Jinhua She**
*School of Automation, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian, Beijing 100081, China
**School of Computer Science, Tokyo University of Technology, 1401-1 Katakura, Hachioji, Tokyo 192-0982, Japan
This paper presents a stabilization method for an underactuated ball-and-beam system (BABS) based on a second-order sliding mode (SOSM) control. The BABS is an underactuated nonlinear system that is widely used to verify nonlinear control performance. Virtual control is introduced to a second-order BABS subsystem to minimize control performance inaccuracy by using model linearization. An actual virtual controller with variable finite-time tracking is achieved using a second-order sliding mode controller. An adaptive robust method is proposed to solve an uncertainty problem with unknown upper bounds, and then a finite-time convergence theory proof is given. Theory, simulation and experiment results verify the efficiency of the BABS controller.
and Jinhua She, “Stabilization of an Underactuated Ball-and-Beam System Using a Second-Order Sliding Mode Control,” J. Adv. Comput. Intell. Intell. Inform., Vol.18, No.2, pp. 121-127, 2014.
-  G. Nugroho and Z. Taha, “Helicopter Motion Control Using Model-Based Sliding Mode Controller,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.12, No.4, pp. 342-347, 2008.
-  G. Bartolini et al., “A Survey of Application of Second-Order Sliding Mode Control to Mechanical Systems,” Int. J. of Control, Vol.76, No.9/10, pp. 875-982, 2003.
-  J. K. Tar, I. J. Rudas, and B. Patkai, “Comparison of Fractional Robust- and Fixed Point Transformations- Based Adaptive Compensation of Dynamic Friction,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.11, No.9, pp. 1062-1071, 2007.
-  L. Marton and B. Lantos, “Sliding Mode Robot Control with Friction and Payload Estimation,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.8, No.5, pp. 553-561, 2004.
-  J. K. Liu and F. C. Sun, “Chattering Free Adaptive Fuzzy Terminal Sliding Mode Control for Second Order Nonlinear System,” J. of Control Theory and Applications, Vol.4, No.4, pp. 385-391, 2006.
-  F. Mazenc, A. Astolfi, and R. Lozano, “Lyapunov Function for the Ball and Beam: Robustness Property,” Proc. of the 38th Conf. on Decision and Control, pp. 1208-1213, 1999.
-  F. Dinuzzo and A. Ferrara, “Higher Order Sliding Mode Controllers With Optimal Reaching,” IEEE Trans. on Automatic Control, Vol.54, No.9, pp. 2126-2136, 2009.
-  A. Levant, “Principles of 2-sliding mode design,” Automatica, Vol.43, pp. 576-586, 2007.
-  R. Olfati-Saber, and A. Megretski, “Controller Design for the Beam-and-Ball System,” Proc. of the 37th IEEE Conf. on Decision Control, pp. 4555-4560, 1998.
-  R. Olfati-Saber, “Normal Forms for Underacutated Mechanical Systems with Symmetry,” IEEE Trans. on Automatica Control, Vol.47, No.2, pp. 305-308, 2002.
-  P. Li and Z. Q. Zheng, “Robust adaptive second-order slidingmode control with fast transient performance,” IET Control Theory and Applications, Vol.6, No.2, pp. 305-312, 2012
-  S. P. Bhat and D. S. Bernstein, “Geometric homogeneity with applications to finite-time stability,” Math Control Signals Systems, Vol.17, No.2, pp. 101-127, 2005.
-  S. P. Bhat and D. S. Bernstein, “Finite-Time Stability of Continuous Autonomous Systems,” SIAM J. on Control and Optimization, Vol.38, No.3, pp. 751-766, 2000.
-  H. J. Chen et al., “Design of Fixed Point Controller for Underactuated Ball-and-Beam System,” Control Engineering of China, Vol.15, No.4, pp. 398-419, 2008.
-  M. Amjad et al., “Fuzzy Logic Control of Ball and Beam System,” Int. Conf. on Education Technology and Computer, Vol.3, pp. 489-493, 2010.
-  J. S. Kim, G. M. Park, and H. L. Choi, “Sliding mode control design under partial state feedback for ball and beam system,” Int. Conf. on Control, Automation and Systems, pp. 1293-1296, 2010.
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