Design of T2FSMC Controller with Minimum Gain Scale Factor by Optimizing Membership Function Using FireFly Algorithm on Mobile Inverted Pendulum

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The combination of FireFly and T2FSMC has succesfully not only in overcoming the chattering and robustness problems on mobile inverted pendulum robot, but also can effectively result optimal gain scale factor  so that the controller can solve those problems more effectively and more robust against disturbances and parameter uncertainties compared with other artificial based optimization methods. This paper investigates more deeply the influence of membership functions on the effectiveness of gain scale factor as well as the robustness of resulted controller. It can be shown through the simulation that an optimal membership function can be found using firefly making the gain scale factor small enough which is very good from the hardware implementation point of view and in suppressing chattering- while still maintaining the robustness against the parameter uncertainties. The robustness comparison between controller based on the proposed optimal gain scale factor with other controllers are also shown in the simulation.
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FireFly Algorithm; Fuzzy Sliding Mode Control; Mobile Inverted Pendulum Robot

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M.F. Abdollah, Proportional integral sliding mode control of a wheeled balancing robot, Master’s thesis, University Teknologi Malaysia, Malaysia, 2006

Anderson, D. (2003). Nbot, a two wheel balancing robot, dpa-www/robo/nbot/.

T. Apostolopoulos and A. Vlachos, Application of the firefly algorithm for solving the economic emissions load dispatch problem, International Journal of Combinatorics, 2011.

F. Grasser, A. D’Arrigo, S. Colombi, A. Russel, Joe: A mobile inverted pendulum, IEEE Transactions on Industrial Electronics 49(2): 107–114, 2002.

J.Keighobadi, Y. Mohamadi, Fuzzy sliding mode control of a non-holonomic wheeled mobile robot, Proceeding of the International MultiConference of Engineers and Computer Scientist 2011, Vol. 2, 2011.

W.Jiwei, X. Lihong, X. Yunshi, A new design method of fuzzy sliding mode controller with faster convergence, IEEE Int. Fuzzy Systems Conference Proceedings. 1999.

JR Castro, O.Castillo, L. Martines. Interval type 2 fuzzy logic toolbox, Engineering Letters, 2007.

Mardlijah, A.Jazidie, B. Widodo, A. Santoso, A new combination method of firefly algorithm and t2fsmc for mobile inverted pendulum robot, Journal of Theoretical and Applied Information Technology 47(2), 2013.

J. Mendel, Uncertain Rule-based Fuzzy Logic Systems: Introduction and new directions (Prentice Hall, NJ, 2001).

M. Y. Hsiao, Tzuu Hseng S, J. Lee, C. Chao, S. Tsai.,Design of interval type 2 fuzzy sliding mode controller, International Journal of Information Sciences p. 178, 2007.

N. M. Abdul Ghani, N. I. Mat Yatim, N. A. Azmi, Comparative assessment for two wheels inverted pendulum mobile robot using robust control, International Conference on Control, Automation and System 2010, KINTEX, Gyeonggi-do, Korea, 2010.

R. Ooi, Balancing a Two-Wheeled Autonomous Robot, final year project, University of Western Australia School of Mechanical Engineering, 2003.

W. Perruquetti, and J. P. Barbot , Sliding Mode Control in Engineering (Marcell Dekker, New York, 2002).

S.W. Nawawi, M.N.Ahmad and J.H.S. Osman, Variable structure control of two-wheels inverted pendulum mobile robot, Regional Postgraduate Conference on Engineering and Science (RPCES 2006), Johore, 2006.

S.W.Nawawi, M.N.Ahmad and J.H. S. Osman, Nonlinear Control Technique for a Class of Wheeled Mobile Robot, (2008) International Review of Automatic Control (IREACO), 1 (4), pp. 528-542.

X. S. Yang, Nature-Inspired Metaheuristic Algorithm (Luniver- Press, 2008).

X. S. Yang, (n.d.). Firefly algorithm, levy flights and global optimization, Research and Development in Intelligent Systems XXVI, pp. 209–218.

F. Q. Zhu, Q. M. Winfield, C. Melhuish, Fuzzy sliding mode control for discrete nonlinear systems, Transactions of China Automation Society 22(2), 2003.


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