Nonlinear Controller For Fuzzy Model Of Double Inverted Pendulums - I. Zamani; M. H. Zarif (Zenodo, 2007)
In this paper a method for designing of nonlinear controller for a fuzzy model of Double Inverted Pendulum is proposed. This system can be considered as a fuzzy large-scale system that includes offset terms and disturbance in each subsystem. Offset terms are deterministic and disturbances are satisfied a matching condition that is mentioned in the paper. Based on Lyapunov theorem, a nonlinear controller is designed for this fuzzy system (as a model reference base) which is simple in computation and guarantees stability. This idea can be used for other fuzzy large- scale systems that include more subsystems Finally, the results are shown. : {"references": ["L. Zadeh, \"Outline of a new approach to the analysis of complex systems and decision processes\", IEEE Trans. Fuzzy Syst. , Vol. 6, pp. 346-360, Aug. 1998", "S. Kawamoto, K. Tada, A. Ishigame, and T. Taniguchi\" Construction of exact fuzzy system for nonlinear system and its stability analysis, \" in Proc. 8th Fuzzy Syst. Symp., Hiroshima, Japan, May 1992, pp. 517-520 (in Japanese's)", "T. Takagi and M. Sugeno, \" Stability Analysis and Design of Fuzzy Control System, \" Fuzzy Sets Syst., Vol. 45, pp. 135-156, 1992", "Wang, H. 0. ., K. Tanaka and M. Griffin, \"An analytical framework of fuzzy modeling and control of nonlinear systems: Stability and design", "Z.H. Xiu G.Ren,\" Stability analysis and systematic design of takagi-sugeno fuzzy control system \" Fuzzy Sets and Systems ,Vol. 151, no 1, pp. 119-138, 2005", "Assem H.Sonbol and M.Sami Fadali,\" TSK fuzzy systems type II and type III stability analysis: continuous case\" IEEE Transaction on Systems, Man, and Cybernetics-Part B: Cybernetics, Vol. 36, No. 1, 2006.", "Assem H. Sonbol and M. Sami Fadali,\" Stability analysis to discrete TSK type\tsystems\" IEEE Transaction on Systems, Man, and \nCybernetics-Part B: Cybernetics, 2006", "W. J. Wang and L. Luoh \"Stability and Stabilization of Fuzzy Large-Scale Systems \"IEEE Transactions on Fuzzy Systems, Vol. 12, No. 3, June 2004.", "F. H. Hsiao and J. D. Hwang \"Stability Analysis of Fuzzy Large-Scale Systems\" IEEE Transaction on Systems, Man, and Cybernetics, Vol. 32, No. 1, February 2001.\n[10] W. J. Wang and W. W. Lin \"Decentralized PDC for Large-Scale T\u2013S Fuzzy Systems\" IEEE Transactions on Fuzzy Systems, Vol. 13, No. 6, December 2005.\n[11] H. Zhang, C. Li, and X. Liao \"Stability Analysis and Hoo Controller Design of Fuzzy Large-Scale Systems Based on Piecewise Lyapunov Functions\" IEEE Transaction on Systems, Man, and Cybernetics, Vol. 36, No. 3, June 2006.\n[12] Y. Y. Cao, Y. X. Sun, and J. Lam. Delay dependent robust Hoo control for uncertain systems with time varying delays. lEE Proceedings: Control Theory and Applications, 143(3):pp.338-344, 1998.\n[13] Gene H. Golub and Charles F. van Loan. Matrix Computations. The JohnsHopkins University Press, Baltimore, 3rd edition, 1996.\n[14] K. Ogata, Discrete Time Control Systems. Published 1995, Prentice Hall."]}