Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
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Construction of T-S Fuzzy Model for Nonlinear Systems

비선형 시스템에 대한 T-S 퍼지 모델 구성

  • 정은태 (창원대학교 제어계측공학과) ;
  • 권성하 (창원대학교 제어계측공학과) ;
  • 이갑래 (평택대학교 정보과학부)
  • Published : 2002.11.01
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Abstract

Two methods of constructing T-S fuzzy model which is equivalent to a given nonlinear system are presented. The first method is to obtain an equivalent T-S fuzzy model by using the sum of linearly independent scalar functions with constant real matrix coefficients. The sum of products of linearly independent scalar functions is used in the second method. The former method is to formulate the procedures of T-S fuzzy modeling dealt in many examples of previous publications; the latter is a new method. By comparing the number of linearly independent functions used in the two methods, we can easily find out which method makes fewer rules than the other. The nonlinear dynamics of an inverted Pendulum on a cart is used as an equivalent T-5 fuzzy modeling example.

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References

  1. T. Takagi and M. Sugeno, 'Fuzzy identification of systems and its applications to modeling and control,' IEEE Trans. Syst., Man, Cybern., Vol. 15, No. 1, pp. 116-132, 1985
  2. H. O. Wang, K. Tanaka, and M. F. Griffin, 'An approach to fuzzy control of Nonlinear systems: Stability and design issues,' IEEE Trans. Fuzzy Syst., Vol. 4, No. 1, pp. 14-23, Feb. 1996 https://doi.org/10.1109/91.481841
  3. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox, The Math Works Inc., 1995
  4. S. Abe, 'Fuzzy function approximators with ellipsoidal regions,' IEEE Trans. Syst. Man, Cybern.-Part B: Cybernetics, Vol. 29, No. 4, pp. 654-661, Aug. 1999 https://doi.org/10.1109/3477.790450
  5. Q. Gan and C. J. Harris, 'Fuzzy local linearization and local basis function expansion in nonlinear system modeling,' IEEE Trans. Syst., Man, Cybern.-Part B: Cybernetics, Vol. 29, No. 4, pp. 559-565, Aug. 1999 https://doi.org/10.1109/3477.775275
  6. J. Abonyi, R. Babuska. and F. Szeifert, 'Fuzzy modeling with multivariate membership functions: Gray-box identification and control design,' IEEE Trans. Syst., Man, Cybern.-Part B: Cybernetics, Vol. 31, No. 5, pp. 755-767, Oct. 2001 https://doi.org/10.1109/3477.956037
  7. J. Yen, L. Wang, and C. W. Gillespie, 'Improving the interpretability of TSK fuzzy models by combining global learning and local learning,' IEEE Trans. Fuzzy Syst., Vol. 6, No. 4, pp. 530-537, Nov. 1998 https://doi.org/10.1109/91.728447
  8. J. Joh, E T. Jeung, W. J. Chung, and S.-H. Kwon, 'A new design method for T-S fuzzy controller with pole placement constraints,' J. Fuzzy Logic and Intelligent Systems, Vol. 7, No. 3, pp. 72-80, Aug. 1997
  9. X. - J. Ma and Z. - Q. Sun, 'Output tracking and regula -tion of nonlinear system based on Takagi-Sugeno fuzzy model,' IEEE Trans. Syst., Man, Cybern.-Part B: Cybernetics, Vol. 30, No. 1, pp. 47-59, Feb. 2000 https://doi.org/10.1109/3477.826946
  10. C.-S. Tseng, B.-S. Chen, H.-J. Uang, 'Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model,' IEEE Trans. Fuzzy Syst., Vol. 9, No. 3, pp. 381-392, June, 2001 https://doi.org/10.1109/91.928735
  11. K. Tanaka, T. Ikeda, and H. O. Wang, 'Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: Quadratic stabilizability, $H^{\infty}$ control theory, and linear matrix inequalities,' IEEE Trans. Fuzzy Syst., Vol. 4, No. 1, pp. 1-13, Feb. 1996 https://doi.org/10.1109/91.481840
  12. K. Tanaka, T. Ikeda, and H. O. wang, 'Fuzzy regulators and fuzzy observers: Relaxed stability conditions and LMI-based design,' IEEE Trans. Fuzzy Syst., Vol. 6, No. 2, pp. 250-265, May 1998 https://doi.org/10.1109/91.669023
  13. H. J. Lee, J. B. Park, and G. Chen, 'Robust fuzzy control of Nonlinear systems with parametric uncertain -ties,' IEEE Trans. Fuzzy Syst., Vol. 9, No. 2, pp. 369-379, Apr. 2001 https://doi.org/10.1109/91.919258
  14. Kap Rai Lee, Jong Hae Kim, Eun Tae Jeung, and Hong Bae Park, 'Output feedback robust $H^{\infty}$ control of uncer -tain fuzzy dynamic systems with time-varying delay,' IEEE Trans. Fuzzy Syst., Vol. 8, No. 6, pp. 657-664, Dec. 2000 https://doi.org/10.1109/91.890325
  15. K. R. Lee, E. T. Jeung, and H. B. Park, 'Robust fuzzy $H^{\infty}$ control for uncertain nonlinear systems via state feedback: An LMI approach,' Fuzzy Sets Syst., Vol. 120, pp. 123-134, May 2001 https://doi.org/10.1016/S0165-0114(99)00078-0
  16. T. Taniguchi, K. Tanaka, H. Ohtake, and H. O. Wang, 'Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems,' IEEE Trans. Fuzzy Syst., Vol. 9, No. 4, pp. 525-538, Aug. 2001 https://doi.org/10.1109/91.940966

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