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Parallel Distributed Fuzzy Sliding Mode Control for Nonlinear Mismatched Uncertain Systems

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Abstract

A new design approach of a parallel distributed fuzzy sliding mode controller for nonlinear systems with mismatched time varying uncertainties is presented in this paper. The nonlinear system is approximated by the Takagi–Sugeno fuzzy linear model. The approximation error between the nonlinear system and the fuzzy linear model is considered as one part of the uncertainty in the uncertain nonlinear system. The time varying uncertainties are assumed to have the format which enables the design of the coefficient matrix of the sliding function to satisfy a sliding coefficient matching condition. With the sliding coefficient matching condition satisfied, a parallel distributed fuzzy sliding mode controller (PDFSC) is designed. The stability and the sliding mode of the fuzzy sliding control system are guaranteed. Also, the nonlinear system is shown to be invariant on the sliding surface. Moreover, the chattering around the sliding surface in the sliding mode control can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed fuzzy sliding mode controller.

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References

  1. Chan ML, Tao CW, Lee TT (2000) Sliding mode controller for linear systems with mismatched time-varying uncertainties. J Franklin Inst 337:105–115

    Article  MATH  MathSciNet  Google Scholar 

  2. Chan SP (1996) An approach to perturbation compensation for variable structure systems. Automatica 32(3):469–473

    Article  MATH  MathSciNet  Google Scholar 

  3. Chang FJ, Twu SH, Chang S (1990) Adaptive chattering alleviation of variable structure systems control. IEE Proc D 137(1):31–39

    MATH  MathSciNet  Google Scholar 

  4. Chen BS, Tseng CS, Uang HJ (1999) Robust design of uncertain dynamic systems via fuzzy linear control. IEEE Trans Fuzzy Syst 7 5:571–585

    Article  Google Scholar 

  5. Choi HH (1998) An explicit formula of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties. Automatica 34(8):1015–1020

    Article  MATH  MathSciNet  Google Scholar 

  6. Driankov D, Hellendoorn H, Reinfrank M (1993) An introduction to fuzzy control. Spring Berlin Heidelberg New York

  7. Espana MD, Ortega RS, Espino JJ (1984) Variable structure systems with chattering reduction: A microprocessor based design. Automatica 20(1):133–134

    Article  MATH  Google Scholar 

  8. Glower JS, Munighan J (1997) Designing fuzzy Controllers from a variable structures standpoint. IEEE Trans Fuzzy Syst 5(1): 138–144

    Article  Google Scholar 

  9. Han H, Murakami S (2003) A design for a class of nonlinear systems with delay time using fuzzy logic. Soft Comput Fusion Found Methodol Appl 74: 252 V257

    Google Scholar 

  10. Hsu KC, Wang WY, Lin PZ (2004) Sliding mode control for uncertain nonlinear systems with multiple inputs containing sector nonlinearities and deadzones. IEEE Trans Syst Man Cybern 34(1):374–380

    Article  Google Scholar 

  11. Hung JY, Gao W, Hung JC (1993) Variable structure control: A survey. IEEE Trans Ind Electro 40(1):2–21

    Article  Google Scholar 

  12. Hwang GC, Lin SC (1992) A stability approach to fuzzy control design for nonlinear systems. Fuzzy Sets Syst 48(3):279–287

    Article  MATH  MathSciNet  Google Scholar 

  13. Hwang YR, Tomizuka M (1994) Fuzzy smoothing algorithms for variable structure systems. IEEE Trans Fuzzy Syst 2:227–284

    Article  Google Scholar 

  14. Hwang CL, Kuo CY (2001) A stable adaptive fuzzy sliding mode control for affine nonlinear systems with application to four-bar linkage systems. IEEE Trans Fuzzy Syst 9(2):238–252

    Article  Google Scholar 

  15. Knight MJ, Sutton R, Burns RS (2003) Fuzzy model based integral action sliding mode control. Soft Comput Fusion of Found Methodol Appl 7(4):244 V251

    Google Scholar 

  16. Lee TT, Tu KY (1997) Design of a fuzzy logic controller as a suction controller. Fuzzy Sets Syst 91(3):305–317

    Article  MathSciNet  Google Scholar 

  17. Lin Y, Cunningham GA III (1995) A new approach to fuzzy neural system modeling. IEEE Trans Fuzzy Syst 3(2):190–198

    Article  Google Scholar 

  18. Shen JC (1997) Designing stabilising controllers and observers for uncertain linear systems with time varying delay. IEE Proc D 144(4):331–334

    MATH  Google Scholar 

  19. Slotine JJ, Li W (1991) Applied nonlinear control. Prentice-Hall, New Jersey

    MATH  Google Scholar 

  20. Sun FC, Sun ZQ, Feng G (1999) An adaptive fuzzy controller based on sliding mode for robot manipulators. IEEE Trans Syst Man Cybern 29(4): 661–667

    Google Scholar 

  21. Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 15:116–132

    MATH  Google Scholar 

  22. Tanaka K, Ikeda T, Wang HO (1996) Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H ∞ control theory, and linear matrix inequalities. IEEE Trans Fuzzy Syst 4(1):1–13

    Article  Google Scholar 

  23. Tao CW, Chan ML, Lee TT (2003) Adaptive fuzzy sliding mode controller for linear systems with mismatched time-varying uncertainties. IEEE Trans Syst Man Cybern 33(2):283–294

    Article  Google Scholar 

  24. Tao CW (2004) Robust control of systems with fuzzy representation of uncertainties. Soft Comput Fusion Found Methodol Appl 8(3):163 V172

    Google Scholar 

  25. Utkin VI (1977) Variable structure systems with sliding modes. IEEE Trans Autom Control AC-22(2):212–221

    Article  MATH  MathSciNet  Google Scholar 

  26. Wang HO, Tanaka K, Griffin MF (1996) An approach to fuzzy control of nonlinear systems: stability and control issues. IEEE Trans Fuzzy Syst 4(1):14–23

    Article  Google Scholar 

  27. Yager RR, Filev DP (1994) Essentials of fuzzy modeling and control. Wiley, New York

    Google Scholar 

  28. Yoo B, Ham W (1998) Adaptive fuzzy sliding mode control of nonlinear system. IEEE Trans Fuzzy Syst 6(2):315–321

    Article  Google Scholar 

  29. Young KD, Ozguner U (1997) Sliding mode design for robust linear optimal control. Automatica 33(7):1313–1323

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical Engineering, National I-Lan University, ILan, Taiwan

    C. W. Tao

  2. Department of Electrical Engineering, National Chung Hsing University, Taichung, Taiwan

    J. S. Taur

Authors
  1. C. W. Tao
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  2. J. S. Taur
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Corresponding author

Correspondence to J. S. Taur.

Additional information

This work is partly supported by the the R.O.C. National Science Council through Grant NSC93-2213-E-197-004.

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Tao, C.W., Taur, J.S. Parallel Distributed Fuzzy Sliding Mode Control for Nonlinear Mismatched Uncertain Systems. Soft Comput 11, 607–616 (2007). https://doi.org/10.1007/s00500-006-0104-4

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  • DOI: https://doi.org/10.1007/s00500-006-0104-4

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