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Fuzzy Controller Design: A Sliding Mode Approach

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Abstract

A fuzzy-sliding mode controller, which is designed by the techniques of the fuzzy logic controller and the sliding mode controller (or called variable structure control), is proposed in this work. Like the sliding mode of the sliding mode control system, the fuzzy-sliding mode control system has a fuzzy-sliding mode. The reason for calling “fuzzy-sliding mode” is that the sliding surface in the proposed scheme is a fuzzy set rather than a crisp set found in the conventional sliding mode control system. In the design of the fuzzy-sliding mode controller, one can easily determine the membership function, observe the fuzzy rules and predict the controlled system behavior. Furthermore, the number of inference rules, which is an exponential function of the number of system state variables in a conventional fuzzy logic controller, is reduced to a linear function of the number of system state variables in the fuzzy-sliding mode control system. Simulation results show that the proposed scheme has the following advantages:

  1. 1.

    The dynamics behavior of the controlled system can be approximately dominated by a fuzzified sliding surface.

  2. 2.

    Fuzzification of the sliding surface will not only increase the robustness to the system nonidealities but also decrease the chattering.

  3. 3.

    The fuzzy-sliding mode controller can control most of the complex ill-defined systems without knowing their mathematical models.

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References

  1. G. J. Klir and T. A. Folger, Fuzzy Sets, Uncertainty, and Information, Prentice-Hall: New Jersey, 1988.

    MATH  Google Scholar 

  2. D. Dubois and H. Prade, Fuzzy sets and systems: theory and applications. Academic press: New York, 1980.

    MATH  Google Scholar 

  3. L. A. Zadeh, “Fuzzy sets”, Information and Control, Vol. 8, pp. 338–353, 1965.

    Article  MATH  MathSciNet  Google Scholar 

  4. L. A. Zadeh, “Outline of a new approach to the analysis of complex systems and decision processes”, IEEE Tran. on Syst. and Cyber., Vol. SMC-3, No. 1, pp. 28–44, 1973.

    MathSciNet  Google Scholar 

  5. C. C. Lee, “Fuzzy logic in control systems: Fuzzy logic controller — Part I”, IEEE Tran. on Syst. Man and Cyber., Vol. 20, No. 2, pp. 404–418, 1990.

    Article  MATH  Google Scholar 

  6. C. C. Lee, “Fuzzy logic in control systems: Fuzzy logic controller — Part II”, IEEE Tran. on Syst. Man and Cyber., Vol. 20, No. 2, pp. 419–435, 1990.

    Article  MATH  Google Scholar 

  7. C. C. Lee, “A self-learning rule-based controller employing approximate reasoning and neural net concepts”, Int. J. of Intel. Syst., Vol. 6, pp. 71–93, 1991.

    Article  Google Scholar 

  8. T. J. Procyk and E. H. Mamdani, “A Linguistic self-organizing process controller”, Automatica, Vol. 15, pp. 15–30, 1979.

    Article  MATH  Google Scholar 

  9. E. H. Mamdani, “Application of fuzzy algorithms for control of simple dynamic plant”, Proc. IEE, Vol. 121, No. 12, pp. 1585–1588, 1974.

    Google Scholar 

  10. E. H. Mamdani, “Application of fuzzy logic to approximate reasoning using linguistic synthesis”, IEEE Tran. on Computers, Vol. C-26, No. 12, pp. 182–1191, 1977.

    Google Scholar 

  11. S. Assilian and E. H. Mamdani, “An experiment in linguistic synthesis with a fuzzy logic controller”, Int. J. Man Mech. Studies, Vol. 7, No. 1, pp. 1–13, 1974.

    Google Scholar 

  12. Y. Y Chen and T. C. Tsao, “A description of the dynamical behavior of fuzzy systems”, IEEE Tran. on Syst. Man and Cyber., Vol. 19, No. 4, pp. 745–755, 1989.

    Article  MathSciNet  Google Scholar 

  13. R. Zhao and R. Govind, “Defuzzification of fuzzy intervals”, Fuzzy Sets and Systems, Vol. 43, pp. 45–55, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  14. M. Mizumoto and H. J. Zimmermann, “Comparison of fuzzy reasoning methods”, Fuzzy Sets and Systems, Vol. 8, pp. 253–283, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  15. V. I. Utkin, Sliding modes and their application in variable structure system, Moscow: Mir, 1978 (English translation).

    Google Scholar 

  16. V. I. Utkin, “Equations of sliding mode discontinuous system, I”, Automat. Remote Control, No. 12, pp. 42–54, 1971.

    Google Scholar 

  17. V. I. Utkin, “Equations of sliding mode discontinuous system, II”, Automat. Remote Control, No. 2, pp. 51–61, 1972.

    Google Scholar 

  18. J. J. Slotine and S. S. Sastry, “Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators”, Int. J. Control, Vol. 38, No. 2, pp. 465–492, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  19. J. J. Slotine, “Sliding controller design for non-linear systems”, Int. J. Control, Vol. 40, No. 2, pp. 421–434, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  20. K. K. D. Young, “Controller design for a manipulator using theory of variable structure systems”, IEEE Tran. on Syst. and Cyber., Vol. SMC-8, No. 2, pp. 101–109, 1978.

    Article  Google Scholar 

  21. K. K. D. Young, P. V. K. Kotovic and V. I. Utkin, “A singular perturbation analysis of high gain feedback system”, IEEE. Tran. on Automatic Control, Vol. AC-22, pp. 931–938, 1977.

    Article  Google Scholar 

  22. K. K. D. Young and H. G. Kwatry, “Variable structure servomechanis design and applications to overspeed protection control”, Automatica, Vol. 18, No. 4, pp. 385–400, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  23. M. Vidyasagar, Nonlinear Systems Analysis, Prentice-Hall: New Jersey, 1993.

    MATH  Google Scholar 

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© 1994 Kluwer Academic Publishers

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Kung, CC., Lin, SC. (1994). Fuzzy Controller Design: A Sliding Mode Approach. In: Fuzzy Reasoning in Information, Decision and Control Systems. International Series on Microprocessor-Based and Intelligent Systems Engineering, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-0-585-34652-6_10

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  • DOI: https://doi.org/10.1007/978-0-585-34652-6_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-2643-4

  • Online ISBN: 978-0-585-34652-6

  • eBook Packages: Springer Book Archive

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