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Autotuning of a Fuzzy PID Controller Based on Fuzzy Gain and Phase Margins: Analysis and Design

  • Otacílio da Mota Almeida
  • Antonio Augusto Rodrigues Coelho
  • Leandro dos Santos Coelho

Abstract

In this paper a new method for autotuning thePID controller gains based on fuzzy rules is proposed and a new rule base for gain and phase margins is derived. The proposed control scheme offers advantages over the conventional fuzzy PID controller (FPID) such as: i) it is necessary only one rule base; ii) it may be completely autotuned, requiring only one relay feedback experiment; and iii) it shows stability and the robustness characteristic is conceptually simple. The fuzzy PID control algorithm has been successfully applied to simulation and practical examples. The application of the describing function for the stability and design of FPID control system is investigated.

Keywords

Membership Function Fuzzy Rule Fuzzy Controller Propose Control Scheme Phase Margin 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Kosko, B. (1992). Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence, Prentice-Hall, Englewood Cliffs, NJ, USA.MATHGoogle Scholar
  2. 2.
    Yager, R. R.; Filev, D.P. (1994). Essentials of fuzzy modeling and control, New York: John Wiley & Sons.Google Scholar
  3. 3.
    Mamdani, E.; Assilian, S. (1975). An experiment in linguistic synthesis with a fuzzy logic controller, Int. J. Man Machine Studies, vol. 7, no. 1, pp. 1–13.MATHCrossRefGoogle Scholar
  4. 4.
    Zadeh, L.A. (1965). Fuzzy sets, Information and Control, vol. 8, pp. 338–353.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Cheng, C. M.; Rees, N. W. (1997). Stability analysis of fuzzy multivariable systems: vector Lyapunov function approach, IEE Proceedings Control Theory and Applications, vol. 144, no. 5, pp. 403–412.MATHCrossRefGoogle Scholar
  6. 6.
    Fischle, K.; Schröder, D. (1999). An improved stable adaptive fuzzy control method, IEEE Transactions on Fuzzy Systems, vol. 7, no. 1, pp. 27–40.CrossRefGoogle Scholar
  7. 7.
    Cuesta, F.; Gordillo, F.; Aracil, J.; Ollero, A. (1999). Stability analysis of nonlinear multivariable Takagi-Sugeno fuzzy control systems, IEEE Transactions on Fuzzy Systems, vol. 7, no. 5, pp. 508–520.CrossRefGoogle Scholar
  8. 8.
    Carvajal, J.; Chen, G.; Ogmen, H. (2000). Fuzzy PID controller: design, performance, evaluation an stability analysis, Information Sciences, vol. 123, pp. 248–270.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Åström, K. J. (1991). Intelligent control, European Control Conference, Grenoble, France, pp. 2328–2339.Google Scholar
  10. 10.
    Wang, Y. G.; Shao, H. H. (1999). PID tuning for improving performance, IEEE Transactions on Control Systems Technology, vol. 7, pp. 457–465.CrossRefGoogle Scholar
  11. 11.
    Astrom, K. J.; Hagglund, T. (1995). PID controllers: theory, design and tuning, Instrument Society of America.Google Scholar
  12. 12.
    Luyben, W. L. (1987). Derivation of transfer function for highly non-linear distillation columns, Ind. Eng. Chem. Process Des. Dev., vol. 26, pp. 2490–2495.Google Scholar
  13. 13.
    Qin, S. J. (1994). “Auto-tuned fuzzy logic control”, Proc. of the American Control Conference, Baltimore, Maryland, USA, pp. 2465–2469.Google Scholar
  14. 14.
    Zhao, Z. Y.; Tomizuka, M.; Isaka, S. (1993). Fuzzy gain scheduling of PID controllers, IEEE Transactions on Systems Man and Cybernetics, vol. 23, no. 5 September/October.Google Scholar
  15. 15.
    Coelho, L. S.; Almeida, O. M.; Coelho, A. A. R. (1998). Intelligent and self-tuning PID controllers: methods and application, Proceedings of XII Brazilian Automatic Control Conference, vol. I, pp.375–380, Uberlandia MG, Brazil.Google Scholar
  16. 16.
    Almeida, O. M.; Coelho, L. S.; Coelho, A. A. R. (1999). Practical robust control to a nonlinear system using auto-tuning fuzzy and sliding-mode approaches, 4 World Congress on Soft Computing.Google Scholar
  17. 17.
    Coelho, L. S.; Almeida, O. M.; Coelho, A. A. R. (2000). Design and tuning of intelligent and self-tuning PID controllers, 5 World Congress on Soft Computing.Google Scholar
  18. 18.
    Woo, Z. W.; Chung, H. Y.; Lin, J. J. (2000). “A PID type fuzzy controller with self-tuning scaling factors”, Fuzzy Sets and Systems, vol. 15, pp. 321–326.CrossRefGoogle Scholar
  19. 19.
    Khalil, H. K., (1996). Nonlinear System, Prentice Hall.Google Scholar
  20. 20.
    Kim, E.; Lee, H. and Park, M. (2000) Limit-cycle prediction of a fuzzy control system based on describing function method, IEEE Transaction on Fuzzy Systems, vol. 8, no. I, pp. 11–22.Google Scholar

Copyright information

© Springer-Verlag London 2002

Authors and Affiliations

  • Otacílio da Mota Almeida
    • 1
  • Antonio Augusto Rodrigues Coelho
    • 1
  • Leandro dos Santos Coelho
    • 2
  1. 1.Department of Automation and SystemsFederal University of Santa CatarinaFlorianópolisBrazil
  2. 2.LAS/CCET/PUCPR Rua Imaculada ConceiçãoPontificia Universidade Católica do ParanáCuritibaBrazil

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