Skip to main content

Fuzzy Control

  • Chapter

Part of the book series: Springer Handbooks ((SHB))

Abstract

Fuzzy control is by far the most successful field of applied fuzzy logic. This chapter discusses human-inspired concepts of fuzzy control. After a short introduction to classical control engineering, three types of very well known fuzzy control concepts are presented: Mamdani-Assilian, Takagi-Sugeno and fuzzy logic-based controllers. Then three real-world fuzzy control applications are discussed. The chapter ends with a conclusion and a future perspective.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   269.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   349.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Abbreviations

COA:

center of area

COG:

center of gravity

DLR:

German Aerospace Center

FCM:

fuzzy c-means algorithm

MOM:

mean of maxima

PID:

proportional-integral-derivative

RAM:

random access memory

RBF:

radial basis function

ROM:

read only memory

References

  1. E.H. Mamdani: Application of fuzzy algorithms for the control of a simple dynamic plant, Proc. IEEE 121(12), 1585–1588 (1974)

    Google Scholar 

  2. S. Yasunobu, S. Miyamoto: Automatic Train Operation System by Predictive Fuzzy Control (North-Holland, Amsterdam 1985) pp. 1–18

    Google Scholar 

  3. Google patents: http://patents.google.com/, last accessed on August 22, 2013

  4. K. Hirota (Ed.): Industrial Applications of Fuzzy Technology (Springer, Tokio 1993)

    Google Scholar 

  5. T. Terano, M. Sugeno: Applied Fuzzy Systems (Academic, Boston 1994)

    MATH  Google Scholar 

  6. R.-E. Precup, H. Hellendoorn: A survey on industrial applications of fuzzy control, Comput. Ind. 62(3), 213–226 (2011)

    Article  Google Scholar 

  7. C. Moewes, R. Kruse: Fuzzy control for knowledge-based interpolation. In: Combining Experimentation and Theory: A Hommage to Abe Mamdani, Studies in Fuzziness and Soft Computing, Vol. 271, ed. by E. Trillas, P.P. Bonissone, L. Magdalena, J. Kacprzyk (Springer, Berlin, Heidelberg 2012) pp. 91–101

    Chapter  Google Scholar 

  8. P. Podržaj, M. Jenko: A fuzzy logic-controlled thermal process for simultaneous pasteurization and cooking of soft-boiled eggs, Chemom. Intell. Lab. Syst. 102(1), 1–7 (2010)

    Article  Google Scholar 

  9. L.A. Zadeh: Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. Syst. Man Cybern. 3(1), 28–44 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  10. L.A. Zadeh: Fuzzy sets, Inf. Control 8(3), 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  11. K. Tanaka, H.O. Wang: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach (Wiley, New York 2001)

    Book  Google Scholar 

  12. K. Michels, F. Klawonn, R. Kruse, A. Nürnberger: Fuzzy Control: Fundamentals, Stability and Design of Fuzzy Controllers, Studies in Fuzziness and Soft Computing, Vol. 200 (Springer, Berlin, Heidelberg 2006)

    MATH  Google Scholar 

  13. K.J. Åström, B. Wittenmark: Adaptive Control (Courier Dover, Mineola 2008)

    Google Scholar 

  14. G.C. Goodwin, S.F. Graebe, M.E. Salgado: Control System Design, Vol. 240 (Prentice Hall, Upper Saddle River 2001)

    Google Scholar 

  15. E.H. Mamdani, S. Assilian: An experiment in linguistic synthesis with a fuzzy logic controller, Int. J. Man-Mach. Stud. 7(1), 1–13 (1975)

    Article  MATH  Google Scholar 

  16. R. Kruse, J. Gebhardt, F. Klawonn: Foundations of Fuzzy Systems (Wiley, Chichester 1994)

    MATH  Google Scholar 

  17. O. Cordón, M.J. del Jesus, F. Herrera: A proposal on reasoning methods in fuzzy rule-based classification systems, Int. J. Approx. Reason. 20(1), 21–45 (1999)

    Article  Google Scholar 

  18. F. Klawonn, J. Gebhardt, R. Kruse: Fuzzy control on the basis of equality relations with an example from idle speed control, IEEE Trans. Fuzzy Syst. 3(3), 336–350 (1995)

    Article  Google Scholar 

  19. F. Klawonn, R. Kruse: Equality relations as a basis for fuzzy control, Fuzzy Sets Syst. 54(2), 147–156 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  20. D. Boixader, J. Jacas: Extensionality based approximate reasoning, Int. J. Approx. Reason. 19(3/4), 221–230 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  21. F. Klawonn, J.L. Castro: Similarity in fuzzy reasoning, Mathw. Soft Comput. 2(3), 197–228 (1995)

    MathSciNet  MATH  Google Scholar 

  22. T. Takagi, M. Sugeno: Fuzzy identification of systems and its applications to modeling and control, IEEE Trans. Syst. Man Cybern. 15(1), 116–132 (1985)

    Article  MATH  Google Scholar 

  23. G. Feng: A survey on analysis and design of model-based fuzzy control systems, IEEE Trans. Fuzzy Syst. 14(5), 676–697 (2006)

    Article  Google Scholar 

  24. L. Wu, X. Su, P. Shi, J. Qiu: A new approach to stability analysis and stabilization of discrete-time ts fuzzy time-varying delay systems, IEEE Trans. Syst. Man Cybern. B: Cybern. 41(1), 273–286 (2011)

    Article  Google Scholar 

  25. K. Tanaka, H. Yoshida, H. Ohtake, H.O. Wang: A sum-of-squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems, IEEE Trans. Fuzzy Syst. 17(4), 911–922 (2009)

    Article  Google Scholar 

  26. L.A. Zadeh: A theory of approximate reasoning, Proc. 9th Mach. Intell. Workshop, ed. by J.E. Hayes, D. Michie, L.I. Mikulich (Wiley, New York 1979) pp. 149–194

    Google Scholar 

  27. L.A. Zadeh: The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Sets Syst. 11(1/3), 197–198 (1983)

    MathSciNet  MATH  Google Scholar 

  28. D. Dubois, H. Prade: Possibility Theory: An Approach to Computerized Processing of Uncertainty (Plenum Press, New York 1988)

    Book  MATH  Google Scholar 

  29. L.A. Zadeh: Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets Syst. 1(1), 3–28 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  30. D. Dubois, H. Prade: The generalized modus ponens under sup-min composition – A theoretical study. In: Approximate Reasoning in Expert Systems, ed. by M.M. Gupta, A. Kandel, W. Bandler, J.B. Kiszka (North-Holland, Amsterdam 1985) pp. 217–232

    Google Scholar 

  31. D. Dubois, H. Prade: Possibility theory as a basis for preference propagation in automated reasoning, 1992 IEEE Int. Conf. Fuzzy Syst. (IEEE, New York 1992) pp. 821–832

    Google Scholar 

  32. M. Schröder, R. Petersen, F. Klawonn, R. Kruse: Two paradigms of automotive fuzzy logic applications. In: Applications of Fuzzy Logic: Towards High Machine Intelligence Quotient Systems, Environmental and Intelligent Manufacturing Systems Series, Vol. 9, ed. by M. Jamshidi, A. Titli, L. Zadeh, S. Boverie (Prentice Hall, Upper Saddle River 1997) pp. 153–174

    Google Scholar 

  33. L.I. Kuncheva: Fuzzy Classifier Design, Studies in Fuzziness and Soft Computing, Vol. 49 (Physica, Heidelberg, New York 2000)

    MATH  Google Scholar 

  34. D. Nauck, R. Kruse: A neuro-fuzzy method to learn fuzzy classification rules from data, Fuzzy Sets Syst. 89(3), 277–288 (1997)

    Article  MathSciNet  Google Scholar 

  35. R. Mikut, J. Jäkel, L. Gröll: Interpretability issues in data-based learning of fuzzy systems, Fuzzy Sets Syst. 150(2), 179–197 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  36. R. Mikut, O. Burmeister, L. Gröll, M. Reischl: Takagi-Sugeno-Kang fuzzy classifiers for a special class of time-varying systems, IEEE Trans. Fuzzy Syst. 16(4), 1038–1049 (2008)

    Article  Google Scholar 

  37. J.A. Dickerson, B. Kosko: Fuzzy function approximation with ellipsoidal rules, IEEE Trans. Syst. Man Cybern. B: Cybern. 26(4), 542–560 (1996)

    Article  Google Scholar 

  38. D. Nauck, R. Kruse: Neuro-fuzzy systems for function approximation, Fuzzy Sets Syst. 101(2), 261–271 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  39. L. Wang, J.M. Mendel: Generating fuzzy rules by learning from examples, IEEE Trans. Syst. Man Cybern. 22(6), 1414–1427 (1992)

    Article  MathSciNet  Google Scholar 

  40. J.C. Bezdek, J. Keller, R. Krisnapuram, N.R. Pal: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing, The Handbooks of Fuzzy Sets, Vol. 4 (Kluwer, Norwell 1999)

    MATH  Google Scholar 

  41. F. Höppner, F. Klawonn, R. Kruse, T. Runkler: Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition (Wiley, New York 1999)

    MATH  Google Scholar 

  42. F. Klawonn, R. Kruse: Automatic generation of fuzzy controllers by fuzzy clustering, 1995 IEEE Int. Conf. Syst. Man Cybern.: Intell. Syst. 21st Century, Vol. 3 (IEEE, Vancouver 1995) pp. 2040–2045

    Chapter  Google Scholar 

  43. F. Klawonn, R. Kruse: Constructing a fuzzy controller from data, Fuzzy Sets Syst. 85(2), 177–193 (1997)

    Article  MathSciNet  Google Scholar 

  44. Z.-W. Woo, H.-Y. Chung, J.-J. Lin: A PID type fuzzy controller with self-tuning scaling factors, Fuzzy Sets Syst. 115(2), 321–326 (2000)

    Article  MATH  Google Scholar 

  45. R. Kruse, P. Held, C. Moewes: On fuzzy data analysis, Stud. Fuzzin. Soft Comput. 298, 351–356 (2013)

    Google Scholar 

  46. O. Cordón, F. Gomide, F. Herrera, F. Hoffmann, L. Magdalena: Ten years of genetic fuzzy systems: Current framework and new trends, Fuzzy Sets Syst. 141(1), 5–31 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  47. C. Moewes, R. Kruse: Evolutionary fuzzy rules for ordinal binary classification with monotonicity constraints. In: Soft Computing: State of the Art Theory and Novel Applications, Studies in Fuzziness and Soft Computing, Vol. 291, ed. by R.R. Yager, A.M. Abbasov, M.Z. Reformat, S.N. Shahbazova (Springer, Berlin, Heidelberg 2013) pp. 105–112

    Chapter  Google Scholar 

  48. D. Nauck, F. Klawonn, R. Kruse: Foundations of Neuro-Fuzzy Systems (Wiley, New York 1997)

    MATH  Google Scholar 

  49. J.C. Hühn, E. Hüllermeier: FR3: A fuzzy rule learner for inducing reliable classifiers, IEEE Trans. Fuzzy Syst. 17(1), 138–149 (2009)

    Article  Google Scholar 

  50. C. Olaru, L. Wehenkel: A complete fuzzy decision tree technique, Fuzzy Sets Syst. 138(2), 221–254 (2003)

    Article  MathSciNet  Google Scholar 

  51. C. Moewes, R. Kruse: Unification of fuzzy SVMs and rule extraction methods through imprecise domain knowledge, Proc. Int. Conf. Inf. Process. Manag. Uncertain. Knowl.-Based Syst. (IPMU-08), ed. by J.L. Verdegay, L. Magdalena, M. Ojeda-Aciego (Torremolinos, Málaga 2008) pp. 1527–1534

    Google Scholar 

  52. C. Moewes, R. Kruse: On the usefulness of fuzzy SVMs and the extraction of fuzzy rules from SVMs, Proc. 7th Conf. Eur. Soc. Fuzzy Logic Technol. (EUSFLAT-2011) and LFA-2011, Vol. 17, ed. by S. Galichet, J. Montero, G. Mauris (Atlantis, Amsterdam, Paris 2011) pp. 943–948

    Google Scholar 

  53. J.C. Bezdek: Fuzzy Mathematics in Pattern Classification, Ph.D. Thesis (Cornell University, Itheca 1973)

    Google Scholar 

  54. J.C. Bezdek: Pattern Recognition with Fuzzy Objective Function Algorithms (Kluwer, Norwell 1981)

    Book  MATH  Google Scholar 

  55. M. Sugeno, T. Yasukawa: A fuzzy-logic-based approach to qualitative modeling, IEEE Trans. Fuzzy Syst. 1(1), 7–31 (1993)

    Article  Google Scholar 

  56. A. Keller, R. Kruse: Fuzzy rule generation for transfer passenger analysis, Proc. 1st Int. Conf. Fuzzy Syst. Knowl. Discovery (FSDK'02), ed. by L. Wang, S.K. Halgamuge, X. Yao (Orchid Country Club, Singapore 2002) pp. 667–671

    Google Scholar 

  57. R. Kruse, C. Döring, M. Lesot: Fundamentals of fuzzy clustering. In: Advances in Fuzzy Clustering and Its Applications, ed. by J.V. de Oliveira, W. Pedrycz (Wiley, Chichester 2007) pp. 3–30

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Christian Moewes .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Moewes, C., Mikut, R., Kruse, R. (2015). Fuzzy Control. In: Kacprzyk, J., Pedrycz, W. (eds) Springer Handbook of Computational Intelligence. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43505-2_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-43505-2_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-43504-5

  • Online ISBN: 978-3-662-43505-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics