Skip to main content

Performance Enhancement of Fuzzy Logic Controller Using Robust Fixed Point Transformation

  • Conference paper
  • First Online:
Recent Global Research and Education: Technological Challenges

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 519))

Abstract

Despite its excellent performance as a controller for linear and non-linear systems, the fuzzy logic controller has certain limitations. For instance, large-scale complex fuzzy systems like multi-input, single-output, or multi-output systems are used in various applications with large number of rules. Furthermore, the results also depend on the selected membership functions, etc. This paper presents a novel framework that instead of reducing the number of rules for a fuzzy logic controller, combines it with a fixed point transformation based adaptive control. The adopted approach is based on the Mamdani-type fuzzy controller and enhanced by the Sigmoid Generated Fixed Point Transformation control strategy to cope with modeling inaccuracies and external disturbances that can arise. The general procedure is applied to a nonlinear Kapitza pendulum. Numerical simulations are validating the applicability of the proposed scheme and demonstrating the controller’s performance.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Institutional subscriptions

Similar content being viewed by others

References

  1. Aracil, J., Gordillo, F., Acosta, J.: Stabilization of oscillations in the inverted pendulum. In: Proceedings of the 15 IFAC World Congress, pp. 261 (2002)

    Google Scholar 

  2. Banach, S.: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales (About the operations in the abstract sets and their application to integral equations). Fund. Math. 3, 133–181 (1922)

    MATH  Google Scholar 

  3. Belman, R., Bentsman, J., Meerkov, S.M.: Vibrational control of a class of nonlinear systems: vibrational stabilization. IEEE Trans. Aut. Control 32(8), 710–716 (1986)

    Article  MATH  Google Scholar 

  4. Dineva, A., Tar, J., Varkonyi-Koczy, A., Piuri, V.: Generalization of a sigmoid generated fixed point transformation from siso to mimo systems. In: IEEE 19th International Conference on Intelligent Engineering Systems (INES2015), 3–5 Sept 2015, Bratislava, Slovakia. pp. 135–140 (2015)

    Google Scholar 

  5. Dineva, A., Tar, J., Varkonyi-Koczy, A., Piuri, V.: Adaptive control of underactuated mechanical systems using improved sigmoid generated fixed point transformation and scheduling strategy. In: IEEE 14th International Symposium on Applied Machine Intelligence and Informatics, 21–23 Jan 2016, Herlany, Slovakia. pp. 193–197 (2016)

    Google Scholar 

  6. Hosseini-Suny, K., Momeni, H., Janabi-Sharifi, F.: Model reference adaptive control design for a teleoperation system with output prediction. J. Intell. Robot Syst. pp. 1–21 (2010). doi:10.1007/s10846-010-9400-4

  7. Khalil, H.: Nonlinear Systems, 2nd ed. Upper Saddle River, Hall (1996)

    Google Scholar 

  8. Lyapunov, A.: A general task about the stability of motion (in Russian). Ph.D. Thesis, University of Kazan, Tatarstan (Russia) (1892)

    Google Scholar 

  9. Margaliot, M., Langholz, G.: New Approaches to Fuzz Modeling and Control: Design and Analysis. World Scientific Publishing, Singapore (2000)

    Book  MATH  Google Scholar 

  10. Miroshnik, I., Odinets, N.: Stabilization of pendulum oscillations around upper position. In: 6th IFAC Syposium on Nonlinear Control Systems (NOLCOS 2004), vol. 3 (2004)

    Google Scholar 

  11. Nguyen, C., Antrazi, S., Zhou Jr., Z.L., Campbell Jr., C.: Adaptive control of a stewart platform-based manipulator. J. Robot. Syst. 10(5), 657–687 (1993)

    Article  Google Scholar 

  12. Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice Hall International Inc., Englewood Cliffs (1991)

    MATH  Google Scholar 

  13. Stephenson, A.: XX. On induced stability. Philos. Mag. Ser. 6 15(86), 233–236 (1908)

    Google Scholar 

  14. Tar, J.: Replacement of Lyapunov function by locally convergent robust fixed point transformations in model based control, a brief summary. J. Adv. Comput. Intell. Intell. Inf. 14(2), 224–236 (2010)

    Google Scholar 

  15. Tar, J.: Towards replacing Lyapunov’s ‘direct’ method in adaptive control of nonlinear systems (invited plenary lecture). In: Proceedings of the Mathematical Methods in Engineering International Symposium (MME), Coimbra, Portugal (2010)

    Google Scholar 

  16. Tar, J.: Adaptive control of smooth nonlinear systems based on lucid geometric interpretation (DSc dissertation). Hungarian Academy of Sciences, Budapest (2012)

    Google Scholar 

  17. Yabuno, H., Goto, K., Aoshima, N.: Swing-up and stabilization of an underactuated manipulator without state feedback of free joint. IEEE Trans. Robot. Autom. 20, 259–365 (2004)

    Article  Google Scholar 

  18. Yabuno, H., Tsumoto, K.: Experimental investigation of a buckled beam under high-frequency excitation. Arch. Appl. Mech. 77(5) (2007)

    Google Scholar 

Download references

Acknowledgments

This work has been sponsored by the Hungarian National Scientific Fund (OTKA 105846). This publication is also the partial result of the Research and Development Operational Programme for the project “Modernisation and Improvement of Technical Infrastructure for Research and Development of J. Selye University in the Fields of Nanotechnology and Intelligent Space”, ITMS 26210120042, co-funded by the European Regional Development Fund.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Adrienn Dineva .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Dineva, A., Várkonyi-Kóczy, A., Tar, J.K., Piuri, V. (2017). Performance Enhancement of Fuzzy Logic Controller Using Robust Fixed Point Transformation. In: Jabłoński, R., Szewczyk, R. (eds) Recent Global Research and Education: Technological Challenges. Advances in Intelligent Systems and Computing, vol 519. Springer, Cham. https://doi.org/10.1007/978-3-319-46490-9_55

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-46490-9_55

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46489-3

  • Online ISBN: 978-3-319-46490-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics