Skip to main content
SpringerLink
Log in

A Tuning of a Fractional Order PID Controller with the Use of Particle Swarm Optimization Method

  • Conference paper
  • First Online:
Artificial Intelligence and Soft Computing (ICAISC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10245))

Included in the following conference series:

Abstract

The paper is devoted to present a new tuning method for Fractional Order PID controller dedicated to temperature control. The proposed method uses Particle Swarm Optimization algorithm. The control plant is described by transfer function with delay. Results of experiments show that the proposed approach assures the good control performance in the sense of known integral cost functions.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

References

  1. Al Aloui, M.A.: Dicretization methods of fractional parallel PID controllers. In: Proceedings of 6th IEEE International Conference on Electronics, Circuits and Systems, ICECS 2009, pp. 327–330 (2009)

    Google Scholar 

  2. Arun, M.K., Biju, U., Rajagopal, N.N., Bagyaveereswaran, V.: Optimal tuning of fractional-order PID controller. In: Suresh, L.P., Panigrahi, B.K. (eds.) Proceedings of the International Conference on Soft Computing Systems. AISC, vol. 397, pp. 401–408. Springer, New Delhi (2016). doi:10.1007/978-81-322-2671-0_38

    Chapter  Google Scholar 

  3. Caponetto, R., Dongola, G., Fortuna, L., Petras, I.: Fractional Order Systems: Modeling and Control Applications. World Scientific Series on Nonlinear Science, Series A, vol. 72. World Scientific Publishing, Singapore (2010)

    Google Scholar 

  4. Dorcak, L., Petras, I., Terpak, J., Zbrojovan, M.: Comparison of the methods for discrete approximation of the fractional-order operator. In: Proceedings of the ICCC 2003 Conference, High Tatras, Slovak Republic, pp. 851–856, 26–29 May 2003. arXiv:math/0306017v1

  5. Dziedzic, K.: The tuning of fractional-order PID controller to high-order, uncertain parameter plant Master thesis prepared at AGH University in 2016 under supervision of K. Oprzędkiewicz (2016)

    Google Scholar 

  6. Kaczorek, T.: Selected Problems in Fractional Systems Theory. Springer, Heidelberg (2011)

    Book  MATH  Google Scholar 

  7. Kennedy, J., Eberhardt, R.: Particle Swarm Optimization, pp. 1942–1948. IEEE (1995). 0-7803-2768-3/95/$4.00 0

    Google Scholar 

  8. Kennedy, J.: Particle swarm optimization. In: Sammut, C., Webb, G.I. (eds.) Encyclopedia of Machine Learning, pp. 760–766. Springer, Heidelberg (2010)

    Google Scholar 

  9. Merikh-Bayat, F.: Rules for selecting the parameters of oustaloup recursive approximation for the simulation of linear feedback systems containing PIλDµ controller. Commun. Nonlinear Sci. Numer. Simulat. 17, 1852–1861 (2012)

    Article  MathSciNet  Google Scholar 

  10. Merikh-Bayat, F., Mirebahrimi, M., Khalili, M.R.: Discrete-time fractional-order PID controller: Definition, tuning, digital realization and some applications. Int. J. Control Autom. Syst. 13(1), 81–90 (2015)

    Article  Google Scholar 

  11. Oprzędkiewicz, K.: A Strejc model-based, semi- fractional (SSF) transfer function model. Automatyka/Automatics 16(2), 145–154 (2012). AGH UST 2012, http://journals.bg.agh.edu.pl/AUTOMAT/2012.16.2/automat.2012.16.2.145.pdf

    Article  Google Scholar 

  12. Oprzędkiewicz, K., Mitkowski, W., Gawin, E.: An estimation of accuracy of oustaloup approximation. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds.) Challenges in Automation, Robotics and Measurement Techniques. AISC, vol. 440, pp. 299–307. Springer, Cham (2016). doi:10.1007/978-3-319-29357-8_27

    Chapter  Google Scholar 

  13. Ostalczyk, P.: Discrete Fractional Calculus: Applications in Control and Image Processing. Series in Computer Vision, vol. 4. World Scientific Publishing, Singapore (2016)

    MATH  Google Scholar 

  14. Oustaloup, A., Levron, F., Mathieu, B., Nanot, F.M.: Frequency-band complex noninteger differentiator: Characterization and synthesis. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. I 47(1), 25–39 (2000)

    Article  Google Scholar 

  15. Padula, F., Visioli, A.: Tuning rules for optimal PID and fractional-order PID controllers. J. Process Control 21(1), 69–81 (2011)

    Article  MATH  Google Scholar 

  16. Petras, I: http://people.tuke.sk/igor.podlubny/USU/matlab/petras/dfod1.m

  17. Petras, I: http://people.tuke.sk/igor.podlubny/USU/matlab/petras/dfod2.m

  18. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

  19. Vinagre, B.M., Podlubny, I., Hernandez, A., Feliu, V.: Some approximations of fractional order operators used in control theory and applications. In: Fractional Calculus and Applied Analysis, vol. 3(3), pp. 231–248 (2000)

    Google Scholar 

Download references

Acknowledgements

This paper was supported by the AGH (Poland) – project no 11.11.120.815.

Author information

Authors and Affiliations

  1. Department of Automatics and Biomedical Engineering, Faculty of Electrotechnics Automatics, Informatics and Biomedical Engineering, AGH University of Science and Technology, Kraków, Poland

    Krzysztof Oprzędkiewicz & Klaudia Dziedzic

Authors
  1. Krzysztof Oprzędkiewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Klaudia Dziedzic
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Krzysztof Oprzędkiewicz .

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Częstochowa, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Częstochowa, Poland

    Marcin Korytkowski

  3. Częstochowa University of Technology, Częstochowa, Poland

    Rafał Scherer

  4. AGH University of Science and Technology, Kraków, Poland

    Ryszard Tadeusiewicz

  5. University of California, Berkeley, California, USA

    Lotfi A. Zadeh

  6. University of Louisville, Louisville, Kentucky, USA

    Jacek M. Zurada

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Oprzędkiewicz, K., Dziedzic, K. (2017). A Tuning of a Fractional Order PID Controller with the Use of Particle Swarm Optimization Method. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2017. Lecture Notes in Computer Science(), vol 10245. Springer, Cham. https://doi.org/10.1007/978-3-319-59063-9_35

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-59063-9_35

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59062-2

  • Online ISBN: 978-3-319-59063-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation