Skip to main content
SpringerLink
Log in

Discrete, Fractional Order, Cancellation Controller. Part I: Idea and Simulations

  • Conference paper
  • First Online:
Automation 2019 (AUTOMATION 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 920))

Included in the following conference series:

Abstract

In the paper the proposition of discrete, fractional order cancellation controller dedicated to control a high order inertial plant is presented. The controller uses the hybrid transfer function model of the plant. Results of simulations show that the proposed controller assures the better control performance than PID controller tuned with the use of known methods.

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 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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-Alaoui, M.A.: Novel digital integrator and differentiator. Electron. Lett. 29(4), 376–378 (1993)

    Article  Google Scholar 

  2. Astrom, K.J., Hagglund, T.: PID Controllers: Theory, Design and Tuning, ISA (1995)

    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, Hackensack (2010)

    Google Scholar 

  4. Charef, A., Sun, H.H., Tsao, Y.Y., Onaral, B.: Fractional system as represented by singularity function. IEEE Trans. Aut. Control 37(9), 1465–1470 (1992)

    Article  Google Scholar 

  5. Chen, Y.Q., Moore, K.L.: Discretization schemes for fractional-order differentiators and integrators. IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 49(3), 363–367 March 2002

    Google Scholar 

  6. Das, S.: Functional Fractional Calculus for System Identification and Controls. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  7. Das, S., Pan, I.: Fractional Order Signal Processing. Springer Briefs in Applied Sciences and Technology (2012). https://doi.org/10.1007/978-3-642-23117-9-2

  8. Dlugosz, M., Skruch, P.: The application of fractional-order models for thermal process modelling inside buildings. J. Build. Phys. I-13, 1–13 (2015)

    Google Scholar 

  9. Dzielinski, A., Sierociuk, D., Sarwas, G.: Some applications of fractional order calculus. Bull. Pol. Acad. Sci. Tech. Sci. 58(4), 583–592 (2010)

    MATH  Google Scholar 

  10. Ishihara, T., Hai-Jiao Guo, H.-J.: Design of optimal disturbance cancellation controllers via modified loop transfer recovery. Syst. Sci. Control Eng. 3(1), 332–339 (2015). https://doi.org/10.1080/21642583.2015.1023470

    Article  Google Scholar 

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

    Book  Google Scholar 

  12. Kaczorek, T., Rogowski, K.: Fractional Linear Systems and Electrical Circuits. Bialystok University of Technology, Bialystok (2014)

    MATH  Google Scholar 

  13. Merrikh-Bayat, F.: Rules for selecting the parameters of Oustaloup recursive approximation for the simulation of linear feedback systems containing PI\(^{\lambda }\)D\(^\upmu \) controller. Commun. Nonlinear Sci. Numer. Simulat. 17, 1852–1861 (2012)

    Article  MathSciNet  Google Scholar 

  14. Merrikh-Bayat, F.: Fractional-order unstable pole-zero cancellation in linear feedback systems. J. Process Control 23(6), 817–825 (2013)

    Article  Google Scholar 

  15. Merrikh-Bayat, F., Salimi, A.: Performance enhancement of non-minimum phase feedback systems by fractional-order cancellation of non-minimum phase zero on the Riemann surface: New theoretical and experimental results, Preprint submitted to Elsevier (2016)

    Google Scholar 

  16. Mitkowski, W., Skruch, P.: Fractional-order models of the supercapacitors in the form of RC ladder networks. Bull. Pol. Acad. Sci. Tech. Sci. 61(3), 581–587 (2013)

    MATH  Google Scholar 

  17. Obraczka, A., Mitkowski, W.: The comparison of parameter identification methods for fractional partial differential equation. Solid State Phenom. 210, 265–270 (2014)

    Article  Google Scholar 

  18. Oprzedkiewicz, K., Mitkowski, W., Gawin, E.: Application of fractional order transfer functions to modeling of high order systems. In: MMAR 2015: 20th International Conference on Methods and Models in Automation and Robotics: 24–27 August 2015, Midzyzdroje, Poland: program, abstracts, proceedings (CD). Szczecin: ZAPOL Sobczyk Sp.j., [2015] + CD. Dod (2015). ISBN: 978-1-4799-8701-6, 978-1-4799-8700-9. ISBN: 978-83-7518-756-4

    Google Scholar 

  19. Oprzedkiewicz, K., Mitkowski, W., Gawin, E.: Parameter identification for non integer order, state space models of heat plant. In: MMAR 2016: 21st International Conference on Methods and Models in Automation and Robotics: 29 August–01 September 2016, Miedzyzdroje, Poland, pp. 184–188 (2016). ISBN: 978-1-5090-1866-6, ISBN: 978-837518-791-5

    Google Scholar 

  20. Oprzedkiewicz, K., Kolacz, T.: A non integer order model of frequency speed control in AC motor. In: Szewczyk, R., Zielinski, C. (eds.) Advances in Intelligent Systems and Computing, vol. 440, pp. 287–298. Springer, Switzerland (2016)

    Chapter  Google Scholar 

  21. Ostalczyk, P.: Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains. Int. J. Appl. Math. Comput. Sci. 22(3), 533–538 (2012)

    Article  MathSciNet  Google Scholar 

  22. Oustaloup, A., Levron, F., Mathieu, B., Nanot, F.M.: Frequency-band complex nonin-teger differentiator: characterization and synthesis. IEEE Trans. Circ. Syst. I Fundam. Theory Appl. I 47(1), 25–39 (2000)

    Article  Google Scholar 

  23. Petras, I.: Fractional order feedback control of a DC motor. J. Electr. Eng. 60(3), 117–128 (2009)

    Google Scholar 

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

  25. Stanislawski, R., Latawiec, K.J., Lukaniszyn, M.: A comparative analysis of laguerre-based approximators to the Grünwald-Letnikov fractional-order difference. Math. Prob. Eng. 2015, 10 (2015). Article ID 512104https://doi.org/10.1155/2015/512104

    Article  Google Scholar 

  26. Tzafestas, S.G. (ed.): Methods and Applications of Intelligent Control. Springer, New York (1997)

    Google Scholar 

  27. Vinagre, B.M., Chen, Y.Q., Petras, I.: Two direct Tustin discretization methods for fractional-order differentiator-integrator. J. Franklin Inst. 340, 349–362 (2003)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This paper was sponsored partially by AGH UST grant no 11.11.120.815.

Author information

Authors and Affiliations

  1. Department of Automatics and Robotics, Faculty of Electrotechnics, Automatics, Informatics and Biomedical Engineering, AGH University of Science and Technology, al. A Mickiewicza 30, 30-059, Krakow, Poland

    Krzysztof Oprzędkiewicz, Łukasz Więckowski & Maciej Podsiadło

Authors
  1. Krzysztof Oprzędkiewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Łukasz Więckowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maciej Podsiadło
    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. Industrial Research Institute for Automation and Measurements PIAP Al, Warsaw, Poland

    Roman Szewczyk

  2. Industrial Research Institute for Automation and Measurements PIAP Al, Warsaw, Poland

    Cezary Zieliński

  3. Industrial Research Institute for Automation and Measurements PIAP Al, Warsaw, Poland

    Małgorzata Kaliczyńska

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Oprzędkiewicz, K., Więckowski, Ł., Podsiadło, M. (2020). Discrete, Fractional Order, Cancellation Controller. Part I: Idea and Simulations. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Automation 2019. AUTOMATION 2019. Advances in Intelligent Systems and Computing, vol 920. Springer, Cham. https://doi.org/10.1007/978-3-030-13273-6_3

Download citation

Publish with us

Policies and ethics

Search

Navigation