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Realization of the Fractional Variable-Order Model with Symmetric Property

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Advances in Non-Integer Order Calculus and Its Applications (RRNR 2018)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 559))

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Abstract

The main contribution of the paper is to show a realization of fractional variable-order electrical model and its symmetric property—it is shown on numerical examples that the composition of two variable-order models designed with opposite value of orders gives an original input function. The fractional order impedances were implemented according to constant-phase element method.

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References

  1. Dzielinski, A., Sarwas, G., Sierociuk, D.: Comparison and validation of integer and fractional order ultracapacitor models. Adv. Differ. Equ. 2011, 11 (2011)

    Article  MathSciNet  Google Scholar 

  2. Macias, M., Sierociuk, D.: Modeling of electrical drive system with flexible shaft based on fractional calculus. In: 2013 14th International Carpathian Control Conference (ICCC), pp. 222–227, May 2013

    Google Scholar 

  3. Macias, M., Sierociuk, D.: An alternative recursive fractional variable-order derivative definition and its analog validation. In: Proceedings of International Conference on Fractional Differentiation and its Applications, Catania, Italy (2014)

    Google Scholar 

  4. Macias, M.: The particular types of fractional variable-order symmetric operators. In: Malinowska, A., Mozyrska, D., Lukasz, S. (eds.) Advances in Non-integer Order Calculus And Its Applications. Lecture Notes in Electrical Engineering. Springer (2019, submitted)

    Google Scholar 

  5. Malesza, W., Sierociuk, D., Macias, M.: Solution of fractional variable order differential equation, pp. 1537–1542. American Control Conference, Chicago (2015)

    Google Scholar 

  6. Neto, J.P., Coelho, R.M., Valério, D., Vinga, S., Sierociuk, D., Malesza, W., Macias, M., Dzieliński, A.: Variable order differential models of bone remodelling. IFAC-PapersOnLine 50(1), 8066–8071 (2017). 20th IFAC World Congress

    Article  Google Scholar 

  7. Ostalczyk, P., Brzezinski, D., Duch, P., Łaski, M., Sankowski, D.: The variable, fractional-order discrete-time PD controller in the IISv1.3 robot arm control. Central Eur. J. Phys. 11(6), 750–759 (2013)

    Google Scholar 

  8. Podlubny, I., Petráš, I., Vinagre, B.M., O’Leary, P., Dorčák, Ľ.: Analogue realizations of fractional-order controllers. Nonlinear Dyn. 29(1), 281–296 (2002). https://doi.org/10.1023/A:1016556604320

    Article  MathSciNet  MATH  Google Scholar 

  9. Sakrajda, P., Sierociuk, D.: Modeling heat transfer process in grid-holes structure changed in time using fractional variable order calculus. In: Babiarz, A., Czornik, A., Klamka, J., Niezabitowski, M. (eds.) Theory and Applications of Non-integer Order Systems, pp. 297–306. Springer, Cham (2017)

    Chapter  Google Scholar 

  10. Sierociuk, D., Dzielinski, A.: New method of fractional order integrator analog modeling for orders 0.5 and 0.25. In: Proceedings of the 16th International Conference on Methods and Models in Automation and Robotics (MMAR), Miedzyzdroje, Poland, pp. 137 –141 (2011)

    Google Scholar 

  11. Sierociuk, D., Macias, M.: Comparison of variable fractional order PID controller for different types of variable order derivatives. In: 2013 14th International Carpathian Control Conference (ICCC), pp. 334–339, May 2013

    Google Scholar 

  12. Sierociuk, D., Malesza, W.: Fractional variable order anti-windup control strategy. Bull. Pol. Acad. Sci. Tech. Sci. 66(4), 427–432 (2018)

    Google Scholar 

  13. Sierociuk, D., Malesza, W., Macias, M.: Equivalent switching strategy and analog validation of the fractional variable order derivative definition. In: Proceedings of European Control Conference 2013, ECC 2013, Zurich, Switzerland, pp. 3464–3469 (2013)

    Google Scholar 

  14. Sierociuk, D., Malesza, W., Macias, M.: On a new definition of fractional variable-order derivative. In: Proceedings of the 14th International Carpathian Control Conference (ICCC), Rytro, Poland, pp. 340–345 (2013)

    Google Scholar 

  15. Sierociuk, D., Twardy, M.: Duality of variable fractional order difference operators and its application to identification. Bull. Pol. Acad. Sci.: Tech. Sci. 62(4), 809–815 (2014)

    Google Scholar 

  16. Sierociuk, D., Malesza, W., Macias, M.: Derivation, interpretation, and analog modelling of fractional variable order derivative definition. Appl. Math. Model. 39(13), 3876–3888 (2015). https://doi.org/10.1016/j.apm.2014.12.009

    Article  MathSciNet  MATH  Google Scholar 

  17. Sierociuk, D., Malesza, W., Macias, M.: Numerical schemes for initialized constant and variable fractional-order derivatives: matrix approach and its analog verification. J. Vibr. Control (2015). https://doi.org/10.1177/1077546314565438

    Article  MATH  Google Scholar 

  18. Sierociuk, D., Malesza, W., Macias, M.: On the recursive fractional variable-order derivative: equivalent switching strategy, duality, and analog modeling. Circ. Syst. Sig. Process. 34(4), 1077–1113 (2015)

    Article  MathSciNet  Google Scholar 

  19. Sierociuk, D., Malesza, W., Macias, M.: On a new symmetric fractional variable order derivative. In: Domek, S., Dworak, P. (eds.) Theoretical Developments and Applications of Non-integer Order Systems. Lecture Notes in Electrical Engineering, vol. 357, pp. 29–39. Springer, Cham (2016)

    Chapter  Google Scholar 

  20. Valsa, J., Vlach, J.: RC models of a constant phase element. Int. J. Circ. Theory Appl. 41(1), 59–67. https://onlinelibrary.wiley.com/doi/abs/10.1002/cta.785

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Acknowledgment

This work was supported by the Polish National Science Center under Grant No. UMO-2014/15/B/ST7/00480.

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Authors and Affiliations

  1. Institute of Control and Industrial Electronics, Warsaw University of Technology, Koszykowa 75, 00-662, Warsaw, Poland

    Michal Macias, Dominik Sierociuk & Wiktor Malesza

Authors
  1. Michal Macias
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  2. Dominik Sierociuk
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  3. Wiktor Malesza
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Corresponding author

Correspondence to Michal Macias .

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Editors and Affiliations

  1. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Agnieszka B. Malinowska

  2. Faculty of Computer Science, Bialystok University of Technology, Białystok, Poland

    Dorota Mozyrska

  3. Faculty of Electrical Engineering, Bialystok University of Technology, Białystok, Poland

    Łukasz Sajewski

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Macias, M., Sierociuk, D., Malesza, W. (2020). Realization of the Fractional Variable-Order Model with Symmetric Property. In: Malinowska, A., Mozyrska, D., Sajewski, Ł. (eds) Advances in Non-Integer Order Calculus and Its Applications. RRNR 2018. Lecture Notes in Electrical Engineering, vol 559. Springer, Cham. https://doi.org/10.1007/978-3-030-17344-9_4

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