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Fractional Order Models of Dynamic Systems

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Automatic Control, Robotics, and Information Processing

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 296))

Abstract

This chapter presents the use of models of non-integer (fractional) order for modeling of dynamic systems. Ultracapacitors have been presented as systems with these types of dynamics. Their internal structure and energy storage method were thoroughly analyzed. The diffusion process used in their operation has in their mathematical description derivatives of non integer order, which confirms the legitimacy of using models of non integer order to describe their dynamics. As part of this chapter, various models of ultracapacitors used to model their dynamics in time and frequency domain are presented. The presented transmittance models have been thoroughly discussed and confirmed by their comparison with properties observed in laboratory experiments with the ultracapacitors. The last chapter presents a fractional order neural network, which, using the differences of the non integer order, despite its simple structure, allows for accurate mapping of the process of charging and discharging ultracapacitors.

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Authors and Affiliations

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

    Andrzej DzieliƄski, Grzegorz Sarwas & Dominik Sierociuk

Authors
  1. Andrzej DzieliƄski
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  2. Grzegorz Sarwas
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  3. Dominik Sierociuk
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Correspondence to Andrzej DzieliƄski .

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Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Piotr Kulczycki

  2. Institute of Control and Computation Engineering, University of Zielona GĂłra, Zielona GĂłra, Poland

    JĂłzef Korbicz

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

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DzieliƄski, A., Sarwas, G., Sierociuk, D. (2021). Fractional Order Models of Dynamic Systems. In: Kulczycki, P., Korbicz, J., Kacprzyk, J. (eds) Automatic Control, Robotics, and Information Processing. Studies in Systems, Decision and Control, vol 296. Springer, Cham. https://doi.org/10.1007/978-3-030-48587-0_5

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