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Accuracy Estimation of the Fractional, Discrete-Continuous Model of the One-Dimensional Heat Transfer Process

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Advanced, Contemporary Control

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1196))

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Abstract

In the paper a new, state space, finite dimensional, non integer order model of a one-dimensional heat transfer process is considered. The proposed model uses a well known finite difference method and fractional Caputo operator to express the time derivative. The second order backward difference describes the derivative along the length. The analytical formula of the step response is given. Accuracy and convergence of the proposed model are numerically analyzed and compared to previously proposed state space model using semigroup approach. Results of simulations point that the good accuracy of the proposed model can be achieved for its relatively low order.

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Acknowledgment

This paper was sponsored by AGH project no 16.16.120.773.

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Authors and Affiliations

  1. Department of Automatic Control and Robotics, AGH University, al. A. Mickiewicza 30, 30-059, Krakow, Poland

    Krzysztof Oprzędkiewicz & Klaudia Dziedzic

Authors
  1. Krzysztof Oprzędkiewicz
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  2. Klaudia Dziedzic
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Corresponding author

Correspondence to Krzysztof Oprzędkiewicz .

Editor information

Editors and Affiliations

  1. Institute of Automatic Control, Lodz University of Technology, Lodz, Poland

    Andrzej Bartoszewicz

  2. Institute of Automatic Control, Lodz University of Technology, Lodz, Poland

    Jacek Kabziński

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

    Janusz Kacprzyk

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Oprzędkiewicz, K., Dziedzic, K. (2020). Accuracy Estimation of the Fractional, Discrete-Continuous Model of the One-Dimensional Heat Transfer Process. In: Bartoszewicz, A., Kabziński, J., Kacprzyk, J. (eds) Advanced, Contemporary Control. Advances in Intelligent Systems and Computing, vol 1196. Springer, Cham. https://doi.org/10.1007/978-3-030-50936-1_96

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