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Fractional-Order Linear System Transformation to the System Described by a Classical Equation

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Advanced, Contemporary Control

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

Abstract

In the paper, a method of “intigeration" of a linear time-invariant continuous or discrete-time system described by fractional-order differential/difference equations is proposed. The word intigeration means a procedure of connecting in series to the fractional plant a fractional element called further an “intigerator" such that the resulting two block system is described by the classical integer order differential/difference equation. The intigerator synthesis method is given. The stability conditions of the integer system are given. The proposed procedure enables to use classical methods of PID control tuning. It may also be used to tune the variable-, fractional – order PID controller.

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Acknowledgments

The work was supported by funds of the Polish National Science Center granted on the basis of decision DEC-2016/23/B/ST7/03686.

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Authors and Affiliations

  1. Lodz University of Technology, Lodz, Poland

    Piotr Ostalczyk

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  1. Piotr Ostalczyk
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Correspondence to Piotr Ostalczyk .

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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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Ostalczyk, P. (2020). Fractional-Order Linear System Transformation to the System Described by a Classical Equation. 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_75

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