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State Feedback Law for Discrete-Time Fractional Order Nonlinear Systems

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Fractional Dynamical Systems: Methods, Algorithms and Applications

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 402))

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Abstract

The analysis of output regulation for fractional nonlinear vibration control system of a smart plate designed by using the optimal LQR controller versus a closed-loop system design based on an integer order model is presented. It is shown that if the output of a linearized fractional system can be regulated to a finite number of steps around a constant output then the output of the nonlinear fractional system can also be regulated in the same number of steps around this output.

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Acknowledgements

The work of A. Koszewnik and E. Pawluszewicz is supported by the University Grant no WZ/WM-IIM/1/2019 of Faculty of Mechanical Engineering, Bialystok University of Technology. The work of P. Burzynski is supported by University Grant no WI/WM-IIM/7/2020 of Faculty of Mechanical Engineering, Bialystok University of Technology.

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Authors and Affiliations

  1. Department of Robotics and Mechatronics, Bialystok University of Technology, 45C, Bialystok, Wiejska, Poland

    Ewa Pawłuszewicz, Andrzej Koszewnik & Piotr Burzynski

Authors
  1. Ewa Pawłuszewicz
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  2. Andrzej Koszewnik
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  3. Piotr Burzynski
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Correspondence to Ewa Pawłuszewicz .

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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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Pawłuszewicz, E., Koszewnik, A., Burzynski, P. (2022). State Feedback Law for Discrete-Time Fractional Order Nonlinear Systems. In: Kulczycki, P., Korbicz, J., Kacprzyk, J. (eds) Fractional Dynamical Systems: Methods, Algorithms and Applications. Studies in Systems, Decision and Control, vol 402. Springer, Cham. https://doi.org/10.1007/978-3-030-89972-1_8

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