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Robust Stability Analysis of Unstable Second Order Plus Time-Delay (SOPTD) Plant by Fractional-Order Proportional Integral (FOPI) Controllers

Author

Listed:
  • Marzieh Asadi

    (Faculty of Electerical Engineering, K.N. Toosi University of Technology, Tehran 19697, Iran)

  • Arash Farnam

    (Department of Electrical Energy, Metals, Mechanical Constructions and Systems, Ghent University, 9000 Ghent, Belgium
    Core Lab EEDT Decision and Control, Flanders Make, 3920 Lommel, Belgium)

  • Hamed Nazifi

    (Renewable Power Generation Research Group, Khaje Nasir University of Technology Branch, ACECR, Tehran 19697, Iran)

  • Sam Roozbehani

    (Renewable Power Generation Research Group, Khaje Nasir University of Technology Branch, ACECR, Tehran 19697, Iran)

  • Guillaume Crevecoeur

    (Department of Electrical Energy, Metals, Mechanical Constructions and Systems, Ghent University, 9000 Ghent, Belgium
    Core Lab EEDT Decision and Control, Flanders Make, 3920 Lommel, Belgium)

Abstract

This study investigates the robust stability analysis of an unstable second order plus time-delay (SOPTD) plant by using Fractional-Order Proportional Integral (FOPI) controllers. We assume that there are simultaneous uncertainties in gain, time-constants, and time-delay of the plant. At first, a graphical method is provided for a robust stability analysis of the closed-loop system. Then, a robust stability checking function is introduced to facilitate the robust stability analysis. Additionally, new bounds are presented to reduce the computational burden for the robust stability analysis. Finally, two examples are provided to show the correctness of the proposed method.

Suggested Citation

  • Marzieh Asadi & Arash Farnam & Hamed Nazifi & Sam Roozbehani & Guillaume Crevecoeur, 2022. "Robust Stability Analysis of Unstable Second Order Plus Time-Delay (SOPTD) Plant by Fractional-Order Proportional Integral (FOPI) Controllers," Mathematics, MDPI, vol. 10(4), pages 1-10, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:567-:d:747675
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    References listed on IDEAS

    as
    1. Margarita Rivero & Sergei V. Rogosin & José A. Tenreiro Machado & Juan J. Trujillo, 2013. "Stability of Fractional Order Systems," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-14, May.
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