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Volume 10 Issue 3
Mar.  2023

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2023  >  10(3): 762-780
M. Ghorbani, M. Tavakoli-Kakhki, A. Tepljakov, and E. Petlenkov, “Robust stability analysis of smith predictor based interval fractional-order control systems: A case study in level control process,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 3, pp. 762–780, Mar. 2023. doi: 10.1109/JAS.2022.105986
Citation: M. Ghorbani, M. Tavakoli-Kakhki, A. Tepljakov, and E. Petlenkov, “Robust stability analysis of smith predictor based interval fractional-order control systems: A case study in level control process,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 3, pp. 762–780, Mar. 2023. doi: 10.1109/JAS.2022.105986
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Robust Stability Analysis of Smith Predictor Based Interval Fractional-Order Control Systems: A Case Study in Level Control Process

doi: 10.1109/JAS.2022.105986
  • 1.

    Department of Computer Systems, Tallinn University of Technology, Tallinn 12618, Estonia

  • 2.

    Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran 1631714191, Iran

Funds:  This work was supported by the Estonian Research Council (PRG658)
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    Abstract
  • The robust stability study of the classic Smith predictor-based control system for uncertain fractional-order plants with interval time delays and interval coefficients is the emphasis of this work. Interval uncertainties are a type of parametric uncertainties that cannot be avoided when modeling real-world plants. Also, in the considered Smith predictor control structure it is supposed that the controller is a fractional-order proportional integral derivative (FOPID) controller. To the best of the authors’ knowledge, no method has been developed until now to analyze the robust stability of a Smith predictor based fractional-order control system in the presence of the simultaneous uncertainties in gain, time-constants, and time delay. The three primary contributions of this study are as follows: i) a set of necessary and sufficient conditions is constructed using a graphical method to examine the robust stability of a Smith predictor-based fractional-order control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictor-based fractional-order control system; ii) an auxiliary function as a robust stability testing function is presented to reduce the computational complexity of the robust stability analysis; and iii) two auxiliary functions are proposed to achieve the control requirements on the disturbance rejection and the noise reduction. Finally, four numerical examples and an experimental verification are presented in this study to demonstrate the efficacy and significance of the suggested technique.

     

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    Highlights

    • Presenting a finite frequency range for verifying the robust stability of a Smith predictor-based control system
    • Obtaining necessary and sufficient conditions for robust stability analysis of a designed Smith predictor-based control system
    • Introducing a robust stability testing function to investigate the robust stability of Smith predictor based fractional-order control system

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