IEEE/CAA Journal of Automatica Sinica
Citation:  M. Ghorbani, M. TavakoliKakhki, A. Tepljakov, and E. Petlenkov, “Robust stability analysis of smith predictor based interval fractionalorder 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 
The robust stability study of the classic Smith predictorbased control system for uncertain fractionalorder 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 realworld plants. Also, in the considered Smith predictor control structure it is supposed that the controller is a fractionalorder 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 fractionalorder control system in the presence of the simultaneous uncertainties in gain, timeconstants, 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 predictorbased fractionalorder control system—the proposed method explicitly determines whether or not the FOPID controller can robustly stabilize the Smith predictorbased fractionalorder 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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