Robust stability analysis of a general class of interval delayed fractional order plants by a general form of fractional order controllers

Abstract

In this paper, the robust stability of interval fractional order plants with one time delay controlled by fractional order controllers is investigated in a general form. For robust stability analysis of the closed loop system by the zero exclusion principle, the distance between the origin and the value set of the characteristic function needs to be checked. It is known that the outer vertices of this value set may change at some switching frequencies and the repetitive calculation of these vertices at switching frequencies leads to additional calculations. In this study initially, new necessary and sufficient conditions are proposed to check the robust stability of a delayed fractional order closed loop system. Then, a novel robust stability testing function is presented based on some vertices, which are fixed for all positive frequencies. Therefore, no additional calculation is needed to obtain the outer vertices of the characteristic function value set for any pair of the switching frequencies. Also, a finite frequency range is presented to reduce the computational cost noticeably. Eventually, three numerical examples are given to verify the efficiency of the results of this paper.

Stabilizing region of fractional‐order proportional integral derivative controllers for interval delayed fractional‐order plants

“…Step 2: Obtain RRB, IRB and CRB and the stability regions by sweeping over 𝜂 ∈ [0, 1] for Δ D r 1 (s) in (21) as stated in Remark 3.…”

“…The study of fractional-order systems with delays has been the subject of great interest during the last decades. Necessary and sufficient conditions for robust stability analysis of interval fractional-order plants with one time-delay by using general form of fractional-order controllers have been presented in [20,21].…”

Robust stabilization of interval fractional‐order plants with an interval time delay by fractional‐order proportional integral derivative controllers

“…Robust stability analysis is fundamental to any control system. Accordingly, various design methods for robust stability analysis of fractional-order systems have been presented in [10,11] by benefiting from the value set concept. The value set method is mainly based on the zero exclusion principle.…”

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

“…In [23,24], Fractional-Order Proportional Integral Derivative (FOPID) controllers were designed to improve the robustness property of first order in addition to dead time systems. Then, in [25,26], some auxiliary functions have been presented for robust stability analysis of interval fractional order systems having time-delay. Moreover, in [27], a graphical tuning method has been proposed to determine the stabilizing regions of FOPI controllers for fractional systems with time-delays by benefiting from the D-decomposition technique.…”