Robust FOPID stabilization of retarded type fractional order plants with interval uncertainties and interval time delay

Ghorbani, Majid; Tavakoli-Kakhki, Mahsan; Estarami, Ali Akbar

doi:10.1016/j.jfranklin.2019.08.035

Cited by 20 publications

(13 citation statements)

References 29 publications

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“…In general, fractional‐order systems' stability and fractional‐order PID controllers's design have been already studied for different applications, for some examples, see refs. [22, 29–35]. More precisely for the case of ISs, in the previous work [36], we have introduced the design of fractional PD μ controllers for ISs without analysing the effects of changing the controller's parameter μ to find the stability in the

(k_{p}, k_{η}, μ)

parameter‐space.…”

Section: Introductionmentioning

confidence: 99%

Fractional‐order controllers for irrational systems

Guel-Cortez

Méndez-Barrios

Kim

et al. 2021

IET Control Theory & Appl

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In this contribution, fractional-order controllers of the type PD and PI are applied to a class of irrational transfer function models that appear in large-scale systems, such as networks of mechanical/electrical elements and distributed parameter systems. More precisely, by considering the fractional-order controller k p + k s in the Laplace domain with −1 ≤ ≤ 1, a stability analysis in the parameter-space (k p , k ,) is presented. Furthermore, as a way to measure the controller robustness, the controller's fragility analysis using the parameter-space (k p , k ,) is derived. Finally, several applications that demonstrate the utility of our results are included.

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(k_{p}, k_{η}, μ)

parameter‐space.…”

Section: Introductionmentioning

confidence: 99%

Fractional‐order controllers for irrational systems

Guel-Cortez

Méndez-Barrios

Kim

et al. 2021

IET Control Theory & Appl

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“…The works 26–29 have made effort to analyze the robust stability of fractional order systems. Based on the zero exclusion principle, the robust stability of LTI delayed fractional order system in the presence of real parametric uncertainties has been studied in the works of Moornani and Haeri 30 and Ghorbani et al 31 Analogously, Zheng and Li 32 presented necessary and sufficient criteria to analyze the robust stability of an interval fractional order plant in the presence of uncertain orders and uncertain coefficients. Furthermore, the robust stability of interval fractional order systems has been investigated in the works of Moornani and Haeri 33 and Tan et al 34 The systems studied in these literature are a special family of the considered fractional order system in Moornani and Haeri 30 .…”

Section: Introductionmentioning

confidence: 99%

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

Ghorbani

Tavakoli-Kakhki

2021

Math Methods in App Sciences

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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.

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“…3,4 In the literature, several principles of stability have been introduced, including the bounded-input bound-output (BIBO) stability which is discussed in this article. For the linear time invariant (LTI) fractional-order (FO) systems, the BIBO stability has been investigated in literature, [5][6][7][8][9][10] whereas the problems of the modern control theory usually contain uncertain parameters. 11,12 In fact, control systems need to be designed to ensure certain essential properties (e.g.…”

Section: Introductionmentioning

confidence: 99%

Robust fractional-order fixed-structure controller design for uncertain non-commensurate fractional plants using fractional Kharitonov theorem

Ebrahimi

Asgari

2021

Proceedings of the Institution of Mechanical Engineers, Part I:

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This article deals with the problem of robust fractional-order fixed-structure controller design for commensurate and non-commensurate fractional-order interval systems using fractional Kharitonov theorem. The contribution of this study is to develop a simple control methodology to stabilize the fractional-order Kharitonov-defined vortex polynomials. Using the idea of robust stability testing function and extending it to the systems under study, the straightforward graphical and systematic procedures are proposed to investigate the robust stability of the system by searching for a non-conservative fractional-order Kharitonov region in the controller parameters plane. This region can establish all the fractional-order controllers that make the uncertain fractional-order systems stable. The relation between the fractional-order Kharitonov region and the parameters of the stabilizing controller is also found. Finally, comparison results with three relevant works are given to illustrate the feasibility of the proposed method.

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Robust FOPID stabilization of retarded type fractional order plants with interval uncertainties and interval time delay

Cited by 20 publications

References 29 publications

Fractional‐order controllers for irrational systems

Fractional‐order controllers for irrational systems

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

Robust fractional-order fixed-structure controller design for uncertain non-commensurate fractional plants using fractional Kharitonov theorem

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