Robust stability analysis of interval fractional-order plants by fractional-order controllers: an approach to reduce additional calculation

Ghorbani, Majid

doi:10.1080/03081079.2020.1832485

Cited by 16 publications

(6 citation statements)

References 42 publications

(65 reference statements)

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“…Again, the method presented in [12] is used to check the stability of ∆(s) in (22). Figure 4 shows the values of ψ(jω) in (23).…”

Section: Illustrative Examplesmentioning

confidence: 99%

“…The works of [19,20] have proven that the value set of fractional-order systems of incommensurate and commensurate orders possessing uncertain coefficients is a parpolygon in the complex plane. Inspired by the results presented in [17,19,20], some value set-based approaches have been presented to inspect the robust stability of fractional-order plants by linear fractional-order controllers in [21,22].…”

Section: Introductionmentioning

confidence: 99%

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

Asadi

Farnam

Nazifi³

et al. 2022

Mathematics

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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.

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“…Again, the method presented in [12] is used to check the stability of ∆(s) in (22). Figure 4 shows the values of ψ(jω) in (23).…”

Section: Illustrative Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Asadi

Farnam

Nazifi³

et al. 2022

Mathematics

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show abstract

“…Then, the robust stability analysis of such systems has been presented by an auxiliary function. Later, the results provided in [13] have been developed to analyze the robust stability of fractional-order controllers for systems having fractional-order characteristic functions in [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

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

Ghorbani,

Tepljakov,

Petlenkov

2023

IET Control Theory & Appl

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This paper concentrates on presenting a reliable procedure to compute the stabilizing region of fractional‐order proportional integral derivative (FOPID) controllers for interval fractional‐order plants having an interval time delay. An interval fractional‐order plant is defined as a fractional‐order transfer function whose denominator and numerator coefficients are all uncertain and lie in specified intervals. Also, an interval time delay points to a delay term whose value varies in a specific interval. The D‐decomposition technique and the value set concept are employed to determine the stabilizing region of FOPID controllers. In this study, first, a theorem is presented to compute the boundary of the value sets of systems having interval time day. Then, a lemma is provided for robust stability analysis of the given closed‐loop control system. For a convenient use of the paper results, an algorithm is proposed to solve the problem of robustly stabilizing interval fractional‐order plants with an interval time delay using FOPID controllers. Finally, four examples are provided to illustrate the proposed procedure.

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“…The robust stability analysis of such interval systems is made easier by this characteristic. Motivated by the findings shown in Moornani and Haeri (2010a), Tan et al (2009) and Moornani and Haeri (2010b), some value set-based approaches for testing the robust stability of interval FO plants by FO controllers have been addressed in Ghorbani and Tavakoli-Kakhki (2020) and Ghorbani (2021).…”

Section: Introductionmentioning

confidence: 99%

On robust stability of second order plus interval time delay plants using Fractional-Order Proportional Integral Derivative controllers

Malik

Asadi

Rezaei

2023

Journal of Vibration and Control

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The robust stability assessment of the second order plus interval time delay (SOPITD) plant controlled by Fractional-Order Proportional Integral Derivative (FOPID) controllers is the focus of this research. A simple graphical procedure for analyzing the robust stability of the interval system is presented based on the zero exclusion condition and the value set concept. The incorporation of an auxiliary function, derived through a judicious application of fundamental geometric principles intrinsic to convex polygons, serves to significantly alleviate the complexity and facilitate the application of the robust stability analysis approach, thereby affording a more streamlined and efficient means of designing robust control systems. Moreover, the computational burden for the robust stability analysis is also reduced by novel bounds. Moreover, a novel robust performance checking function is provided to improve the performance system. Three illustrative examples are then given to support the findings and show their applicability.

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Robust stability analysis of interval fractional-order plants by fractional-order controllers: an approach to reduce additional calculation

Cited by 16 publications

References 42 publications

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

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

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

On robust stability of second order plus interval time delay plants using Fractional-Order Proportional Integral Derivative controllers

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