Robustness analysis and design of fractional order Iλ Dμ controllers using the small gain theorem

Azarmi, Roohallah; Tavakoli-Kakhki, Mahsan; Fatehi, Alireza; Sedigh, Ali Khaki

doi:10.1080/00207179.2018.1476982

Cited by 8 publications

(3 citation statements)

References 47 publications

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“…In Zheng et al (2016), a graphical tuning method of FOPID controllers for an interval fractional order plant has been proposed. A simple method to tune the parameters of a fractional integral-fractional derivative controller to compensate stable first order transfer functions without time delay has been presented in Azarmi et al (2018).…”

Section: Introductionmentioning

confidence: 99%

Robust stabilizability of fractional order proportional integral controllers for fractional order plants with uncertain parameters: A new value set based approach

Ghorbani

Tavakoli-Kakhki

2019

Journal of Vibration and Control

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In this paper, a new value set based approach is presented to study the robust stability of a fractional order plant with parametric uncertainty of the interval type by using a fractional order proportional integral controller. The concept of interval uncertainty means that the parameters of the system transfer functions are uncertain parameters that each adopts a value in a real interval. Based on the zero exclusion principle, it is necessary to check whether the value set of the characteristic polynomial for the infinite frequency range [Formula: see text] includes the origin or not. To this end, in this paper, an auxiliary function is defined. The sign of this auxiliary function within a finite frequency range verifies whether the origin is included in the value set of the characteristic polynomial or not. The upper bound and the lower bound of this finite frequency range are obtained using the triangle inequality. Finally, the results of the numerical examples are provided, which confirm the effectiveness of the paper results.

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Section: Introductionmentioning

confidence: 99%

Robust stabilizability of fractional order proportional integral controllers for fractional order plants with uncertain parameters: A new value set based approach

Ghorbani

Tavakoli-Kakhki

2019

Journal of Vibration and Control

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“…Figure 9 represents the block diagram of ROCIP with an SCA-based FOPID controller. To obtain the desired specifications, (21) and (22) are solved using SCA. The optimal parameters (K a , K b , K c , α and β) of PI α D β controller obtained are The FOPID controller for the specified design criteria is given as…”

Section: Design Of Fopid Controllermentioning

confidence: 99%

“…Fractional integral-fractional derivative controller using small gain theorem and sensitivity function analysis to achieve desired PM and (ω gc ) is discussed by Azarmi et al [22]. Liu and Zhang [23] designed an FOPID controller based on the Bode optimal reference model and flat phase property that ensures desired transient performance characteristics.…”

Section: Introductionmentioning

confidence: 99%

Sine Cosine Algorithm Assisted FOPID Controller Design for Interval Systems Using Reduced-Order Modeling Ensuring Stability

Bokam

Patnana

Varshney³

et al. 2020

Algorithms

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The focus of present research endeavor was to design a robust fractional-order proportional-integral-derivative (FOPID) controller with specified phase margin (PM) and gain cross over frequency (ωgc) through the reduced-order model for continuous interval systems. Currently, this investigation is two-fold: In the first part, a modified Routh approximation technique along with the matching Markov parameters (MPs) and time moments (TMs) are utilized to derive a stable reduced-order continuous interval plant (ROCIP) for a stable high-order continuous interval plant (HOCIP). Whereas in the second part, the FOPID controller is designed for ROCIP by considering PM and ωgc as the performance criteria. The FOPID controller parameters are tuned based on the frequency domain specifications using an advanced sine-cosine algorithm (SCA). SCA algorithm is used due to being simple in implementation and effective in performance. The proposed SCA-based FOPID controller is found to be robust and efficient. Thus, the designed FOPID controller is applied to HOCIP. The proposed controller design technique is elaborated by considering a single-input-single-output (SISO) test case. Validity and efficacy of the proposed technique is established based on the simulation results obtained. In addition, the designed FOPID controller retains the desired PM and ωgc when implemented on HOCIP. Further, the results proved the eminence of the proposed technique by showing that the designed controller is working effectively for ROCIP and HOCIP.

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Coefficients and Delay Estimation of the General Form of Fractional Order Systems Using Non-Ideal Step Inputs

2020

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Robustness analysis and design of fractional order I^λ D^μ controllers using the small gain theorem

Cited by 8 publications

References 47 publications

Robust stabilizability of fractional order proportional integral controllers for fractional order plants with uncertain parameters: A new value set based approach

Robust stabilizability of fractional order proportional integral controllers for fractional order plants with uncertain parameters: A new value set based approach

Sine Cosine Algorithm Assisted FOPID Controller Design for Interval Systems Using Reduced-Order Modeling Ensuring Stability

Coefficients and Delay Estimation of the General Form of Fractional Order Systems Using Non-Ideal Step Inputs

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