Optimal F-domain stabilization technique for reduction of commensurate fractional-order SISO systems

Mahata, Shibendu; Herencsár, Norbert; Alagöz, Barış Baykant; Yeroğlu, Celaleddin

doi:10.1007/s13540-022-00014-6

Cited by 5 publications

(2 citation statements)

References 46 publications

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“…A data-driven realization and model order reduction (MOR) for linear fractional-order system (FoS) by applying the Loewner matrix method is proposed in [17]. A novel method of fractional-order single-input, single-output systems reduction is presented in [18], in which the F-plane is used to minimise the reduced order model's (ROM) frequency response inaccuracy in comparison to the original system. Moreover, the model order reduction techniques which were proposed by using grey wolf optimization blended with Pade approximation and factor division method are illustrated in [19,20], but these hybrid techniques are applicable for fxed systems.…”

Section: Introductionmentioning

confidence: 99%

Reduction of High Dimensional Noninteger Commensurate Systems Based on Differential Evolution

Kumar

Ramarao

Kumar³

et al. 2023

International Transactions on Electrical Energy Systems

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This work relates to the reduction of a noninteger commensurate high dimensional system. The essential objective of this article is to come up with an approximating technique to replace the original high dimensional system with a low dimensional model preserving the properties of the original system in its shortened model. Superiority of the proposed technique is exhibited by correlating the reduced model with the models of other current methods. The simulation results are cited to approve that the recommended technique has high efficiency with a closing value of time-domain specifications. Conclusively, more logical comparisons were made between other existing methods. The performance indices are calculated for both original system and reduced model system and presented in the manuscript.

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Section: Introductionmentioning

confidence: 99%

Reduction of High Dimensional Noninteger Commensurate Systems Based on Differential Evolution

Kumar

Ramarao

Kumar³

et al. 2023

International Transactions on Electrical Energy Systems

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“…A recent work has demonstrated the effectiveness of the F-domain-based approach in the reduced order modeling of FO commensurate system [17]. While realizing FO filters with optimization techniques exist in the literature [10,16,25], this paper is the first attempt to design the analog FOBF directly in the complex F-plane optimally.…”

Section: Introductionmentioning

confidence: 99%

Optimized fractional-order Butterworth filter design in complex F-plane

Mahata¹,

Herencsár

Kubánek

et al. 2022

Fract Calc Appl Anal

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This paper introduces a new technique to optimally design the fractional-order Butterworth low-pass filter in the complex F-plane. Design stability is assured by incorporating the critical phase angle as an inequality constraint. The poles of the proposed approximants reside on the unit circle in the stable region of the F-plane. The improved accuracy of the suggested scheme as compared to the recently published literature is demonstrated. A mixed-integer genetic algorithm which considers the parallel combinations of resistors and capacitors for the Valsa network is used to optimize the frequency responses of the fractional-order capacitor emulators as part of the experimental verification using the Sallen–Key filter topology. The total harmonic distortion and spurious-free dynamic range of the practical 1.5th-order Butterwoth filter are measured as 0.13% and 62.18 dBc, respectively; the maximum and mean absolute relative magnitude errors are 0.03929 and 0.02051, respectively.

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Optimal approximation of analog PID controllers of complex fractional-order

Mahata¹,

Herencsár

Maione

2023

Fract Calc Appl Anal

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Complex fractional-order (CFO) transfer functions, being more generalized versions of their real-order counterparts, lend greater flexibility to system modeling. Due to the absence of commercial complex-order fractance elements, the implementation of CFO models is challenging. To alleviate this issue, a constrained optimization approach that meets the targeted frequency responses is proposed for the rational approximation of CFO systems. The technique generates stable, minimum-phase, and real-valued coefficients based approximants, which are not always feasible for the curve-fitting approach reported in the literature. Stability and performance studies of the CFO proportional-integral-derivative (CFOPID) controllers for the Podlubny’s, the internal model control, and the El-Khazali’s forms are considered to demonstrate the feasibility of the proposed technique. Simulation results highlight that, for a practically reasonable order, all the designs achieve good agreement with the theoretical characteristics. Performance comparisons with the CFOPID controller approximants determined by the Oustaloup’s CFO differentiator based substitution method justify the proposed approach.

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Optimal F-domain stabilization technique for reduction of commensurate fractional-order SISO systems

Cited by 5 publications

References 46 publications

Reduction of High Dimensional Noninteger Commensurate Systems Based on Differential Evolution

Reduction of High Dimensional Noninteger Commensurate Systems Based on Differential Evolution

Optimized fractional-order Butterworth filter design in complex F-plane

Optimal approximation of analog PID controllers of complex fractional-order

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