Fractional-Order Devices

Optimal integer-order transfer function approximation of linear time-invariant fractional-order systems (FOS) using a straightforward approach is proposed here. The error between the rational approximant and the FOS (commensurate/noncommensurate/oscillatory types etc.) is minimised directly in the frequency domain, subject to design stability constraints, by using the colliding bodies optimisation (CBO) algorithm. Comparisons with other well-known metaheuristics regarding the computational time and the design effort expended in parameter tuning justify the efficiency of the proposed method. The CBOoptimised models achieve a superior solution quality regarding both the magnitude and phase responses in comparison to the reported literature. Analogue circuit implementations of the models using the current feedback operational amplifier are also presented. Simulations carried out in OrCAD PSPICE environment validate the practical efficacy of the proposed models.

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“…are the Hurwitz determinants [32]. The constraints defined in (9) ensure the generation of a stable transfer function.…”

Section: Optimisation Problem Formulationmentioning

confidence: 99%

Optimal approximation of fractional‐order systems with model validation using CFOA

Mahata

Kar

Mandal

2019

IET signal process.

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“…Energies 2020, xx, 5 2 of 14 calculus [5][6][7][8][9][10][11][12]. Usually, these models are formulated in terms of equivalent circuits containing a constant phase element (CPE) sometimes called a capacitor of fractional order or a fractal element [13][14][15]. This element has an impedance with a frequency dependence proportional to (jω) −α .…”

Section: Introductionmentioning

confidence: 99%

Memory Effect and Fractional Differential Dynamics in Planar Microsupercapacitors Based on Multiwalled Carbon Nanotube Arrays

2020

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The development of portable electronic devices has greatly stimulated the need for miniaturized power sources. Planar supercapacitors are micro-scale electrochemical energy storage devices that can be integrated with other microelectronic devices on a chip. In this paper, we study the behavior of microsupercapacitors with in-plane interdigital electrodes of carbon nanotube array under sinusoidal excitation, step voltage input and sawlike voltage input. Considering the anomalous diffusion of ions in the array and interelectrode space, we propose a fractional-order equivalent circuit model that successfully describes the measured impedance spectra. We demonstrate that the response of the investigated micro-supercapacitors is linear and the system is time-invariant. The numerical inversion of the Laplace transforms for electric current response in an equivalent circuit with a given impedance leads to results consistent with potentiostatic measurements and cyclic voltammograms. The use of electrodes based on an ordered array of nanotubes reduces the role of nonlinear effects in the behavior of a supercapacitor. The effect of the disordering of nanotubes with increasing array height on supercapacitor impedance is considered in the framework of a distributed-order subdiffusion model.

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“…In the modified Fricke model depicted in Fig. 1(b) the capacitive element of the Fricke model is replaced by a fractional-order capacitor (FOC) or so-called capacitive constant phase element (CPE), whose impedance is Z CPE = 1/s α C in the s-domain, where C denotes pseudo-capacitance (with unit Farad•sec α−1 or F•sec α−1 ) and α is its order in range 0 < α < 1 [7]. The impedance of FOC has frequency dependent real part and its magnitude varies by -20α dB per decade of frequency, while the phase is constant in full frequency range and equal to -απ/2.…”

Section: Introductionmentioning

confidence: 99%

An Empirical Study of Fatigue-Induced Electrical Impedance Models of Biceps Tissues

Herencsár

2020

2020 12th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT)

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Electrical impedance myography (EIM) is a noninvasive approach to muscle assessment based on the measurement of the electrical impedance in frequency range of interest. In this paper, fatigue-induced electrical impedance models of biceps tissues are investigated. After the dataset used is briefly described, complete set of parameters of the modified Fricke model, utilizing Foster I RC network-based fractional-order capacitor (FOC), are computed. The goodness of fitting of proposed FOCs and bioimpedance models were evaluated visually and statistically. The fit accuracy of designed electrical impedance models is R 2 R,X ≥ 0.9978. Proposed models provide more intuitive representation of the electrical behavior of biceps tissues. EIA standard compliant E96 series lumped parameter-based practical models give an appropriate explanation of fatigue effect on biceps tissues from resistance and capacitance point of view.

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Fractional-Order Devices

Cited by 59 publications

References 0 publications

Optimal approximation of fractional‐order systems with model validation using CFOA

Optimal approximation of fractional‐order systems with model validation using CFOA

Memory Effect and Fractional Differential Dynamics in Planar Microsupercapacitors Based on Multiwalled Carbon Nanotube Arrays

An Empirical Study of Fatigue-Induced Electrical Impedance Models of Biceps Tissues

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