Realizability of Fractional-Order Impedances by Passive Electrical Networks Composed of a Fractional Capacitor and RLC Components

Sarafraz, Mohammad Saeed; Tavazoei, Mohammad Saleh

doi:10.1109/tcsi.2015.2482340

Cited by 57 publications

(23 citation statements)

References 38 publications

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“…Consider a single‐port passive network composed of some RLC components and its fractional order counterpart [49] which constructed by replacing the inductors/capacitors of the network with fractional inductors/capacitors (In a fractional inductor with order α and pseudo‐inductance L , the relation between current ( i ) and voltage ( v ) is described by equality

v false(t false) = L_{0} D_{t}^{α} i false(t false)

where

_{0} D_{t}^{α}

denotes the fractional derivative operator [50]. The impedance of such a fractional inductor equals

z false(s false) = L s^{α}

in the Laplace domain.…”

Section: Some Subsequent Resultsmentioning

confidence: 99%

Magnitude–frequency responses of fractional order systems: properties and subsequent results

Tavazoei

2016

IET Control Theory & Applications

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v false(t false) = L_{0} D_{t}^{α} i false(t false)

where

_{0} D_{t}^{α}

denotes the fractional derivative operator [50]. The impedance of such a fractional inductor equals

z false(s false) = L s^{α}

in the Laplace domain.…”

Section: Some Subsequent Resultsmentioning

confidence: 99%

Magnitude–frequency responses of fractional order systems: properties and subsequent results

Tavazoei

2016

IET Control Theory & Applications

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“…A fractional-order electrical network used in [41] as a resonator with the resonance frequency ωr = (LC) −1/(α+β) . [35] [36] [37], fractional-order oscillators [38], fractionalorder passive impedances [39] [40], fractional-order resonators [41] [42] (see Fig. 1), and fractional-order phase-locked loops [43].…”

Section: Circuits and Systems Modeled By Nonlinear Fractional-ordmentioning

confidence: 99%

Nonlinear Fractional-Order Circuits and Systems: Motivation, A Brief Overview, and Some Future Directions

Tavazoei

Tavakoli-Kakhki

Bizzarri

2020

IEEE Open J. Circuits Syst.

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In recent years, fractional-order differential operators, and the dynamic models constructed based on these generalized operators have been widely considered in design and practical implementation of electrical circuits and systems. Simultaneously, facing with fractional-order dynamics and the nonlinear ones in electrical circuits and systems enforces us to use more advanced tools (in comparison to those commonly used in design and analysis of linear fractional-order/nonlinear integer-order circuits and systems) for their analysis, design, and implementation. Discussing on such a motivation, this tutorial paper aims to provide an overview on the recent achievements in proposing effective tools for analysis and design of nonlinear fractional-order circuits and systems. Moreover, some open problems, which can specify future directions for continuing research works on the aforementioned subject, are discussed.

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“…So far, there are only a few commercially available fractional-order passive components. The fractional-order modeling for passive components are developed from empirical results [17,18], or equivalent models of the passive components described by the fractional-order definition [19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

A modified modeling and dynamical behavior analysis method for fractional-order positive Luo converter

Jia

Liu

2020

PLoS ONE

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Compared to the integer-order modeling, the fractional-order modeling can achieve higher accuracy for designing and analyzing the DC-DC power converters. However, its applications in pulse width modulation (PWM) converters are limited due to the computational complexities. In this paper, a modified fractional-order modeling methodology for DC-DC converters is proposed, and its effectiveness is verified on the fractional-order positive Luo converters. Instead of using fractional-order calculus, the proposed methodology analyzes the harmonic components of the PWM converters by utilizing the non-linear vector differential equations of the periodically time-variant system. The final solution of the state variables is composed of two parts: the steady-state solution and the transient solution. The approximate steady state solution can be obtained by using the equivalent small parameter (ESP) method and the harmonic balance theory, while the main part of the transient solution can be obtained according to the explicit Grü nwald-Letnikov (GL) approximation. In addition, the influence of the fractional orders on the performance of the DC-DC converters, and on the dynamic behaviors of the fractional-orders systems are also discussed in this paper. Compared to the conventional fractional-order numerical models, the proposed model is able to present the time-domain information more precisely, which helps to better reveal and analyze the non-linear behaviors of the DC-DC converters. The effectiveness of the work is demonstrated by the simulation and experimental results of the equivalent circuits built with fractional-order components.

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Realizability of Fractional-Order Impedances by Passive Electrical Networks Composed of a Fractional Capacitor and RLC Components

Cited by 57 publications

References 38 publications

Magnitude–frequency responses of fractional order systems: properties and subsequent results

Magnitude–frequency responses of fractional order systems: properties and subsequent results

Nonlinear Fractional-Order Circuits and Systems: Motivation, A Brief Overview, and Some Future Directions

A modified modeling and dynamical behavior analysis method for fractional-order positive Luo converter

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