Fractional-Order Two-Port Networks

Fouda, Mohammed E.; Elwakil, Ahmed S.; Radwan, Ahmed G.; Maundy, Brent

doi:10.1155/2016/5976301

Cited by 15 publications

(8 citation statements)

References 10 publications

(10 reference statements)

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“…Therefore, it is necessary to study fractional order network synthesis. However, fractional order network synthesis is in its infancy, [10] and [11] can realize integer order RLC two-port terminated one fractional order element, [12] proposes a synthesis method of fractional order two-port. And progress has also been made in the design of fractional order oscillator [13], fractional order filter [14], fractional order devices [15] and analysis of fractional order circuits [16].…”

Section: Introductionmentioning

confidence: 99%

Extended Darlington Synthesis of Fractional Order Immittance Function With Two Element Orders

Liang

Zheng

2019

IEEE Access

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Actual circuits have fractional order characteristics essentially. With the widespread application of fractional order circuits and the great strides in the manufacturing of fractional order elements in recent years, passive synthesis of fractional order circuit becomes an important research content. In this paper, classical Darlington's synthesis is extended to the two-variable case. Based on two-variable Darlington's synthesis and variable substitution, synthesis of fractional order immittance function with two element orders is proposed. Finally, an example is given to illustrate the calculation process.INDEX TERMS Fractional order, passive circuit, network synthesis, circuit theory.

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Section: Introductionmentioning

confidence: 99%

Extended Darlington Synthesis of Fractional Order Immittance Function With Two Element Orders

Liang

Zheng

2019

IEEE Access

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“…Such circuits can be designed specifically to have tailored responses with rather complex dynamics. [47][48][49][50][51][52][53] Furthermore, they enable analog realizations of fractionalorder controllers as discussed in the work by Petráš 54 as well as the works by Podlubny et al, 55 Charef, 56 and Luo and Chen. 57 Further advances on the stability of linear systems with fractional-order elements were extensively discussed by Petráš 58 as well as Radwan et al 59 A descriptor system approach was proposed by Tavazoei and Haeri.…”

Section: Introductionmentioning

confidence: 99%

Measurement and control of emergent phenomena emulated by resistive-capacitive networks, using fractional-order internal model control and external adaptive control

Galvão

Hadjiloucas

2019

Review of Scientific Instruments

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A fractional-order internal model control technique is applied to a three-dimensional resistive-capacitive network to enforce desired closedloop dynamics of first order. In order to handle model mismatch issues resulting from the random allocation of the components within the network, the control law is augmented with a model-reference adaptive strategy in an external loop. By imposing a control law on the system to obey first order dynamics, a calibrated transient response is ensured. The methodology enables feedback control of complex systems with emergent responses and is robust in the presence of measurement noise or under conditions of poor model identification. Furthermore, it is also applicable to systems that exhibit higher order fractional dynamics. Examples of feedback-controlled transduction include cantilever positioning in atomic force microscopy or the control of complex de-excitation lifetimes encountered in many types of spectroscopies, e.g., nuclear magnetic, electron-spin, microwave, multiphoton fluorescence, Förster resonance, etc. The proposed solution should also find important applications in more complex electronic, microwave, and photonic lock-in problems. Finally, there are further applications across the broader measurement science and instrumentation community when designing complex feedback systems at the system level, e.g., ensuring the adaptive control of distributed physiological processes through the use of biomedical implants.

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“…The synthesis method in [26, 27] can realise the single‐port networks composed of a fractional capacitor and a integer‐order RLC network. Fouda , et al [28] proposed a synthesis method of fractional‐order two‐port network, and the authors in [29, 30] designed fractional‐order oscillators based on fractional‐order network synthesis theory. Based on multivariable network synthesis theory [31], Jing and Liang [32] proposed a new synthesis method recently.…”

Section: Introductionmentioning

confidence: 99%

Synthesis of passive fractional‐order LCn‐port with three element orders

Liang

Zheng

2018

IET Circuits, Devices & Systems

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Fractional-order circuits find a widespread use in different engineering applications. The problem of realising fractional-order circuits has been discussed by several authors, however, it is far from being solved. Realising fractional-order resistorless passive network with three element orders is been studied. At first, this study extends the two-variable reactance matrix synthesis method to three-variable case, and then proposes a synthesis method of fractional-order reactance matrix with three element orders by variable substitution. The process in above methods mainly involves variable substitution, decomposition of three-variable reactance matrix, extraction of unit inductors, Laurent series expansion, spectral factorisation of two-variable positive semidefinite Hermitian matrix and synthesis of univariable reactance matrix. Then the above-mentioned synthesis process is illustrated by two examples.

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Fractional-Order Two-Port Networks

Cited by 15 publications

References 10 publications

Extended Darlington Synthesis of Fractional Order Immittance Function With Two Element Orders

Extended Darlington Synthesis of Fractional Order Immittance Function With Two Element Orders

Measurement and control of emergent phenomena emulated by resistive-capacitive networks, using fractional-order internal model control and external adaptive control

Synthesis of passive fractional‐order LCn‐port with three element orders

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