Approximation of the Fractional-Order Laplacian sα As a Weighted Sum of First-Order High-Pass Filters

被引：60

作者：

AbdelAty, A. M. ^{[1
]}

Elwakil, A. S. ^{[2
,3
]}

Radwan, A. G. ^{[3
,4
]}

Psychalinos, C. ^{[5
]}

Maundy, B. J. ^{[6
]}

机构：

[1] Fayoum Univ, Engn Math & Phys Dept, Al Fayyum 63514, Egypt

[2] Univ Sharjah, Dept Elect & Comp Engn, Sharjah 27272, U Arab Emirates

[3] Nile Univ, Nanoelect Integrated Syst Ctr, Giza 16453, Egypt

[4] Cairo Univ, Engn Math & Phys Dept, Giza 12613, Egypt

[5] Univ Patras, Phys Dept, Elect Lab, Rion 26504, Greece

[6] Univ Calgary, Dept Elect & Comp Engn, Calgary, AB T2N 1N4, Canada

来源：

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS | 2018年 / 65卷 / 08期

关键词：

Fractional-order circuits; fractional-order capacitors; fractional-order integration/differentiation; DIFFERENTIATOR; REALIZATION; CAPACITORS; DESIGN; POWER;

D O I：

10.1109/TCSII.2018.2808949

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

A new approximation method of the fractional-order Laplacian operator s(alpha) is introduced. The approximation is based on a weighted sum of first-order filter sections and its analytical proof is given. The optimal high-pass filter section parameters that cover six frequency decades are obtained using the flower pollination algorithm while the effect of the number of filter sections on the accuracy of the approximation is investigated. Approximations of fractional-order capacitors of orders alpha = 0.5 and alpha = 0.7 synthesized in Foster-II form are given as a validating example. Further, an active emulator of a fractional-order differentiator function based on this technique is also proposed and experimentally validated.

引用

页码：1114 / 1118

页数：5

共 29 条

[11] Power and energy analysis of fractional-order electrical energy storage devices [J].

Fouda, M. E. ;

Elwakil, A. S. ;

Radwan, A. G. ;

Allagui, A. .

ENERGY, 2016, 111 :785-792

[12] Identification of Fractional-Order Transfer Functions Using a Step Excitation [J].

Jacyntho, Luiz Antonio ;

Minhoto Teixeira, Marcelo Carvalho ;

Assuncao, Edvaldo ;

Cardim, Rodrigo ;

Harrop Galvao, Roberto Kawakami ;

Hadjiloucas, Sillas .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS, 2015, 62 (09) :896-900

[13] High-Power Fractional-Order Capacitor With 1 < α < 2 Based on Power Converter [J].

Jiang, Yanwei ;

Zhang, Bo .

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, 2018, 65 (04) :3157-3164

[14] Solid-state fractional capacitor using MWCNT-epoxy nanocomposite [J].

John, Dina A. ;

Banerjee, Susanta ;

Bohannan, Gary W. ;

Biswas, Karabi .

APPLIED PHYSICS LETTERS, 2017, 110 (16)

[15] Studies on fractional order differentiators and integrators: A survey [J].

Krishna, B. T. .

SIGNAL PROCESSING, 2011, 91 (03) :386-426

[16] A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments [J].

Li, HongSheng ;

Luo, Ying ;

Chen, YangQuan .

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, 2010, 18 (02) :516-520

[17] H-INFINITY OPTIMIZED WAVE-ABSORBING CONTROL - ANALYTICAL AND EXPERIMENTAL RESULTS [J].

MATSUDA, K ;

FUJII, H .

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS, 1993, 16 (06) :1146-1153

[18]

Morrison R., 1959, IRE T CIRCUIT THEORY, V6, P310, DOI [10.1109/TCT.1959.1086554, DOI 10.1109/TCT.1959.1086554]

[19] Frequency-band complex noninteger differentiator: Characterization and synthesis [J].

Oustaloup, A ;

Levron, F ;

Mathieu, B ;

Nanot, FM .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 2000, 47 (01) :25-39

[20] ON REALIZATION OF A CONSTANT-ARGUMENT IMMITTANCE OR FRACTIONAL OPERATOR [J].

ROY, SCD .

IEEE TRANSACTIONS ON CIRCUIT THEORY, 1967, CT14 (03) :264-&

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