Special Issue "Fractional-Order Circuits & Systems Design and Applications"

A special issue of Electronics (ISSN 2079-9292). This special issue belongs to the section "Circuit and Signal Processing".

Deadline for manuscript submissions: 31 May 2021.

Special Issue Editor

Prof. Dr. Dominik Sierociuk
E-Mail Website
Guest Editor
Faculty of Electrical Engineering; Institute of Control & Industrial Electronics Warsaw University of Technology, Warsaw, 00-662, Poland
Interests: fractional calculus; variable fractional order operators; analog modellig of fractional constant and variable order systems

Special Issue Information

Dear Colleagues,

Fractional calculus is a generalization of traditional differential calculus into the case whereas derivatives and integrals can be not only of integer orders but also of non-integer–fractional orders. This calculus was found to be a very efficient and valuable tool in many areas of science. One excellent example of using fractional order calculus in electrical engineering is modelling ultracapacitors. Based on an accurate fractional order model, it was possible to explain some interesting phenomena like loss of capacity equivalence with respect to growing frequency and that the resonance frequency of an ultracapacitor-coil circuit is not equal to the frequency for maximum current.

These and other results of modelling electrical elements and devices based on fractional calculus provided strong motivation to explore fractional circuits theory and applications.

The purpose of this Special Issue is to gather original research articles reflecting the latest developments in both theory and applications of fractional order circuits. The areas of interest include, but are not limited to, modelling of electrical and electronic devices like the new generation of ultracapacitors, batteries, fuel cells, analog modelling of constant and variable order operators and systems, fractional order filters, analysis, synthesis, and design methods for circuits with fractional order elements.

Prof. Dr. Dominik Sierociuk
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Electronics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Fractional caluclus
  • Modelling electronic and electrical devices
  • Analog modelling of constant and variable order operators and systems
  • Analysis methods for fractional order circuits
  • Design methods for fractional order circuits
  • Circuits for chaotic fractional order systems

Published Papers (6 papers)

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Research

Open AccessArticle
The Frequency and Real-Time Properties of the Microcontroller Implementation of Fractional-Order PID Controller
Electronics 2021, 10(5), 524; https://doi.org/10.3390/electronics10050524 - 24 Feb 2021
Viewed by 310
Abstract
The paper presents time, frequency, and real-time properties of a fractional-order PID controller (FOPID) implemented at a STM 32 platform. The implementation uses CFE approximation and discrete version of a Grünwald–Letnikov operator (FOBD). For these implementations, experimental step responses and Bode frequency responses [...] Read more.
The paper presents time, frequency, and real-time properties of a fractional-order PID controller (FOPID) implemented at a STM 32 platform. The implementation uses CFE approximation and discrete version of a Grünwald–Letnikov operator (FOBD). For these implementations, experimental step responses and Bode frequency responses were measured. Real-time properties of the approximations are also examined and analyzed. Results of tests show that the use of CFE approximation allows to better keep the soft real-time requirements with an accuracy level a bit worse than when using the FOBD. The presented results can be employed in construction-embedded fractional control systems implemented at platforms with limited resources. Full article
(This article belongs to the Special Issue Fractional-Order Circuits & Systems Design and Applications)
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Open AccessArticle
Time-Domain Analysis of Fractional Electrical Circuit Containing Two Ladder Elements
Electronics 2021, 10(4), 475; https://doi.org/10.3390/electronics10040475 - 17 Feb 2021
Viewed by 391
Abstract
The paper is devoted to the theoretical and experimental analysis of an electric circuit consisting of two elements that are described by fractional derivatives of different orders. These elements are designed and performed as RC ladders with properly selected values of resistances and [...] Read more.
The paper is devoted to the theoretical and experimental analysis of an electric circuit consisting of two elements that are described by fractional derivatives of different orders. These elements are designed and performed as RC ladders with properly selected values of resistances and capacitances. Different orders of differentiation lead to the state-space system model, in which each state variable has a different order of fractional derivative. Solutions for such models are presented for three cases of derivative operators: Classical (first-order differentiation), Caputo definition, and Conformable Fractional Derivative (CFD). Using theoretical models, the step responses of the fractional electrical circuit were computed and compared with the measurements of a real electrical system. Full article
(This article belongs to the Special Issue Fractional-Order Circuits & Systems Design and Applications)
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Open AccessArticle
Fractional PIλD Controller Design for a Magnetic Levitation System
Electronics 2020, 9(12), 2135; https://doi.org/10.3390/electronics9122135 - 13 Dec 2020
Cited by 1 | Viewed by 432
Abstract
Currently, there are no formalized methods for tuning non-integer order controllers. This is due to the fact that implementing these systems requires using an approximation of the non-integer order terms. The Oustaloup approximation method of the sα fractional derivative is intuitive and widely adopted in the design of fractional-order PIλD controllers. It requires special considerations for real-time implementations as it is prone to numerical instability. In this paper, for design and tuning of fractional regulators, we propose two methods.The first method relies on Nyquist stability criterion and stability margins. We base the second on parametric optimization via Simulated Annealing of multiple performance indicators. We illustrate our methods with a case study of the PIλD controller for the Magnetic Levitation System. We illustrate our methods’ efficiency with both simulations and experimental verification in both nominal and disturbed operation. Full article
(This article belongs to the Special Issue Fractional-Order Circuits & Systems Design and Applications)
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Open AccessArticle
Random Number Generator with Long-Range Dependence and Multifractal Behavior Based on Memristor
Electronics 2020, 9(10), 1607; https://doi.org/10.3390/electronics9101607 - 01 Oct 2020
Cited by 2 | Viewed by 723
Abstract
Random number generators are used in areas such as encryption and system modeling, where some of these exhibit fractal behaviors. For this reason, it is interesting to make use of the memristor characteristics for the random number generation. Accordingly, the objective of this [...] Read more.
Random number generators are used in areas such as encryption and system modeling, where some of these exhibit fractal behaviors. For this reason, it is interesting to make use of the memristor characteristics for the random number generation. Accordingly, the objective of this article is to evaluate the performance of a chaotic memristive system as a random number generator with fractal behavior and long-range dependence. To achieve the above, modeling memristor and its corresponding chaotic systems is performed, from which a random number generator is constructed. Subsequently, the Hurst parameter for the detection of long-range dependence is estimated and a fractal analysis of the synthesized data is performed. Finally, a comparison between the model proposed in the research and the β-MWM algorithm is made. The results obtained show that the data synthesized from the proposed generator have a variable Hurst parameter and both monofractal and multifractal behavior. The main contribution of this research is the proposal of a new model for the synthesis of traces with long-range dependence and fractal behavior based on the non-linearity of the memristor. Full article
(This article belongs to the Special Issue Fractional-Order Circuits & Systems Design and Applications)
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Open AccessArticle
Modeling and Analysis of the Fractional-Order Flyback Converter in Continuous Conduction Mode by Caputo Fractional Calculus
Electronics 2020, 9(9), 1544; https://doi.org/10.3390/electronics9091544 - 21 Sep 2020
Cited by 2 | Viewed by 633
Abstract
In order to obtain more realistic characteristics of the converter, a fractional-order inductor and capacitor are used in the modeling of power electronic converters. However, few researches focus on power electronic converters with a fractional-order mutual inductance. This paper introduces a fractional-order flyback [...] Read more.
In order to obtain more realistic characteristics of the converter, a fractional-order inductor and capacitor are used in the modeling of power electronic converters. However, few researches focus on power electronic converters with a fractional-order mutual inductance. This paper introduces a fractional-order flyback converter with a fractional-order mutual inductance and a fractional-order capacitor. The equivalent circuit model of the fractional-order mutual inductance is derived. Then, the state-space average model of the fractional-order flyback converter in continuous conduction mode (CCM) are established. Moreover, direct current (DC) analysis and alternating current (AC) analysis are performed under the Caputo fractional definition. Theoretical analysis shows that the orders have an important influence on the ripple, the CCM operating condition and transfer functions. Finally, the results of circuit simulation and numerical calculation are compared to verify the correctness of the theoretical analysis and the validity of the model. The simulation results show that the fractional-order flyback converter exhibits smaller overshoot, shorter setting time and higher design freedom compared with the integer-order flyback converter. Full article
(This article belongs to the Special Issue Fractional-Order Circuits & Systems Design and Applications)
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Open AccessFeature PaperArticle
Analog Realization of a Fractional Recursive Variable-Type and Order Operator for a Particular Switching Strategy
Electronics 2020, 9(5), 855; https://doi.org/10.3390/electronics9050855 - 21 May 2020
Viewed by 736
Abstract
In this paper, we propose a method of practical realization and an actual, physical hardware implementation of a fractional variable-type and order difference operator that switches between two (i.e., B - and D -type) variable-order definitions. After the theoretical model of such a switch, we report the experimental validation on an analog model to prove its adequacy. The tests prove with great certainty that the proposed model and the realization behave correctly. They also let the authors assume that the proposed method is the only one suitable for this case, based on the counterexamples presented. Full article
(This article belongs to the Special Issue Fractional-Order Circuits & Systems Design and Applications)
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