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Fractal Fract
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Fractional-Order Circuits and Systems
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Fractional-Order Circuits and Systems

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: closed (31 January 2021) | Viewed by 19161

Special Issue Editor

Dr. Todd Freeborn

E-Mail Website
Guest Editor
Electrical and Computer Engineering, The University of Alabama, 3016 SERC, Tuscaloosa, AL 35487, USA
Interests: fractional-order circuits; fractional filters; bioimpedance

Special Issue Information

Dear Colleagues,

The field of fractional-order circuits and systems refers to a class of electronics that incorporate concepts from fractional calculus into their modeling and design. These concepts, focused on non-integer order differentiation and integration mathematical operations, are being explored across many fields of science and engineering. Focusing on their integration into electronic circuits, these concepts are being explored to design analog filtering circuits, oscillators, and control systems. The fractional order offered with these design approaches provides additional flexibility and tuning for target specifications. Additionally, the use of circuit elements with fractional-order impedances are being widely explored to model the electrical characteristics of biological materials and energy storage devices (e.g., supercapacitors, batteries).

The focus of this Special Issue is to continue to advance research on topics relating to the theory, design, implementation, and application of fractional-order circuits and systems. Topics that are invited for submission include (but are not limited to):

  • Fractional-order circuit theory;
  • Fractional-order filter and oscillator designs and realizations;
  • Fractional-order control systems and implementation;
  • Digital and analog approximations for realization of fractional-order systems;
  • Active and passive designs of fractional-order elements;
  • Applications of fractional-order circuit models for biology and biomedicine;
  • Applications of fractional-order circuit models for energy storage elements.

Dr. Todd Freeborn
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 submissions that pass pre-check are 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. Fractal and Fractional is an international peer-reviewed open access monthly 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 2700 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.

Published Papers (6 papers)

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Research

15 pages, 2237 KiB  
Article
Cole-Impedance Model Representations of Right-Side Segmental Arm, Leg, and Full-Body Bioimpedances of Healthy Adults: Comparison of Fractional-Order
by Todd J. Freeborn and Shelby Critcher
Fractal Fract. 2021, 5(1), 13; https://doi.org/10.3390/fractalfract5010013 - 28 Jan 2021
Cited by 13 | Viewed by 4603
Abstract
The passive electrical properties of a biological tissue, referred to as the tissue bioimpedance, are related to the underlying tissue physiology. These measurements are often well-represented by a fractional-order equivalent circuit model, referred to as the Cole-impedance model. Objective: Identify if there are [...] Read more.
The passive electrical properties of a biological tissue, referred to as the tissue bioimpedance, are related to the underlying tissue physiology. These measurements are often well-represented by a fractional-order equivalent circuit model, referred to as the Cole-impedance model. Objective: Identify if there are differences in the fractional-order (α) of the Cole-impedance parameters that represent the segmental right-body, right-arm, and right-leg of adult participants. Hypothesis: Cole-impedance model parameters often associated with tissue geometry and fluid (R∞, R1, C) will be different between body segments, but parameters often associated with tissue type (α) will not show any statistical differences. Approach: A secondary analysis was applied to a dataset collected for an agreement study between bioimpedance spectroscopy devices and dual-energy X-ray absoptiometry, identifying the Cole-model parameters of the right-side body segments of N=174 participants using a particle swarm optimization approach. Statistical testing was applied to the different groups of Cole-model parameters to evaluate group differences and correlations of parameters with tissue features. Results: All Cole-impedance model parameters showed statistically significant differences between body segments. Significance: The physiological or geometric features of biological tissues that are linked with the fractional-order (α) of data represented by the Cole-impedance model requires further study to elucidate. Full article
(This article belongs to the Special Issue Fractional-Order Circuits and Systems)
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21 pages, 5769 KiB  
Article
Optimal V-Plane Robust Stabilization Method for Interval Uncertain Fractional Order PID Control Systems
by Sevilay Tufenkci, Bilal Senol, Radek Matušů and Baris Baykant Alagoz
Fractal Fract. 2021, 5(1), 3; https://doi.org/10.3390/fractalfract5010003 - 03 Jan 2021
Cited by 5 | Viewed by 2932
Abstract
Robust stability is a major concern for real-world control applications. Realization of optimal robust stability requires a stabilization scheme, which ensures that the control system is stable and presents robust performance for a predefined range of system perturbations. This study presented an optimal [...] Read more.
Robust stability is a major concern for real-world control applications. Realization of optimal robust stability requires a stabilization scheme, which ensures that the control system is stable and presents robust performance for a predefined range of system perturbations. This study presented an optimal robust stabilization approach for closed-loop fractional order proportional integral derivative (FOPID) control systems with interval parametric uncertainty and uncertain time delay. This stabilization approach, which is carried out in a v-plane, relies on the placement of the minimum angle system pole to a predefined target angle within the stability region of the first Riemann sheet. For this purpose, tuning of FOPID controller coefficients was performed to minimize a root angle error that is defined as the squared difference of minimum angle root of interval characteristic polynomials and the desired target angle within the stability region of the v-plane. To solve this optimization problem, a particle swarm optimization (PSO) algorithm was implemented. Findings of the study reveal that tuning of the target angle can also be used to improve the robust control performance of interval uncertain FOPID control systems. Illustrative examples demonstrated the effectiveness of the proposed v-domain, optimal, robust stabilization of FOPID control systems. Full article
(This article belongs to the Special Issue Fractional-Order Circuits and Systems)
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20 pages, 5996 KiB  
Article
5G Poor and Rich Novel Control Scheme Based Load Frequency Regulation of a Two-Area System with 100% Renewables in Africa
by Hady H. Fayek
Fractal Fract. 2021, 5(1), 2; https://doi.org/10.3390/fractalfract5010002 - 23 Dec 2020
Cited by 10 | Viewed by 2779
Abstract
Remote farms in Africa are cultivated lands planned for 100% sustainable energy and organic agriculture in the future. This paper presents the load frequency control of a two-area power system feeding those farms. The power system is supplied by renewable technologies and storage [...] Read more.
Remote farms in Africa are cultivated lands planned for 100% sustainable energy and organic agriculture in the future. This paper presents the load frequency control of a two-area power system feeding those farms. The power system is supplied by renewable technologies and storage facilities only which are photovoltaics, biogas, biodiesel, solar thermal, battery storage and flywheel storage systems. Each of those facilities has 150-kW capacity. This paper presents a model for each renewable energy technology and energy storage facility. The frequency is controlled by using a novel non-linear fractional order proportional integral derivative control scheme (NFOPID). The novel scheme is compared to a non-linear PID controller (NPID), fractional order PID controller (FOPID), and conventional PID. The effect of the different degradation factors related to the communication infrastructure, such as the time delay and packet loss, are modeled and simulated to assess the controlled system performance. A new cost function is presented in this research. The four controllers are tuned by novel poor and rich optimization (PRO) algorithm at different operating conditions. PRO controller design is compared to other state of the art techniques in this paper. The results show that the PRO design for a novel NFOPID controller has a promising future in load frequency control considering communication delays and packet loss. The simulation and optimization are applied on MATLAB/SIMULINK 2017a environment. Full article
(This article belongs to the Special Issue Fractional-Order Circuits and Systems)
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11 pages, 994 KiB  
Article
LMI Criteria for Admissibility and Robust Stabilization of Singular Fractional-Order Systems Possessing Poly-Topic Uncertainties
by Xuefeng Zhang and Jia Dong
Fractal Fract. 2020, 4(4), 58; https://doi.org/10.3390/fractalfract4040058 - 15 Dec 2020
Cited by 8 | Viewed by 1789
Abstract
The issue of robust admissibility and control for singular fractional-order systems (FOSs) with polytopic uncertainties is investigated in this paper. Firstly, a new method based on linear matrix inequalities (LMIs) is presented to solve the admissibility problems of uncertain linear systems. Then, a [...] Read more.
The issue of robust admissibility and control for singular fractional-order systems (FOSs) with polytopic uncertainties is investigated in this paper. Firstly, a new method based on linear matrix inequalities (LMIs) is presented to solve the admissibility problems of uncertain linear systems. Then, a solid criterion of robust admissibility and a corresponding state feedback controller are derived, which overcome the conservatism of the existing results. Finally, for the sake of demonstrating the validity of proposed results, some relevant examples are provided. Full article
(This article belongs to the Special Issue Fractional-Order Circuits and Systems)
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17 pages, 817 KiB  
Article
Optimal Modelling of (1 + α) Order Butterworth Filter under the CFE Framework
by Shibendu Mahata, Rajib Kar and Durbadal Mandal
Fractal Fract. 2020, 4(4), 55; https://doi.org/10.3390/fractalfract4040055 - 03 Dec 2020
Cited by 9 | Viewed by 2942
Abstract
This paper presents the optimal rational approximation of (1+α) order Butterworth filter, where α ∊ (0,1) under the continued fraction expansion framework, by employing a new cost function. Two simple techniques based on the constrained optimization and the optimal pole-zero placements [...] Read more.
This paper presents the optimal rational approximation of (1+α) order Butterworth filter, where α ∊ (0,1) under the continued fraction expansion framework, by employing a new cost function. Two simple techniques based on the constrained optimization and the optimal pole-zero placements are proposed to model the magnitude-frequency response of the fractional-order lowpass Butterworth filter (FOLBF). The third-order FOLBF approximants achieve good agreement to the ideal characteristic for six decades of design bandwidth. Circuit realization using the current feedback operational amplifier is presented, and the modelling efficacy is validated in the OrCAD PSPICE platform. Full article
(This article belongs to the Special Issue Fractional-Order Circuits and Systems)
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15 pages, 4851 KiB  
Article
Realization of Cole–Davidson Function-Based Impedance Models: Application on Plant Tissues
by Stavroula Kapoulea, Costas Psychalinos and Ahmed S. Elwakil
Fractal Fract. 2020, 4(4), 54; https://doi.org/10.3390/fractalfract4040054 - 30 Nov 2020
Cited by 10 | Viewed by 2590
Abstract
The Cole–Davidson function is an efficient tool for describing the tissue behavior, but the conventional methods of approximation are not applicable due the form of this function. In order to overcome this problem, a novel scheme for approximating the Cole–Davidson function, based on [...] Read more.
The Cole–Davidson function is an efficient tool for describing the tissue behavior, but the conventional methods of approximation are not applicable due the form of this function. In order to overcome this problem, a novel scheme for approximating the Cole–Davidson function, based on the utilization of a curve fitting procedure offered by the MATLAB software, is introduced in this work. The derived rational transfer function is implemented using the conventional Cauer and Foster RC networks. As an application example, the impedance model of the membrane of mesophyll cells is realized, with simulation results verifying the validity of the introduced procedure. Full article
(This article belongs to the Special Issue Fractional-Order Circuits and Systems)
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