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Fractal Fract
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Advance on the Fractal and Fractional Calculus in Electrical and...
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Advance on the Fractal and Fractional Calculus in Electrical and Electronic Engineering

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

Deadline for manuscript submissions: closed (30 June 2024) | Viewed by 8505

Special Issue Editors

Dr. Kang-Jia Wang

E-Mail Website
Guest Editor
School of Physics and Electronic Information Engineering; Henan Polytechnic University, Jiaozuo 454003, China
Interests: fractal and fractional calculus; nonlinear vibration
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Inés Tejado

E-Mail Website
Guest Editor
Industrial Engineering School, University of Extremadura, 06006 Badajoz, Spain
Interests: fractional dynamics; fractional-order nonlinear systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractal and fractional calculus have seen many developments over the past years and, as a result, many classical models in electrical and electronic engineering are today being analysed using them, such as in the case of circuits, filters, oscillators, impedances, control systems, and so on. It has been demonstrated that fractal and fractional calculus applied to electrical and electronic engineering can provide more flexibility, as well as the possibility for modeling complex phenomena under the extreme conditions, such as porous media, microgravity, diffusion, etc.

The focus of this Special Issue is to continue to advance research on topics relating to the theory, design, implementation, and application of fractal and fractional calculus to the electrical and electronic engineering fields. Topics that are invited for submission include (but are not limited to):

  • Advanced theory of the fractal and fractional calculus in electrical and electronic Engineering;
  • Fractal and fractional circuits;
  • Fractal and fractional filters;
  • Fractal and fractional oscillators;
  • Fractional-order control systems;
  • Fractal and fractional differential equations in electrical and electronic engineering

Dr. Kang-Jia Wang
Prof. Dr. Inés Tejado
Guest Editors

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.

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  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
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  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

Further information on MDPI's Special Issue polices can be found here.

Published Papers (5 papers)

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Research

12 pages, 1562 KiB  
Article
Two-Dimensional Time-Fractional Nonlinear Drift Reaction–Diffusion Equation Arising in Electrical Field
by Anjuman, Andrew Y. T. Leung and Subir Das
Fractal Fract. 2024, 8(8), 456; https://doi.org/10.3390/fractalfract8080456 - 2 Aug 2024
Cited by 2 | Viewed by 1012
Abstract
Diffusion equations play a crucial role in various scientific and technological domains, including mathematical biology, physics, electrical engineering, and mathematics. This article presents a new formulation of the diffusion equation in the context of electrical engineering. Specifically, the behaviour of the physical quantity [...] Read more.
Diffusion equations play a crucial role in various scientific and technological domains, including mathematical biology, physics, electrical engineering, and mathematics. This article presents a new formulation of the diffusion equation in the context of electrical engineering. Specifically, the behaviour of the physical quantity of charge carriers (such as concentration) is examined within semiconductor materials. The primary focus of this work is to solve the two-dimensional, time-fractional, nonlinear drift reaction–diffusion equation by applying an appropriate numerical scheme. In recent years, researchers working on nonlinear diffusion equations have proposed several numerical methods, with the shifted airfoil collocation method being one such efficient technique for solving nonlinear partial differential equations. This collocation approach effectively reduces the considered two-dimensional, time-fractional, nonlinear drift reaction–diffusion equation to a system of algebraic equations. The efficiency and effectiveness of the proposed method are validated through an error analysis, comparing the exact solution and the proposed numerical solution for a specific form of the considered mathematical model. The variations in the concentration of charge carriers, driven by the effects of drift and reaction terms, are displayed graphically as the system transitions from a fractional order to an integer order. Full article
(This article belongs to the Special Issue Advance on the Fractal and Fractional Calculus in Electrical and Electronic Engineering)
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21 pages, 1581 KiB  
Article
A Low Power Analog Integrated Fractional Order Type-2 Fuzzy PID Controller
by Vassilis Alimisis, Nikolaos P. Eleftheriou, Evangelos Georgakilas, Christos Dimas, Nikolaos Uzunoglu and Paul P. Sotiriadis
Fractal Fract. 2024, 8(4), 234; https://doi.org/10.3390/fractalfract8040234 - 16 Apr 2024
Viewed by 1398
Abstract
This paper introduces an analog integrated fractional order type-2 fuzzy PID control system. Current approaches frequently depend on energy-intensive embedded digital systems, consuming substantial energy levels ranging from a few μW to mW. To address this limitation we propose a fully analog design [...] Read more.
This paper introduces an analog integrated fractional order type-2 fuzzy PID control system. Current approaches frequently depend on energy-intensive embedded digital systems, consuming substantial energy levels ranging from a few μW to mW. To address this limitation we propose a fully analog design offering insights into the potential of analog circuits for powerefficient robust control in complex and uncertain environments. It consists of Gaussian function, min/max, Operational transcoductance amplifier circuits and Resistor-Capacitor networks for the implementation of the fractional-order components. Crafted for operation under a reduced voltage supply (0.6 V), the controller attains minimal power usage (861.8 nW), facilitating uninterrupted, extended-term functioning. Post-layout simulation results confirm the proper operation of the proposed design. The proposed system is designed and simulated using the Cadence IC Suite in a TSMC 90 nm CMOS process. Full article
(This article belongs to the Special Issue Advance on the Fractal and Fractional Calculus in Electrical and Electronic Engineering)
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25 pages, 9327 KiB  
Article
Application of Tilt Integral Derivative for Efficient Speed Control and Operation of BLDC Motor Drive for Electric Vehicles
by Khairy Sayed, Hebatallah H. El-Zohri, Adel Ahmed and Mohamed Khamies
Fractal Fract. 2024, 8(1), 61; https://doi.org/10.3390/fractalfract8010061 - 16 Jan 2024
Cited by 5 | Viewed by 2300
Abstract
This study presents the tilt integral derivative (TID) controller technique for controlling the speed of BLDC motors in order to improve the real-time control of brushless direct current motors in electric vehicles. The TID controller is applied to the considered model to enhance [...] Read more.
This study presents the tilt integral derivative (TID) controller technique for controlling the speed of BLDC motors in order to improve the real-time control of brushless direct current motors in electric vehicles. The TID controller is applied to the considered model to enhance its performance, e.g., torque and speed. This control system manages the torque output, speed, and position of the motor to ensure precise and efficient operation in EV applications. Brushless direct current motors are becoming more and more popular due to their excellent torque, power factor, efficiency, and controllability. The differences between PID, TID, and PI controllers are compared. The outcomes demonstrated that the TID control enhanced the torque and current stability in addition to the BLDC system’s capacity to regulate speed. TID controllers provide better input power for BLDC (brushless DC) drives than PI and PID controllers do. Better transient responsiveness and robustness to disturbances are features of TID controller design, which can lead to more effective use of input power. TID controllers are an advantageous choice for BLDC drive applications because of their increased performance, which can result in increased system responsiveness and overall efficiency. In an experimental lab, a BLDC motor drive prototype is implemented in this study. To fully enhance the power electronic subsystem and the brushless DC motor’s real-time performance, a test bench was also built. Full article
(This article belongs to the Special Issue Advance on the Fractal and Fractional Calculus in Electrical and Electronic Engineering)
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18 pages, 1694 KiB  
Article
Fractional-Order LCL Filters: Principle, Frequency Characteristics, and Their Analysis
by Junhua Xu, Ermeng Zeng, Xiaocong Li, Guopeng He, Weixun Liu and Xuanren Meng
Fractal Fract. 2024, 8(1), 38; https://doi.org/10.3390/fractalfract8010038 - 5 Jan 2024
Cited by 1 | Viewed by 1482
Abstract
The fractional-order LCL filter, composed of two fractional-order inductors and one fractional-order capacitor, is a novel fractional-order π-type circuit introduced in recent years. Based on mathematical modeling, this article comprehensively studies the principles and frequency characteristics of fractional-order LCL filters. Five critical properties [...] Read more.
The fractional-order LCL filter, composed of two fractional-order inductors and one fractional-order capacitor, is a novel fractional-order π-type circuit introduced in recent years. Based on mathematical modeling, this article comprehensively studies the principles and frequency characteristics of fractional-order LCL filters. Five critical properties are derived and rigorously demonstrated. One of the most significant findings is that we identify the necessary and sufficient condition for resonance in fractional-order LCL filters when the sum of the orders of the fractional-order inductors and the fractional-order capacitor is equal to 2, which provides a theoretical foundation for effectively avoiding resonance in fractional-order LCL filters. The correctness of our theoretical derivation and analysis was confirmed through digital simulations. This study reveals that fractional-order LCL filters exhibit more versatile operational characteristics than traditional integer-order LCL filters, paving the way for broader application prospects. Full article
(This article belongs to the Special Issue Advance on the Fractal and Fractional Calculus in Electrical and Electronic Engineering)
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21 pages, 7578 KiB  
Article
Adaptive Residual Useful Life Prediction for the Insulated-Gate Bipolar Transistors with Pulse-Width Modulation Based on Multiple Modes and Transfer Learning
by Wujin Deng, Yan Gao, Wanqing Song, Enrico Zio, Gaojian Li, Jin Liu and Aleksey Kudreyko
Fractal Fract. 2023, 7(8), 614; https://doi.org/10.3390/fractalfract7080614 - 9 Aug 2023
Cited by 3 | Viewed by 1204
Abstract
Currently, residual useful life (RUL) prediction models for insulated-gate bipolar transistors (IGBT) do not focus on the multi-modal characteristics caused by the pulse-width modulation (PWM). To fill this gap, the Markovian stochastic process is proposed to model the mode transition process, due to [...] Read more.
Currently, residual useful life (RUL) prediction models for insulated-gate bipolar transistors (IGBT) do not focus on the multi-modal characteristics caused by the pulse-width modulation (PWM). To fill this gap, the Markovian stochastic process is proposed to model the mode transition process, due to the memoryless properties of the grid operation. For the estimation of the mode transition probabilities, transfer learning is utilized between different control signals. With the continuous mode switching, fractional Weibull motion (fWm) of multiple modes is established to model the stochasticity of the multi-modal IGBT degradation. The drift and diffusion coefficients are adaptively updated in the proposed RUL prediction model. In the case study, two sets of the real thermal-accelerated IGBT aging data are used. Different degradation modes are extracted from the meta degradation data, and then fused to be a complex health indicator (CHI) via a multi-sensor fusion algorithm. The RUL prediction model based on the fWm of multiple modes can reach a maximum relative prediction error of 2.96% and a mean relative prediction error of 1.78%. The proposed RUL prediction model with better accuracy can reduce the losses of the power grid caused by the unexpected IGBT failures. Full article
(This article belongs to the Special Issue Advance on the Fractal and Fractional Calculus in Electrical and Electronic Engineering)
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