分数阶器件、电路和系统的仿真方法、建模方法和物理实现的最新进展 "特刊客座编辑

IF 1.6 4区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC International Journal of Numerical Modelling-Electronic Networks Devices and Fields Pub Date : 2024-10-09 DOI:10.1002/jnm.3305
Jesus M. Munoz-Pacheco, Viet-Thanh Pham
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From a science and engineering point of view, there are still open problems in fractional calculus, ranging from numerical aspects and modeling techniques to the design and implementation of devices, circuits, and systems. For instance, optimized simulation methods are still needed to compute a proper solution considering the whole memory contributions of fractional operators but simultaneously reducing the computational effort. Classical fractional calculus definitions, as well as new operators (fractional-fractal, fractional operators in the complex plane, variable order calculus, etc.), should continue being explored to obtain novel models of physical phenomena at different levels of abstraction and descriptions, such as physical, circuit, macro, behavioral, and functional. In fractional-order devices, circuits, and systems, one of the challenges consists of implementing the fractional integrodifferential operator as integrators and derivators in the frequency domain, that is, <span></span><math>\n <semantics>\n <mrow>\n <msup>\n <mi>s</mi>\n <mi>α</mi>\n </msup>\n </mrow>\n <annotation>$$ {s}^{\\alpha } $$</annotation>\n </semantics></math> <span></span><math>\n <semantics>\n <mrow>\n <mi>α</mi>\n <mo>∈</mo>\n <mi>R</mi>\n </mrow>\n <annotation>$$ \\alpha \\in R $$</annotation>\n </semantics></math> using approximation methods aiming for flexible and non-bulky realizations as there is no fabricated fractional-order capacitor yet commercially available.</p><p>The papers in this special issue are devoted to stimulating new ideas and methods and enabling the extension of numerous applications using fractional-order devices, circuits, and systems. High-quality contributions to numerical modeling, design, optimization, and implementation of devices and systems have been reported. In the paper “Fractional order capacitance behavior due to hysteresis effect of ferroelectric material on GaN HEMT devices [<span>1</span>],” Pyngrope et al. introduced a novel fractional-order capacitance model using the Grünwald–Letnikov derivative. The presented study is especially relevant to cope with the complex nature of the aluminum scandium nitride (AlScN) gate capacitance in GaN HEMTs (Gallium nitride (GaN))-High Electron Mobility Transistors, which have become the forefront of the semiconductor industry. The accuracy of the proposed model is demonstrated by numerous error metrics, gathering a robust mechanism for accurately characterizing GaN HEMT capacitance. In this manner, the proposed model represents a powerful approach to accurately describe the GaN HEMT capacitance as fractional order derivatives allow the modeling of noninteger order systems.</p><p>In the paper “Fractional-calculus analysis of the dynamics of typhoid fever with the effect of vaccination and carriers [<span>2</span>],” Jan et al. presented a novel epidemic model for typhoid fever with vaccination and carriers via Caputo-Fabrizio operator to minimize a global public health problem that affects considerable people annually. The findings highlighted the effectiveness of fractional order to describe the memory effects in the proposed model. In the paper “Design and performance analysis of 8-port multi-service quad-band MIMO antenna for automotive communication [<span>3</span>],” Arumugam et al. proposed a low-profile compact 8-port multiband antenna with polarization diversity principle for automotive communication. The presented design resonates at frequencies of 1.8, 2.4, 5.2, and 5.8 GHz for GSM, ISM bands, and WLAN wireless services tested on vehicular to intravehicular environments.</p><p>In the paper “Advanced tree-seed optimization based fractional-order PID controller design for simplified decoupled industrial tank systems [<span>4</span>],” Rajagopalan et al. analyzed the multiple issues of coupled tank systems by considering nonlinear dynamics, time delays, uncertainties, and cross-coupling effects. As a result, the study employed a fractional-order proportional–integral–derivative (FOPID) controller to regulate the level of a coupled tank system. In addition, the controller was optimized using a tree seed algorithm. Numerical experiments on distinct interconnected tank systems evidenced the efficiency of the fractional controller. In the paper “Exponential stability and numerical analysis of Timoshenko system with dual-phase-lag thermoelasticity [<span>5</span>],” Bouraoui et al. investigated the well-posedness and stability of a thermoelastic Timoshenko system with non-Fourier heat conduction. In particular, a dual-phase-lag (DPL) model with two thermal relaxation times was considered. The semigroup approach and Gearhart–Prüss theorem were valuable tools to demonstrate the existence, uniqueness, and exponential stability, respectively. Finally, in the paper “Comparative analysis of uncontrollable angles in direct torque and stator flux control and rotor flux control strategies: A numerical and experimental study [<span>6</span>],” Alshbib et al. reported an analysis of uncontrollable angles (UAs) in the direct torque control (DTC) algorithm at different operating conditions, including parameter variations in two distinct strategies: Direct torque and stator flux control (DTC-SC) and (DTC-RC). 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From a science and engineering point of view, there are still open problems in fractional calculus, ranging from numerical aspects and modeling techniques to the design and implementation of devices, circuits, and systems. For instance, optimized simulation methods are still needed to compute a proper solution considering the whole memory contributions of fractional operators but simultaneously reducing the computational effort. Classical fractional calculus definitions, as well as new operators (fractional-fractal, fractional operators in the complex plane, variable order calculus, etc.), should continue being explored to obtain novel models of physical phenomena at different levels of abstraction and descriptions, such as physical, circuit, macro, behavioral, and functional. 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High-quality contributions to numerical modeling, design, optimization, and implementation of devices and systems have been reported. In the paper “Fractional order capacitance behavior due to hysteresis effect of ferroelectric material on GaN HEMT devices [<span>1</span>],” Pyngrope et al. introduced a novel fractional-order capacitance model using the Grünwald–Letnikov derivative. The presented study is especially relevant to cope with the complex nature of the aluminum scandium nitride (AlScN) gate capacitance in GaN HEMTs (Gallium nitride (GaN))-High Electron Mobility Transistors, which have become the forefront of the semiconductor industry. The accuracy of the proposed model is demonstrated by numerous error metrics, gathering a robust mechanism for accurately characterizing GaN HEMT capacitance. 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In the paper “Exponential stability and numerical analysis of Timoshenko system with dual-phase-lag thermoelasticity [<span>5</span>],” Bouraoui et al. investigated the well-posedness and stability of a thermoelastic Timoshenko system with non-Fourier heat conduction. In particular, a dual-phase-lag (DPL) model with two thermal relaxation times was considered. The semigroup approach and Gearhart–Prüss theorem were valuable tools to demonstrate the existence, uniqueness, and exponential stability, respectively. Finally, in the paper “Comparative analysis of uncontrollable angles in direct torque and stator flux control and rotor flux control strategies: A numerical and experimental study [<span>6</span>],” Alshbib et al. reported an analysis of uncontrollable angles (UAs) in the direct torque control (DTC) algorithm at different operating conditions, including parameter variations in two distinct strategies: Direct torque and stator flux control (DTC-SC) and (DTC-RC). 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引用次数: 0

摘要

目前,分数微积分(FC)与物理学和工程学中显示非局部性和长记忆效应的现象建模有关。特别是,分数阶算子提供了一种以更高精度表示物理现象的绝佳方法,因为与经典微积分不同,分数阶算子捕捉到了所有过去事件的贡献,而经典微积分的性质只是局部的。因此,小数阶可以作为一种额外的自由度,用于改进各个领域的实际应用,如模拟和数字电路、混沌理论、电子设备、密码学、控制、信号处理、机器人学、滤波器理论、生物学、风力涡轮机、粘弹性研究、铁磁材料等。从科学和工程的角度来看,分数微积分仍有许多未解决的问题,从数值方面和建模技术到设备、电路和系统的设计与实现,不一而足。例如,仍然需要优化的模拟方法来计算适当的解决方案,既要考虑到分数算子的整个内存贡献,又要减少计算量。应继续探索经典的分数微积分定义以及新的算子(分数-分数、复平面中的分数算子、变阶微积分等),以便在不同的抽象和描述层次(如物理、电路、宏观、行为和功能)上获得物理现象的新模型。在分数阶器件、电路和系统中,面临的挑战之一是如何在频域中将分数积分微分算子作为积分器和导数器来实现,即 s α $$ {s}^\{alpha } $ α∈ R$ α∈ R$ {s}^\{alpha }。本特刊中的论文致力于激发新思路和新方法,使分数阶器件、电路和系统的众多应用得以扩展。本特刊中的论文致力于激发新思路、新方法,并使分数阶器件、电路和系统的应用得以扩展。这些论文对器件和系统的数值建模、设计、优化和实现做出了高质量的贡献。在题为 "GaN HEMT 器件上铁电材料的滞后效应导致的分数阶电容行为[1]"的论文中,Pyngrope 等人利用 Grünwald-Letnikov 导数引入了一种新型分数阶电容模型。该研究特别适用于氮化镓 HEMT(氮化镓(GaN))--高电子迁移率晶体管中氮化铝钪(AlScN)栅极电容的复杂性质,氮化镓 HEMT 已成为半导体行业的前沿技术。大量误差指标证明了所提模型的准确性,为准确表征 GaN HEMT 电容建立了一个强大的机制。在论文 "Fractional-calculus analysis of the dynamics of typhoid fever with the effect of vaccination and carriers [2]"中,Jan 等人通过 Caputo-Fabrizio 算子提出了一种新颖的伤寒流行病模型,其中包括疫苗接种和带菌者,以尽量减少每年影响大量人口的全球公共卫生问题。研究结果凸显了分数阶描述拟议模型中记忆效应的有效性。在论文 "Design and performance analysis of 8-port multi-service quad-band MIMO antenna for automotive communication [3]"(用于汽车通信的 8 端口多业务四频 MIMO 天线的设计和性能分析[3])中,Arumugam 等人提出了一种用于汽车通信的具有极化分集原理的低剖面紧凑型 8 端口多频段天线。在论文 "Advanced tree-seed optimization based fractional-order PID controller design for simplified decoupled industrial tank systems [4]"中,Rajagopalan 等人通过考虑非线性动力学、时间延迟、不确定性和交叉耦合效应,分析了耦合罐系统的多种问题。因此,该研究采用了分数阶比例-积分-派生(FOPID)控制器来调节耦合罐系统的液位。此外,还使用树种子算法对控制器进行了优化。
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Guest Editorial for the Special Issue on “Recent Advances in Simulation Methods, Modelling Approaches, and Physical Implementation of Fractional-Order Devices, Circuits, and Systems”

Fractional calculus (FC) is currently associated with phenomena modeling that shows nonlocality and long memory effects in physics and engineering. In particular, the fractional-order operators provide an excellent approach to representing a physical phenomenon with improved accuracy because they capture the contributions from all past events contrary to classical calculus, whose nature is only local. For those reasons, the fractional order can be used as an extra degree of freedom to improve practical applications in various fields, such as analog and digital circuits, chaos theory, electronic devices, cryptography, control, signal processing, robotics, theory of filters, biology, wind turbines, viscoelastic studies, ferromagnetic materials, and so on. From a science and engineering point of view, there are still open problems in fractional calculus, ranging from numerical aspects and modeling techniques to the design and implementation of devices, circuits, and systems. For instance, optimized simulation methods are still needed to compute a proper solution considering the whole memory contributions of fractional operators but simultaneously reducing the computational effort. Classical fractional calculus definitions, as well as new operators (fractional-fractal, fractional operators in the complex plane, variable order calculus, etc.), should continue being explored to obtain novel models of physical phenomena at different levels of abstraction and descriptions, such as physical, circuit, macro, behavioral, and functional. In fractional-order devices, circuits, and systems, one of the challenges consists of implementing the fractional integrodifferential operator as integrators and derivators in the frequency domain, that is, s α $$ {s}^{\alpha } $$ α R $$ \alpha \in R $$ using approximation methods aiming for flexible and non-bulky realizations as there is no fabricated fractional-order capacitor yet commercially available.

The papers in this special issue are devoted to stimulating new ideas and methods and enabling the extension of numerous applications using fractional-order devices, circuits, and systems. High-quality contributions to numerical modeling, design, optimization, and implementation of devices and systems have been reported. In the paper “Fractional order capacitance behavior due to hysteresis effect of ferroelectric material on GaN HEMT devices [1],” Pyngrope et al. introduced a novel fractional-order capacitance model using the Grünwald–Letnikov derivative. The presented study is especially relevant to cope with the complex nature of the aluminum scandium nitride (AlScN) gate capacitance in GaN HEMTs (Gallium nitride (GaN))-High Electron Mobility Transistors, which have become the forefront of the semiconductor industry. The accuracy of the proposed model is demonstrated by numerous error metrics, gathering a robust mechanism for accurately characterizing GaN HEMT capacitance. In this manner, the proposed model represents a powerful approach to accurately describe the GaN HEMT capacitance as fractional order derivatives allow the modeling of noninteger order systems.

In the paper “Fractional-calculus analysis of the dynamics of typhoid fever with the effect of vaccination and carriers [2],” Jan et al. presented a novel epidemic model for typhoid fever with vaccination and carriers via Caputo-Fabrizio operator to minimize a global public health problem that affects considerable people annually. The findings highlighted the effectiveness of fractional order to describe the memory effects in the proposed model. In the paper “Design and performance analysis of 8-port multi-service quad-band MIMO antenna for automotive communication [3],” Arumugam et al. proposed a low-profile compact 8-port multiband antenna with polarization diversity principle for automotive communication. The presented design resonates at frequencies of 1.8, 2.4, 5.2, and 5.8 GHz for GSM, ISM bands, and WLAN wireless services tested on vehicular to intravehicular environments.

In the paper “Advanced tree-seed optimization based fractional-order PID controller design for simplified decoupled industrial tank systems [4],” Rajagopalan et al. analyzed the multiple issues of coupled tank systems by considering nonlinear dynamics, time delays, uncertainties, and cross-coupling effects. As a result, the study employed a fractional-order proportional–integral–derivative (FOPID) controller to regulate the level of a coupled tank system. In addition, the controller was optimized using a tree seed algorithm. Numerical experiments on distinct interconnected tank systems evidenced the efficiency of the fractional controller. In the paper “Exponential stability and numerical analysis of Timoshenko system with dual-phase-lag thermoelasticity [5],” Bouraoui et al. investigated the well-posedness and stability of a thermoelastic Timoshenko system with non-Fourier heat conduction. In particular, a dual-phase-lag (DPL) model with two thermal relaxation times was considered. The semigroup approach and Gearhart–Prüss theorem were valuable tools to demonstrate the existence, uniqueness, and exponential stability, respectively. Finally, in the paper “Comparative analysis of uncontrollable angles in direct torque and stator flux control and rotor flux control strategies: A numerical and experimental study [6],” Alshbib et al. reported an analysis of uncontrollable angles (UAs) in the direct torque control (DTC) algorithm at different operating conditions, including parameter variations in two distinct strategies: Direct torque and stator flux control (DTC-SC) and (DTC-RC). Using data from wide speed, stator and rotor variations, and load changes, the proposed control can be practical to diverse operation modes such as variable speed, variable stator and rotor resistance, and variable load. Experimental tests on a DS1103 platform verified the theoretical analysis.

The Guest Editors are excited to present this special issue. We expect our collected works to inspire researchers to strive for further advances in the emerging fields of devices, circuits, and systems and their applications under fractional-order calculus. The Guest Editors would like to thank the authors of all the high-quality papers submitted on this research topic. We would also like to thank Prof. Giovanni Crupi (Editor-in-Chief of Int J Numer Model) for facilitating this special issue and the reviewers and the Journal's Editorial Board for being very encouraging and supportive. We hope you enjoy reading this special issue in this exciting and fast-evolving field as much as we have done!

The authors declare no conflicts of interest.

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来源期刊
CiteScore
4.60
自引率
6.20%
发文量
101
审稿时长
>12 weeks
期刊介绍: Prediction through modelling forms the basis of engineering design. The computational power at the fingertips of the professional engineer is increasing enormously and techniques for computer simulation are changing rapidly. Engineers need models which relate to their design area and which are adaptable to new design concepts. They also need efficient and friendly ways of presenting, viewing and transmitting the data associated with their models. The International Journal of Numerical Modelling: Electronic Networks, Devices and Fields provides a communication vehicle for numerical modelling methods and data preparation methods associated with electrical and electronic circuits and fields. It concentrates on numerical modelling rather than abstract numerical mathematics. Contributions on numerical modelling will cover the entire subject of electrical and electronic engineering. They will range from electrical distribution networks to integrated circuits on VLSI design, and from static electric and magnetic fields through microwaves to optical design. They will also include the use of electrical networks as a modelling medium.
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