scholarly journals Analog Realization of Fractional-Order Capacitor and Inductor via the Caputo–Fabrizio Derivative

2021 ◽  
Vol 25 (3) ◽  
pp. 291-300
Author(s):  
Manjie Ran ◽  
◽  
Xiaozhong Liao ◽  
Da Lin ◽  
Ruocen Yang
Keyword(s):  
Numerical Simulation ◽  
Mathematical Models ◽  
Fractional Order ◽  
Circuit Simulation ◽  
Circuit Analysis ◽  
Electrical Characteristics ◽  
Electronic Components ◽  
Electrical Circuits ◽  
Impedance Models

Capacitors and inductors have been proven to exhibit fractional-order characteristics. Therefore, the establishment of fractional-order models for circuits containing such components is of great significance in practical circuit analysis. This study establishes the impedance models of fractional-order capacitors and inductors based on the Caputo–Fabrizio derivative and performs the analog realization of fractional-order electronic components. The mathematical models of fractional RC, RL, and RLC electrical circuits are deduced and verified via a comparison between the numerical simulation and the corresponding circuit simulation. The electrical characteristics of the fractional circuits are analyzed. This study not only enriches the models of fractional capacitors and inductors, but can also be applied to the description of circuit characteristics to obtain more accurate results.

Fractional-Order Modeling and Simulation of Magnetic Coupled Boost Converter in Continuous Conduction Mode

2018 ◽  
Vol 28 (05) ◽  
pp. 1850061 ◽  
Author(s):  
Zirui Jia ◽  
Chongxin Liu
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Fractional Order ◽  
Transfer Functions ◽  
Circuit Simulation ◽  
Boost Converter ◽  
Averaged Model ◽  
Conduction Mode ◽  
State Average ◽  
Continuous Conduction Mode

By using fractional-order calculus theory and considering the condition that capacitor and inductor are naturally fractional, we construct the fractional mathematical model of the magnetic coupled boost converter with tapped-inductor in the operation of continuous conduction mode (CCM). The fractional state average model of the magnetic coupled boost converter in CCM operation is built by exploiting state average modeling method. In these models, the effects of coupling factor, which is viewed as one generally, are directly pointed out. The DC component, the AC component, the transfer functions and the requirements of the magnetic coupled boost converter in CCM operation are obtained and investigated on the basis of the state averaged model as well as its fractional mathematical model. Using the modified Oustaloup’s method for filter approximation algorithm, the derived models are simulated and compared using Matlab/Simulink. In order to further verify the fractional model, circuit simulation is implemented. Furthermore, the differences between the fractional-order mathematical models and the corresponding integer-order mathematical models are researched. Results of the model and circuit simulations validate the effectiveness of theoretical analysis.

scholarly journals Drive-Response Synchronization of a Fractional-Order Hyperchaotic System and Its Circuit Implementation

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Darui Zhu ◽  
Chongxin Liu ◽  
Bingnan Yan
Keyword(s):  
Numerical Simulation ◽  
Fractional Order ◽  
Circuit Simulation ◽  
Hyperchaotic System ◽  
Oscillator Circuit ◽  
Response System ◽  
Fractional Oscillator ◽  
Simulation Results ◽  
The Stability ◽  
Synchronization Scheme

A novel fractional-order hyperchaotic system is proposed; the theoretical analysis and numerical simulation of this system are studied. Based on the stability theory of fractional calculus, we propose a novel drive-response synchronization scheme. In order to achieve this synchronization control, the Adams-Bashforth-Moulton algorithm is studied. And then, a drive-response synchronization controller is designed to realize the synchronization of the drive and response system, and the simulation results are given. At last, the fractional oscillator circuit of the new fractional-order hyperchaotic system is designed based on the EWB software, and it is verified that the simulation results of the fractional-order oscillator circuit are consistent with the numerical simulation results through circuit simulation.

scholarly journals Complexity and Chimera States in a Network of Fractional-Order Laser Systems

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 341
Author(s):  
Shaobo He ◽  
Hayder Natiq ◽  
Santo Banerjee ◽  
Kehui Sun
Keyword(s):  
Numerical Simulation ◽  
Numerical Solution ◽  
Bifurcation Diagram ◽  
Fractional Order ◽  
Dynamical Model ◽  
Chimera States ◽  
Laser Systems ◽  
Complexity Algorithm ◽  
Derivative Order

By applying the Adams-Bashforth-Moulton method (ABM), this paper explores the complexity and synchronization of a fractional-order laser dynamical model. The dynamics under the variance of derivative order q and parameters of the system have examined using the multiscale complexity algorithm and the bifurcation diagram. Numerical simulation outcomes demonstrate that the system generates chaos with the decreasing of q. Moreover, this paper designs the coupled fractional-order network of laser systems and subsequently obtains its numerical solution using ABM. These solutions have demonstrated chimera states of the proposed fractional-order laser network.

scholarly journals A Comparison of Time-Domain Implementation Methods for Fractional-Order Battery Impedance Models

Energies ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4415
Author(s):  
Brian Ospina Agudelo ◽  
Walter Zamboni ◽  
Eric Monmasson
Keyword(s):  
Fractional Order ◽  
Time Domain ◽  
Li Ion Batteries ◽  
Simulation Framework ◽  
Frequency Range ◽  
Interesting Approach ◽  
Li Ion ◽  
Impedance Parameters ◽  
Impedance Models ◽  
Made In

This paper is a comparative study of the multiple RC, Oustaloup and Grünwald–Letnikov approaches for time domain implementations of fractional-order battery models. The comparisons are made in terms of accuracy, computational burden and suitability for the identification of impedance parameters from time-domain measurements. The study was performed in a simulation framework and focused on a set of ZARC elements, representing the middle frequency range of Li-ion batteries’ impedance. It was found that the multiple RC approach offers the best accuracy–complexity compromise, making it the most interesting approach for real-time battery simulation applications. As for applications requiring the identification of impedance parameters, the Oustaloup approach offers the best compromise between the goodness of the obtained frequency response and the accuracy–complexity requirements.

The Calculation Method of Accurate Shaping Curve of Inside Right-Angle Step in Cross Wedge Rolling

2010 ◽  
Vol 37-38 ◽  
pp. 1416-1420 ◽  
Author(s):  
Ran Zhao ◽  
Kang Sheng Zhang ◽  
Zheng Huan Hu
Keyword(s):  
Numerical Simulation ◽  
Mathematical Models ◽  
Contact Zone ◽  
Calculation Method ◽  
Cross Wedge Rolling ◽  
Forming Process

Deep study on Inside Right-angle Step (IRS) forming process was conducted to improve the precision of its (IRS) forming. According to its actual forming process, the zone, or the undeformed zone, was looked as semi-spiral declined cone and excluded the contact zone. A new algorithm was developed for calculating the size of the undeformed zone. More simple mathematical models and expressions weredeveloped for solving the shaping curve. The model was verified in terms of its simplicity and correctness based on the numerical simulation.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

scholarly journals APPLICATION OF ABOODH TRANSFORM ON SOME FRACTIONAL ORDER MATHEMATICAL MODELS

2020 ◽  
Vol 20 (3) ◽  
pp. 661-672
Author(s):  
JAWARIA TARIQ ◽  
JAMSHAD AHMAD
Keyword(s):  
Mathematical Models ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Physical Phenomena ◽  
Convergent Solution

In this work, a new emerging analytical techniques variational iteration method combine with Aboodh transform has been applied to find out the significant important analytical and convergent solution of some mathematical models of fractional order. These mathematical models are of great interest in engineering and physics. The derivative is in Caputo’s sense. These analytical solutions are continuous that can be used to understand the physical phenomena without taking interpolation concept. The obtained solutions indicate the validity and great potential of Aboodh transform with the variational iteration method and show that the proposed method is a good scheme. Graphically, the movements of some solutions are presented at different values of fractional order.

scholarly journals LabVIEW Interface for Controlling a Test Bench for Photovoltaic Modules and Extraction of Various Parameters

2015 ◽  
Vol 6 (3) ◽  
pp. 498 ◽  
Author(s):  
Abderrezak Guenounou ◽  
Ali Malek ◽  
Michel Aillerie ◽  
Achour Mahrane
Keyword(s):  
Numerical Simulation ◽  
Mathematical Models ◽  
Energy Production ◽  
Test Bench ◽  
Graphical Interface ◽  
Detailed Report ◽  
Photovoltaic Modules ◽  
Pv Modules ◽  
Computer Controlled ◽  
Physical Phenomena

Numerical simulation using mathematical models that take into account physical phenomena governing the operation of solar cells is a powerful tool to predict the energy production of photovoltaic modules prior to installation in a given site. These models require some parameters that manufacturers do not generally give. In addition, the availability of a tool for the control and the monitoring of performances of PV modules is of great importance for researchers, manufacturers and distributors of PV solutions. In this paper, a test and characterization protocol of PV modules is presented. It consists of an outdoor computer controlled test bench using a LabVIEW graphical interface. In addition to the measuring of the IV characteristics, it provides all the parameters of PV modules with the possibility to display and print a detailed report for each test. After the presentation of the test bench and the developed graphical interface, the obtained results based on an experimental example are presented.

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