A Fractional Order Circuit Model of the PT

2013 ◽  
Vol 860-863 ◽  
pp. 2304-2308
Author(s):  
Feng Gao ◽  
Gui Shu Liang ◽  
Xin Liu
Keyword(s):  
Theoretical Analysis ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Magnetization Curve ◽  
Circuit Model ◽  
Core Model ◽  
Iron Core ◽  
Saturation Phenomenon ◽  
Nonlinear Part ◽  
Simulation Results

This paper presents a new digital potential transformer (PT) model. Due to the effect of hysteresis and saturation phenomenon, the magnetization curve of iron core has a strong nonlinear. From the perspective of hysteresis effect of iron core, this article presents a PT core model using the theory of fractional calculus, then propose a new PT circuit model. The model simulates the nonlinear part of iron core using the fractional order expressions and can reflect the feature of saturation. Finally it shows the correctness and validity of the model through the theoretical analysis and simulation results.

Fractional Order Modeling and Analysis of Buck-Boost Converter

2015 ◽  
Vol 789-790 ◽  
pp. 842-848
Author(s):  
Li Feng Yi ◽  
Kai Ru Zhang ◽  
Jun Liu
Keyword(s):  
Mathematical Model ◽  
Theoretical Analysis ◽  
Fractional Calculus ◽  
Simulation Model ◽  
Fractional Order ◽  
Theoretical Foundation ◽  
Boost Converter ◽  
Modeling And Analysis ◽  
Simulation Results ◽  
Conduction Mode

Considered the theoretical foundation of fractional order, the fractional mathematical model of the Buck-Boost converter in continuous conduction mode operation is built and analyzed in theory. Based on the improved Oustaloup fractional calculus for filter algorithm, the simulation model is framed by using the Matlab/Simulink software. And the simulation results are compared with that of integer order. It proves the correctness of the fractional order mathematical model and the theoretical analysis.

Bivariate Module-Phase Synchronization of a Fractional-Order Lorenz System in Different Dimensions

2013 ◽  
Vol 8 (3) ◽  
Author(s):  
Xing-Yuan Wang ◽  
Hao Zhang
Keyword(s):  
Numerical Simulation ◽  
Phase Space ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Lorenz System ◽  
Phase Synchronization ◽  
High Dimensional ◽  
Different Dimensions ◽  
Simulation Results ◽  
First Time

Based on the classic Lorenz system, this paper studies the problem of bivariate module-phase synchronizations in a fractional-order Lorenz system, bivariate module-phase synchronizations in a fractional-order spatiotemporal coupled Lorenz system, and malposed module-phase synchronization in a fractional-order spatiotemporal coupled Lorenz system. It is the first time, to our knowledge, that module-phase synchronization in fractional-order high-dimensional systems is applied. According to the fractional calculus techniques and spatiotemporal theory, we design controllers and achieve synchronizations both in module space and phase space at the same time. In the simulation, we discuss the bivariate module-phase synchronization and malposed module-phase synchronization. The numerical simulation results demonstrate the validity of controllers.

scholarly journals Stabilization and Tracking Control of Inverted Pendulum Using Fractional Order PID Controllers

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Sunil Kumar Mishra ◽  
Dinesh Chandra
Keyword(s):  
Fractional Calculus ◽  
Fractional Order ◽  
Tracking Control ◽  
Inverted Pendulum ◽  
Fitness Function ◽  
Pid Controllers ◽  
Simulink Model ◽  
System A ◽  
Simulation Results ◽  
Fractional Order Pid

This work focuses on the use of fractional calculus to design robust fractional-order PID (PIλDμ) controller for stabilization and tracking control of inverted pendulum (IP) system. A particle swarm optimisation (PSO) based direct tuning technique is used to design two PIλDμcontrollers for IP system without linearizing the actual nonlinear model. The fitness function is minimized by running the SIMULINK model of IP system according to the PSO program in MATLAB. The performance of proposed PIλDμcontrollers is compared with two PID controllers. Simulation results are also obtained by adding disturbances to the model to show the robustness of the proposed controllers.

The Simulation Study of New Boost-ZVT Circuit Based on Pspice

2014 ◽  
Vol 644-650 ◽  
pp. 3821-3824
Author(s):  
Yue Feng Wu
Keyword(s):  
Theoretical Analysis ◽  
Simulation Study ◽  
Circuit Model ◽  
Soft Switching ◽  
Simulation Based ◽  
Simulation Results ◽  
Low Efficiency ◽  
Switch Temperature ◽  
Switch Circuit

Because the shortcoming of the traditional Boost-ZVT has large shutdown losses for the auxiliary switch on hard-working, the circuit has disadvantage of low efficiency. The paper discusses a new Boost-ZVT circuit, and the new circuit designs the absorption circuit in the auxiliary switch circuit to achieve soft turn-off. Compared to ordinary Boost-ZVT circuit, all the switches work in a state of soft-switching for an improved Boost-ZVT circuit. So the new Boost-ZVT circuit can improve the efficiency of the system, at the same time it can eliminate the interference because of switch temperature rising, and can ensure the reliability of the whole system. Finally, the paper builds circuit model and make simulation based on PSPICE, and the simulation results show that the theoretical analysis is correct.

scholarly journals Realization of a fractional-order RLC circuit via constant phase element

2021 ◽  
Author(s):  
Riccardo Caponetto ◽  
Salvatore Graziani ◽  
Emanuele Murgano
Keyword(s):  
Experimental Data ◽  
Carbon Black ◽  
Fractional Order ◽  
Constant Phase Element ◽  
Polymeric Matrix ◽  
Fractional Order Systems ◽  
New Device ◽  
Rlc Circuit ◽  
Simulation Results

AbstractIn the paper, a fractional-order RLC circuit is presented. The circuit is realized by using a fractional-order capacitor. This is realized by using carbon black dispersed in a polymeric matrix. Simulation results are compared with the experimental data, confirming the suitability of applying this new device in the circuital implementation of fractional-order systems.

Mkhitar Djrbashian and his contribution to Fractional Calculus

2020 ◽  
Vol 23 (6) ◽  
pp. 1797-1809
Author(s):  
Sergei Rogosin ◽  
Maryna Dubatovskaya
Keyword(s):  
Cauchy Problem ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Approximation Theory ◽  
Fractional Derivatives ◽  
Complex Analysis ◽  
Integral Transforms ◽  
Modern Theory ◽  
Survey Paper ◽  
The Cauchy Problem

Abstract This survey paper is devoted to the description of the results by M.M. Djrbashian related to the modern theory of Fractional Calculus. M.M. Djrbashian (1918-1994) is a well-known expert in complex analysis, harmonic analysis and approximation theory. Anyway, his contributions to fractional calculus, to boundary value problems for fractional order operators, to the investigation of properties of the Queen function of Fractional Calculus (the Mittag-Leffler function), to integral transforms’ theory has to be understood on a better level. Unfortunately, most of his works are not enough popular as in that time were published in Russian. The aim of this survey is to fill in the gap in the clear recognition of M.M. Djrbashian’s results in these areas. For same purpose, we decided also to translate in English one of his basic papers [21] of 1968 (joint with A.B. Nersesian, “Fractional derivatives and the Cauchy problem for differential equations of fractional order”), and were invited by the “FCAA” editors to publish its re-edited version in this same issue of the journal.

scholarly journals Current-Mode Third-Order Quadrature Oscillator Using CDTAs

2009 ◽  
Vol 2009 ◽  
pp. 1-5 ◽  
Author(s):  
Jiun-Wei Horng
Keyword(s):  
Theoretical Analysis ◽  
Phase Difference ◽  
Oscillation Frequency ◽  
Current Mode ◽  
Third Order ◽  
Quadrature Oscillator ◽  
Oscillation Condition ◽  
Transconductance Amplifiers ◽  
Simulation Results ◽  
A Current

This paper describes a current-mode third-order quadrature oscillator based on current differencing transconductance amplifiers (CDTAs). Outputs of two current-mode sinusoids with90°phase difference are available in the quadrature oscillator circuit. The oscillation condition and oscillation frequency are orthogonal controllable. The proposed circuit employs only grounded capacitors and is ideal for integration. Simulation results are included to confirm the theoretical analysis.

scholarly journals Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Wang ◽  
Yuangui Zhou ◽  
Jianyi Xue ◽  
Delan Zhu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Wide Class ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Order System ◽  
Fractional Order Calculus ◽  
Simulation Results ◽  
The Stability

We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

New repetitive motion planning scheme with cube end-effector planning precision for redundant robotic manipulators

Robotica ◽  
2021 ◽  
pp. 1-22
Author(s):  
Limin Shen ◽  
Yuanmei Wen
Keyword(s):  
Theoretical Analysis ◽  
Motion Planning ◽  
Robotic Manipulators ◽  
Robotic Manipulator ◽  
Repetitive Motion ◽  
End Effector ◽  
Difference Formula ◽  
Planning Scheme ◽  
Simulation Results ◽  
The Difference

Abstract Repetitive motion planning (RMP) is important in operating redundant robotic manipulators. In this paper, a new RMP scheme that is based on the pseudoinverse formulation is proposed for redundant robotic manipulators. Such a scheme is derived from the discretization of an existing RMP scheme by utilizing the difference formula. Then, theoretical analysis and results are presented to show the characteristic of the proposed RMP scheme. That is, this scheme possesses the characteristic of cube pattern in the end-effector planning precision. The proposed RMP scheme is further extended and studied for redundant robotic manipulators under joint constraint. Based on a four-link robotic manipulator, simulation results substantiate the effectiveness and superiority of the proposed RMP scheme and its extended one.

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