scholarly journals Application of Fractional-Order Calculus to Improve the Mathematical Model of a Two-Mass System with a Long Shaft

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1854
Author(s):  
Andriy Lozynskyy ◽  
Andriy Chaban ◽  
Tomasz Perzyński ◽  
Andrzej Szafraniec ◽  
Lidiia Kasha
Keyword(s):  
Mathematical Model ◽  
Fractional Order ◽  
Mass System ◽  
Electric Drives ◽  
Distributed Parameters ◽  
Time Space ◽  
Joint Coordinates ◽  
Sufficient Degree ◽  
Fractional Order Integrator ◽  
The Mathematical Model

Based on the general theory of fractional order derivatives and integrals, application of the Caputo–Fabrizio operator is analyzed to improve a mathematical model of a two-mass system with a long shaft and concentrated parameters. Thus, the real transmission of complex electric drives, which consist of long shafts with a sufficient degree of adequacy, is presented as a two-mass system. Such a system is described by ordinary fractional order differential equations. In addition, it is well known that an elastic mechanical wave, propagating along a drive transmission with a long stiff shaft, creates a retardation effect on distribution of the time–space angular velocity, the rotation angle of the shaft, and its elastic moment. The approach proposed in the current work helps to take in account the moving elastic wave along the shaft of electric drive mechanism. On this basis, it is demonstrated that the use of the fractional order integrator in the model for the elastic moment enables it to reproduce real transient processes in the joint coordinates of the system. It also provides an accuracy equivalent to the model with distributed parameters. The distance between the traditional model and the model in which the fractional integral is used for the elastic moment modelling in a two-mass system, with a long shaft, is analyzed.

scholarly journals Solution of Fractional Order System of Bagley-Torvik Equation Using Evolutionary Computational Intelligence

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Muhammad Asif Zahoor Raja ◽  
Junaid Ali Khan ◽  
Ijaz Mansoor Qureshi
Keyword(s):  
Genetic Algorithm ◽  
Neural Networks ◽  
Mathematical Model ◽  
Fractional Order ◽  
Computational Intelligence ◽  
Pattern Search ◽  
Fractional Order System ◽  
Order System ◽  
Search Technique ◽  
The Mathematical Model

A stochastic technique has been developed for the solution of fractional order system represented by Bagley-Torvik equation. The mathematical model of the equation was developed with the help of feed-forward artificial neural networks. The training of the networks was made with evolutionary computational intelligence based on genetic algorithm hybrid with pattern search technique. Designed scheme was successfully applied to different forms of the equation. Results are compared with standard approximate analytic, stochastic numerical solvers and exact solutions.

scholarly journals CMOS OTA-Based Filters for Designing Fractional-Order Chaotic Oscillators

2021 ◽  
Vol 5 (3) ◽  
pp. 122
Author(s):  
Martín Alejandro Valencia-Ponce ◽  
Perla Rubí Castañeda-Aviña ◽  
Esteban Tlelo-Cuautle ◽  
Victor Hugo Carbajal-Gómez ◽  
Victor Rodolfo González-Díaz ◽  
...  
Keyword(s):  
Fractional Order ◽  
Complementary Metal Oxide Semiconductor ◽  
Cmos Technology ◽  
Oxide Semiconductor ◽  
Chaotic Oscillators ◽  
Operational Transconductance Amplifiers ◽  
Fractional Order Integrator ◽  
The Mathematical Model ◽  
Good Agreement

Fractional-order chaotic oscillators (FOCOs) have shown more complexity than integer-order chaotic ones. However, the majority of electronic implementations were performed using embedded systems; compared to analog implementations, they require huge hardware resources to approximate the solution of the fractional-order derivatives. In this manner, we propose the design of FOCOs using fractional-order integrators based on operational transconductance amplifiers (OTAs). The case study shows the implementation of FOCOs by cascading first-order OTA-based filters designed with complementary metal-oxide-semiconductor (CMOS) technology. The OTAs have programmable transconductance, and the robustness of the fractional-order integrator is verified by performing process, voltage and temperature variations as well as Monte Carlo analyses for a CMOS technology of 180 nm from the United Microelectronics Corporation. Finally, it is highlighted that post-layout simulations are in good agreement with the simulations of the mathematical model of the FOCO.

Parametric Analysis of the Ride Comfort of Indian Railway Vehicle

2021 ◽  
Vol 13 (4) ◽  
Author(s):  
Rakesh Chandmal Sharma ◽  
Sono Bhardawaj ◽  
Mohd Avesh ◽  
Neeraj Sharma
Keyword(s):  
Mathematical Model ◽  
Parametric Analysis ◽  
Degrees Of Freedom ◽  
Ride Comfort ◽  
Rear Wheel ◽  
Railway Vehicle ◽  
Mass System ◽  
Rail Vehicle ◽  
Indian Railway ◽  
The Mathematical Model

This paper focuses to the parametric analysis of Indian Railway Rajdhani (LHB) coach. A suitable mathematical model of 40 degrees of freedom (DOF) is formulated by Lagrangian method. The mathematical model of rail-vehicle is modelled by considering eleven mass system containing of backseat support (without cushion), a seat, a car body, two (front and Rear) bolsters, two (front and Rear) bogie frame and four wheelaxles (front bogie front and rear wheel axles and rear bogie front and rear wheel axles. The vehicle is simulated to travel at speed of 100 km/hr on a tangent track. The results from the simulation are validated by comparing the same with the results from experimental data which is acquired from research designs and standards organization (RDSO), Lucknow (India). The parametric analysis is performed to estimate the effect of different parameters of rail-vehicle on the ride behaviour.

The Filtering Mechanism Modeling and Simulation of Passive Power Filter Based on Differentiator Circuit

2012 ◽  
Vol 430-432 ◽  
pp. 1593-1596
Author(s):  
Wan Neng Yu ◽  
Su Wen Li ◽  
Min Ying Zheng
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Fractional Order ◽  
Integer Order ◽  
Filter Performance ◽  
Power Filter ◽  
Fractional Order Differential Equations ◽  
Passive Power ◽  
The Mathematical Model

Traditional continuous-time filters are of integer order which the power loss of passive power filter is general very much. However, using fractional calculus, filters may also be represented by the more general fractional-order differential equations. In this work, firstly, the passive elements were described with fractional-order differential equations depending on the introduction of fractional calculus application research. Secondly, the mathematical model of fractional-order filters was derived and discussed which includes high impedance at a certain frequency and low impedance at others, and the integer-order filters are only a tight subset of fractional-order filters that are testified. At last, the filter design idea to the fractional-order domain is developed and the better filter performance of the fractional-order passive power filter is validated by the mathematical model analysis and simulation results.

Fractional Order Thermoelastic Waves of Cylindrical Gold Nano-Beam

2013 ◽  
Author(s):  
Hamdy M. Youssef ◽  
Khaled A. Elsibai ◽  
Alaa A. El-Bary
Keyword(s):  
Mathematical Model ◽  
Fractional Order ◽  
Thermal Load ◽  
Laplace Transforms ◽  
Thermal Waves ◽  
Governing Equations ◽  
Elastic Parameters ◽  
The Impact ◽  
The Mathematical Model ◽  
Thermoelastic Waves

In this work, a mathematical model of cylindrical nano-beam with constant elastic parameters with fractional order heat conduction will be constructed. The governing equations of the mathematical model will be taken when the beam is quiescent first. Laplace transforms techniques will be used to get the general solution for any set of boundary conditions. The solution will be obtained for a certain model when the beam is subjected to thermal load. Inversion of Laplace transforms will be obtained numerically, and the results will be presented graphically with some comparisons to study the impact of thermal load and the effect of the fractional order parameter on the speed of progress of mechanical and thermal waves through the beam.

scholarly journals Mathematical model of a flexible asymmetrical rotor for active magnetic bearing reaction wheel

2018 ◽  
Vol 158 ◽  
pp. 01025
Author(s):  
Miroslav Polyakov ◽  
Anatoliy Lipovtsev ◽  
Vladimir Lyanzburg
Keyword(s):  
Mathematical Model ◽  
Lagrange Equation ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Active Magnetic Bearings ◽  
Ansys Software ◽  
Mass System ◽  
Linear Elastic ◽  
Orbit Control ◽  
The Mathematical Model

The paper introduces the mathematical model of rotor for active magnetic bearing reaction/momentum wheels, used as actuator in spacecraft attitude and orbit control system. Developed model is used for estimation of critical speeds and forced oscillation magnitudes with a glance of the rotor modes. Rotor is considered as a two-mass system, consisting of a shaft and a rim, active magnetic bearings are assumed to be a linear elastic springs. The equations of the rotor motion are derived using the Lagrange equation. Developed model is verified by comparing the calculated Campbell diagrams with the results of the finite-element modal analysis, performed in the ANSYS software.

scholarly journals Mathematical Model of Self-Discharge for Supercapacitors

2020 ◽  
Vol 13 (5) ◽  
pp. 77-81
Author(s):  
Sheryl Dinglasan Fenol ◽  
◽  
Felicito S. Caluyo
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Fractional Order ◽  
Discharge Behavior ◽  
Constant Phase Elements ◽  
The Mathematical Model

Self-discharge is one of the most important considerations in manufacturing supercapacitors. This paper discussed two dynamic mathematical models of self-discharge behavior of supercapacitor from the concept of regular capacitor mechanisms and impedance of an R-C circuit, and constant phase elements (CPE), impedance of R-CPE, and fractional- order derivatives. The mathematical model was derived from each other to show their equality and relationships.

scholarly journals Mathematical modeling of bioprocesses with the use of fractional order derivatives

2021 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Vladimira Rumenova Suvandzhieva
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Fractional Order ◽  
Classical Case ◽  
Integer Order ◽  
Wolfram Mathematica ◽  
Specific Behaviour ◽  
Mathematica Software ◽  
The Mathematical Model ◽  
Derivatives Of

This work brings together two recently discussed topics: mathematical modeling of a bioreactor and working with derivatives of non-integer order. Generally, it turns out that it is reasonable to replace the integer order derivatives in some of the already well known mathematical models describing bioprocesses with fractional order ones. However, the specific structure of such type of derivatives makes the study of the properties of the models a real challenge. This work contains primary results for modeling of a bioreactor with appropriately selected numerical approximations. Different scenarios are taken into consideration: starting from the simplest one - without mortality and then complicating by adding nonzero mortality term. In the classical case the solution of the system of differential equations describing the process has a specific behaviour in terms of monotonicity. Therefore, the focus of the further examinations is to find out whether it is possible to generalize the model into a fractional order one such that the key properties considering monotonicity still hold. The results show that the latter requires certain dependencies between the orders of the derivatives in the mathematical model. The hypothesis is based on two types of experiments which are described in detail. Lotka-Volterra and Monod specific growth rate are used in the mathematical model. The paper contains figures which illustrate the results from different numerical computations performed via Wolfram Mathematica software.

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