Mathematical model for the analysis of group modes of induction motors when fed from a common source.

2020 ◽  
Vol 14 (1) ◽  
pp. 30-33
Author(s):  
E. NIEMTSEV ◽  
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Induction Motors ◽  
Common Source ◽  
Electric Drives ◽  
Group Operation ◽  
Operating Modes ◽  
Asynchronous Motors ◽  
The Right ◽  
Maintenance Personnel

The article analyzes the operating modes and transients that occur when starting, stopping and changing the load in electric drives with induction motors. The relevance of the need for such studies for drives with powerful asynchronous motors that are connected to the same energy source and start or stop at the same time is proved. The information obtained will allow maintenance personnel and the available automation and telecommunications facilities to make the right and timely decisions for the effective management of electric drives. A mathematical model has been compiled for analyzing the modes of group operation of asynchronous motors powered by a common source in order to determine the parameters of such work. When creating the model, the voltage of the power source, as well as the parameters and design features of induction motors, were chosen as the initial parameters. The developed mathematical model contains a system of differential equations for the analysis of group operation of induction motors and demonstrates the possibilities of developing the theory of group operation of asynchronous motors. As an auxiliary mathematical technique for recording the physical properties of asynchronous motors, the concept of the inverse submatrix was used, and when composing differential equations, the asymmetry of the voltage at the load nodes was taken into account. The developed mathematical model makes it possible to determine the principles for diagnosing the operation of groups of induction motors connected to a common source by registering current ripples arising in the supply network and changing the consumed power and thus indirectly increase the reliability of asynchronous motors in electric drives of technological mechanisms under various load conditions.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

scholarly journals An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Alexander Arguchintsev ◽  
Vasilisa Poplevko
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Hyperbolic Equations ◽  
Control Methods ◽  
The Right ◽  
The Cost ◽  
Optimal Control Methods

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.

Filippov solutions of vector Dirichlet problems

2020 ◽  
Vol 70 (2) ◽  
pp. 401-416
Author(s):  
Hana Machů
Keyword(s):  
Differential Equations ◽  
The State ◽  
State Variables ◽  
Dirichlet Problems ◽  
Filippov Solutions ◽  
Natural Notion ◽  
Growth Restrictions ◽  
The One ◽  
The Right ◽  
Effective Growth

Abstract If in the right-hand sides of given differential equations occur discontinuities in the state variables, then the natural notion of a solution is the one in the sense of Filippov. In our paper, we will consider this type of solutions for vector Dirichlet problems. The obtained theorems deal with the existence and localization of Filippov solutions, under effective growth restrictions. Two illustrative examples are supplied.

scholarly journals Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1309
Author(s):  
P. R. Gordoa ◽  
A. Pickering
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Elliptic Functions ◽  
Coupled System ◽  
Ultrasonic Waves ◽  
Partial Differential ◽  
Special Cases ◽  
Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

Mathematical model implementation in conditions of uncertainty and possible risks

2021 ◽  
pp. 137-145
Author(s):  
A. Kravtsov ◽  
◽  
D. Levkin ◽  
O. Makarov ◽  
◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Mathematical Model ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Layer Structure ◽  
Boundary Value ◽  
Goal Function ◽  
Cauchy Problems ◽  
System Of Differential Equations

The article presents the theoretical and methodological principles for forecasting and mathematical modeling of possible risks in technological and biotechnological systems. The authors investigated in details the possible approach to the calculation of the goal function and its parameters. Considerable attention is paid to substantiating the correctness of boundary value problems and Cauchy problems. In mechanics, engineering, and biology, Cauchy problems and boundary value problems of differential equations are used to model physical processes. It is important that differential equations have a single physically sound solution. The authors of this article investigate the specific features of boundary value problems and Cauchy problems with boundary conditions in a two-point medium, and determine the conditions for the correctness of such problems in the spaces of power growth functions. The theory of pseudo-differential operators in the space of generalized functions was used to prove the correctness of boundary value problems. The application of the obtained results will make it possible to guarantee the correctness of mathematical models built in conditions of uncertainty and possible risks. As an example of a computational mathematical model that describes the state of the studied object of non-standard shape, the authors considered the boundary value problem of the system of differential equations of thermal conductivity for the embryo under the action of a laser beam. For such a boundary value problem, it is impossible to guarantee the existence and uniqueness of the solution of the system of differential equations. To be sure of the existence of a single solution, it is necessary either not to take into account the three-layer structure of the microbiological object, or to determine the conditions for the correctness of the boundary value problem. Applying the results obtained by the authors, the correctness of the boundary value problem of systems of differential equations of thermal conductivity for the embryo is proved taking into account the three-layer structure of the microbiological object. This makes it possible to increase the accuracy and speed of its implementation on the computer. Key words: forecasting, risk, correctness, boundary value problems, conditions of uncertainty

Efficiency Increasing of Traction Electric Drives with Induction Motors and Vector Control System

2021 ◽  
Vol 92 (9) ◽  
pp. 476-480
Author(s):  
Yu. M. Inkov ◽  
A. S. Kosmodamianskiy ◽  
A. A. Pugachev ◽  
S. V. Morozov
Keyword(s):  
Control System ◽  
Vector Control ◽  
Induction Motors ◽  
Electric Drives ◽  
Vector Control System

DIFFERENTIAL EQUATIONS FOR TRAIN STARTING WITH ELASTIC CONNECTIONS

2021 ◽  
Vol 2 ◽  
pp. 18-26
Author(s):  
I.P. POPOV
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Friction Force ◽  
Static Friction ◽  
Longitudinal Vibrations ◽  
Maximum Tension ◽  
Inert Mass ◽  
The Moment ◽  
Elastic Couplings ◽  
Selection Of

The starting mode for the train is the most difficult. An effective method of pulling is the selection of coupling clearances. In this case, the cars are set in motion sequentially and the inert mass, as well as the static friction force immediately at the moment of starting, are minimal. This method has two significant drawbacks - a small fixed value of the gaps in the couplings and the shock nature of the impulse transfer. These disadvantages can be avoided by using elastically deformable couplings. The aim of this work is to construct a mathematical model of "easy" starting of a train with elastic couplings. The softening of the train start-off mode is essentially due to the replacement of the simultaneous start-off of the sections with alternate ones. To exclude longitudinal vibrations of the composition, after reaching the maximum tension of the coupling, the possibility of its harmonic compression should be mechanically blocked.

scholarly journals Resolvent of nonautonomous linear delay functional differential equations

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Joël Blot ◽  
Mamadou I. Koné
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Differentiable Function ◽  
Functional Differential Equations ◽  
Initial Value ◽  
Complete Proof ◽  
Right Hand ◽  
Linear Delay ◽  
Functional Differential ◽  
The Right

AbstractThe aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] under the assumption alone of the continuity of the right-hand side with respect to the time,when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.

scholarly journals Complex Electronic Protection for Low-voltage Three-phase Induction Motors

2020 ◽  
Vol 11 ◽  
pp. 11-17
Author(s):  
Gabriel Nicolae Popa ◽  
Corina Maria Diniș
Keyword(s):  
Induction Motors ◽  
Low Voltage ◽  
Short Circuit ◽  
Electronic Devices ◽  
General Purpose ◽  
Two Phase ◽  
Dc Voltage ◽  
Electric Drives ◽  
Normal Limits ◽  
Three Phase

Low-voltage three-phase induction motors are most often used in industrial electric drives. Electric motors must be protected by electric and/or electronic devices against: short-circuit, overloads, asymmetrical currents, two-phase voltage operation, under-voltage, and over-temperature. To design the electronic protection currents, voltages and temperature must be measured to determine whether they fall within normal limits. The electronic protection was design into low capacity PLC. The paper presents the designs and analysis of complex electronic protection for general purpose low-voltage three-phase induction motors. The electronic protection has Hall transducers and conversion electronic devices for AC currents to DC voltages, AC voltages to DC voltage, temperature to DC voltage, a low capacity PLC, switches, motor’s power contactors, and signalling lamps has been developed. Experiments with complex electronic protection, for different faults are presented. The proposed protection has the advantages of incorporating all usual protections future for the low-voltage three-phase induction motors.

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