scholarly journals Analysis of modern modeling methods in problems of stabilization of motions of mechatronic systems with differential constraints

2018 ◽  
Vol 7 (2.23) ◽  
pp. 9
Author(s):  
Krasinskiy A.Ya ◽  
Krasinskaya E.M.
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Operating Mode ◽  
Mechatronic Systems ◽  
Natural Behavior ◽  
Holonomic Constraints ◽  
Operating Modes ◽  
Modeling Methods ◽  
Nonlinear Mathematical Models ◽  
Steady Motions

The most important problem of controlling mechatronic systems is the development of methods for the fullest possible application of the properties of our own (without the application of controls) motions of the object for the optimal use of all available resources. The basis of this can be a non-linear mathematical model of the object, which allows to determine the degree of minimally necessary interference in the natural behavior of an object with the purpose of stable implementation of a given operating mode. The operating modes of the vast majority of modern mechatronic systems are realized due to the steady motions (equilibrium positions and stationary motions) of their mechanical components, and often these motions are constrained by connections of various kinds. The paper gives an analysis of methods for obtaining nonlinear mathematical models in stabilization problems of mechanical systems with differential holonomic and non-holonomic constraints. 

INDUSTRIAL POLLUTION AND ASTHMA: A MATHEMATICAL MODEL

2000 ◽  
Vol 08 (04) ◽  
pp. 347-371 ◽  
Author(s):  
MINI GHOSH
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Differential Equations ◽  
Mathematical Models ◽  
Stability Theory ◽  
Industrial Pollution ◽  
Air Pollutant ◽  
Logistic Growth ◽  
Nonlinear Mathematical Models

In this paper, some nonlinear mathematical models are proposed and analyzed to study the spread of asthma due to inhaled pollutants from Industry. The following two types of demographics are considered here; (i) population with constant immigration, (ii) population with logistic growth. In each type of demography, the following three cases have been considered regarding the release of pollutant into the environment; (i) when emission of the pollutant into the environment is constant, (ii) when emission of the pollutant is population dependent, and (iii) when emission of the pollutant is periodic. Using stability theory of differential equations and computer simulation, it is shown that due to an increase in the air pollutant, the asthmatic (diseased) population increases in the region under consideration.

scholarly journals Asymptotic Properties of One Mathematical Model in Food Engineering under Stochastic Perturbations

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3013
Author(s):  
Leonid Shaikhet
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Numerical Simulations ◽  
Wide Class ◽  
Asymptotic Properties ◽  
Nonlinear Mathematical Model ◽  
Simple Criterion ◽  
Stochastic Perturbations ◽  
Food Engineering ◽  
Nonlinear Mathematical Models

For the example of one nonlinear mathematical model in food engineering with several equilibria and stochastic perturbations, a simple criterion for determining a stable or unstable equilibrium is reported. The obtained analytical results are illustrated by detailed numerical simulations of solutions of the considered Ito stochastic differential equations. The proposed criterion can be used for a wide class of nonlinear mathematical models in different applications.

scholarly journals INVESTIGATION OF OPERATING MODES OF FREQUENCY-REGULATED ELECTRIC DRIVE OF PUMPJACK

2019 ◽  
Vol 20 (11-12) ◽  
pp. 56-64
Author(s):  
R. F. Yarish ◽  
A. R. Garifullina ◽  
R. I. Garifullin ◽  
A. N. Yakunin
Keyword(s):  
Mathematical Model ◽  
Electric Drive ◽  
Electric Motor ◽  
Frequency Converter ◽  
Operating Mode ◽  
Operating Modes ◽  
Dynamometer Card ◽  
The Mathematical Model

The analysis of the operating modes of the frequency-controlled electric drive of the pumpjack with the use of dynamometer cards, wattmeter diagrams and the mathematical model of the pump-jack, the effect of the shape of the dynamometer card on the operating mode of the electric motor of the pumpjack is determined. The ways of protection of the transistors in the frequency converter from voltage increase are considered at the transition of the electric motor to the regeneration.

scholarly journals Identification of a mathematical model for a single-shaft power-generating GTE

Energetika ◽  
2021 ◽  
Vol 67 (1) ◽  
Author(s):  
Anatoly Tarelin ◽  
Alexander Lyutikov ◽  
Iryna Annopolska
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Gas Turbine ◽  
Parametric Identification ◽  
Turbine Engines ◽  
Gas Turbine Engines ◽  
Variable Parameters ◽  
Operating Modes ◽  
Model Linearization ◽  
The Mathematical Model

The design and development processes of gas turbine engines rely on the usage of mathematical models representing the physics of engine functioning processes. One way of increasing the validity of a mathematical model is its identification based on engine test results. The identification of mathematical models of modern power-generating gas turbine engines (GTEs) presents a demanding and time-consuming task due to the necessity to identify the main controlled engine parameters determined in the course of experimental studies depending on a large number of the parameters that are not controlled during the experiment. In this regard the actual direction of reducing the labour intensity of the process of mathematical model identification is using identification program complexes. The object of the study was to solve the problem of structural-parametrical identification of the power-generating GTE functioning model detailing the turbine flow path calculations to the level of blade rows in order to obtain the GTE mathematical model that describes the characteristics of a real engine with given accuracy. To achieve the objective, the following problems were solved: variable parameters, controlled parameters and characteristics, ranges of their variations were selected from the total number of the mathematical model input data, the objective functions were defined; the task of the parametric identification according to the results of bench tests through GTE operating modes was performed; analytical approximating dependences for correcting coefficients (variable parameters) were obtained; structural-parametric identification of the mathematical model was performed. The novelty of the obtained results is the identification of the mathematical model of the nonlinear component GTE of the second level performed without model linearization (without its level lowering) by using the Optimum software packages. The methodological approach for the parametric identification of the mathematical model is proposed. This approach allows reducing the number of variable parameters under the modes lower that the maximum. It shows that the identified model allows obtaining the prediction results of the GTE parameters and characteristics through operating modes with a deviation of no more than 1.4% from the experimental data and, therefore, it will allow reduction of terms and an increase in the quality of power unit development.

scholarly journals Mathematical Model of a Tonal Rail Chain without Insulating Joints with Current Receiver in Shunt Mode

2021 ◽  
Vol 22 (3) ◽  
pp. 312-320
Author(s):  
Ravshan M. Aliev
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Electric Current ◽  
Traffic Light ◽  
Operating Modes ◽  
Analysis And Synthesis ◽  
Critical Location ◽  
Theoretical Issues ◽  
Analytical Expressions

Abstract One of the drawbacks of the currently used tonal rail chains without insulating joints is that when the train approaches the controlled section, the train begins to shunt this section at some distance before entry on him. In connection with the traffic light moves on this distance. But being that this distance depends on many variables, it constantly changes these variables. For eliminate this drawback, instead of the traditional potential receiver it is proposed to use electric current track receiver, which has a clear boundary fixation entry of train on the controlled section. By now developed and used methods for determining the main analytical expressions for analysis and synthesis tonal rail circuits with potential receivers in various operating modes, and the theoretical issues of tonal rail chains with current receivers were practically not considered, in this connection, the article considers the development of mathematical models for determining the absolute shunt sensitivity of tonal rail chains without isolating joints with current receivers and methods for calculating determination of the critical location of the minimum shunt sensitivity. The obtained expressions differ significantly from the known equations of absolute shunt sensitivity and the critical location of the minimum value of the shunt sensitivity and will allow to spend analyzing, synthesis and design of tonal rail chains without isolating joints with current receivers, that will allow to increase the safety of train traffic.

A mathematical model and an algorithm for sampling sets of components on the Assembly enterprises of space technology

2018 ◽  
Vol 15 (1) ◽  
pp. 39-55
Author(s):  
V. B. Rudakov ◽  
V. M. Makarov ◽  
M. I. Makarov
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Space Technology ◽  
Economic Costs ◽  
Problem Statement ◽  
Optimal Plan ◽  
Product Mix ◽  
Technical Parameters ◽  
Complex Products ◽  
Assembly Plants

The article considers the problem of determining the rational plans of the input sampling reliability and technical parameters of components of space technology, the totality of which is supplied to the Assembly plants for the manufacture of complex products of space technology. Problem statement and mathematical model based on the minimization of the economic costs of control and losses related to the risks of taking wrong decisions, are given in the article. The properties of the mathematical models are investigated, the algorithm for its optimization is developed. The result is an optimal plan for the sampling of sets of components, which includes: an optimal product mix subject to mandatory control of the aggregate and optimum risks of first and second kind, when acceptance number of statistical plan is zero. The latter circumstance is due to the high requirements of reliability and technical parameters of products of space technology.

Rapid determination of glomerular filtration rate by single-bolus inulin: a comparison of estimation analyses

1998 ◽  
Vol 84 (6) ◽  
pp. 2154-2162 ◽  
Author(s):  
Cord Sturgeon ◽  
Albert D. Sam ◽  
William R. Law
Keyword(s):  
Mathematical Model ◽  
Glomerular Filtration Rate ◽  
Mathematical Models ◽  
Glomerular Filtration ◽  
Filtration Rate ◽  
Rapid Determination ◽  
Constant Infusion ◽  
Sprague Dawley ◽  
Single Bolus ◽  
Sprague Dawley Rats

Rapid measurement of glomerular filtration rate (GFR) by an inulin single-bolus technique would be useful, but its accuracy has been questioned. We hypothesized that reported inaccuracies reflect the use of inappropriate mathematical models. GFR was measured in 14 intact and 5 unilaterally nephrectomized conscious male Sprague-Dawley rats (mean weight 368 ± 12 g) by both single-bolus (25 mg/kg) and constant-infusion techniques (0.693 mg ⋅ kg−1 ⋅ min−1). The temporal decline in plasma inulin concentration was analyzed through biexponential curve fitting, which accounted for renal inulin loss before complete vascular and interstitial mixing. We compared our mathematical model based on empirical rationale with those of other investigators whose studies suggest inaccuracy of single-bolus methods. Our mathematical model yielded GFR values by single bolus that agreed with those obtained by constant infusion [slope = 0.94 ± 0.16 (SE); y intercept = 0.23 ± 0.64; r = 0.82]. In comparison to the data obtained by constant inulin infusion, this method yielded a very small bias of −0.0041 ± 0.19 ml/min. Two previously reported models yielded unsatisfactory values (slope = 1.46 ± 0.34, y intercept = 0.47 ± 1.5, r = 0.72; and slope = 0.17 ± 1.26, y intercept = 17.15 ± 5.14, r = 0.03). The biases obtained by using these methods were −2.21 ± 0.42 and −13.90 ± 1.44 ml/min, respectively. The data indicate that when appropriate mathematical models are used, inulin clearance after single-bolus delivery can be used to measure GFR equivalent to that obtained by constant infusion of inulin. Attempts to use methods of analysis for simplicity or expediency can result in unacceptable measurements relative to the clinical range of values seen.

Twin Models

1970 ◽  
Vol 19 (1-2) ◽  
pp. 141-141
Author(s):  
L. Gedda ◽  
G. Brenci ◽  
M. T. Lun
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Genetic Parameters ◽  
Simultaneous Recording ◽  
Theoretical Relationship ◽  
Twin Models

The theoretical relationship between the distribution of a given trait in a population of twin pairs and several genetic parameters has been examined. In particular, a series of mathematical models has been worked out, that, when applied to a twin population, nonselected for the occurrence of a given trait and nondiagnosed as to zygosity, leads to an estimate of:1) The MZ: DZ ratio in the population;2) The frequency of the genotype responsible for a given trait;3) The probability of manifestation of the trait;4) The value of epistatic factors.A further mathematical model affords the estimate of linkage in the hypothesis of simultaneous recording of more than one trait.

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.

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