Identification of heat exchangers according to the criterion of energy efficiency

The article presents the results of the analysis of the characteristics of heat exchangers methods for determining their mathematical models. The necessity of the availability of the mathematical model during the synthesis of automatic control systems with desired properties. The method of identification of the thermal control object by the testing control action is proposed. Since technological control objects always be an energy of interaction the energy efficiency criterion applied for automatic formation of the control action. Also the analytical self-adjusting system with a reference model in the form of an integrating link was applied. From the analytical researches it follows that the movement of the system along the optimal trajectory occurs at a constant speed and does not depend on the properties of the control object, and the optimal control depends on the properties of the control object, time, and technological requirements. It is shown that mathematical models of heat exchangers of the first and second orders are determined quite simply. The accuracy of the mathematical model parameters is limited only by the accuracy of the experimental data. The quality of control systems with desired properties, synthesized by experimental, and accurate models are virtually indistinguishable.

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The identification of a device based on a Peltier element by the least squares method

Proceedings of the Russian higher school Academy of sciences ◽

10.17212/1727-2769-2020-1-2-17-27 ◽

2020 ◽

pp. 17-27

Author(s):

Vladimir Grinkevich ◽

Keyword(s):

Mathematical Model ◽

Least Squares ◽

Least Squares Method ◽

Control Object ◽

Object Identification ◽

Model Parameters ◽

Peltier Element ◽

Transport Delay ◽

Non Linear ◽

The Mathematical Model

The evaluation of the mathematical model parameters of a non-linear object with a transport delay is considered in this paper. A temperature controlled stage based on a Peltier element is an identification object in the paper. Several input signal implementations are applied to the input of the identification object. The least squares method is applied for the calculation of the non-linear differential equitation parameters which describe the identification object. The least squares method is used due to its simplicity and the possibility of identification non-linear objects. The parameters values obtained in the process of identification are provided. The plots of temperature changes in the temperature control system with a controller designed based on the mathematical model of the control object obtained as a result of identification are shown. It is found that the mathematical model obtained in the process of identification may be applied to design controllers for non-linear systems, in particular for a temperature stage based on a Peltier element, and for self-tuning controllers. However, the least square method proposed in the paper cannot estimate the transport delay time. Therefore it is required to evaluate the time delay by temperature transient processes. Dynamic object identification is applied when it is required to obtain a mathematical model structure and evaluate the parameters by an input and output control object signal. Also, identification is applied for auto tuning of controllers. A mathematical model of a control object is required to design the controller which is used to provide the required accuracy and stability of control systems. Peltier elements are applied to design low-power and small- size temperature stage . Hot benches based on a Peltier element can provide the desired temperature above and below ambient temperature.

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Symmetric Control Systems

Herald of the Bauman Moscow State Technical University Series Instrument Engineering ◽

10.18698/0236-3933-2021-2-37-51 ◽

2021 ◽

pp. 37-51

Author(s):

A.I. Diveev ◽

E.A. Sofronova

Keyword(s):

Mathematical Model ◽

Optimal Control ◽

Optimal Control Problem ◽

Control Problem ◽

Control Systems ◽

Control Object ◽

Terminal State ◽

Initial State ◽

Phase Constraints ◽

The Mathematical Model

The paper focuses on the properties of symmetric control systems, whose distinctive feature is that the solution of the optimal control problem for an object, the mathematical model of which belongs to the class of symmetric control systems, leads to the solution of two problems. The first optimal control problem is the initial one; the result of its solution is a function that ensures the optimal movement of the object from the initial state to the terminal one. In the second problem, the terminal state is the initial state, and the initial state is the terminal state. The complexity of the problem being solved is due to the increase in dimension when the models of all objects of the group are included in the mathematical model of the object, as well as the emerging dynamic phase constraints. The presence of phase constraints in some cases leads to the target functional having several local extrema. A theorem is proved that under certain conditions the functional is not unimodal when controlling a group of objects belonging to the class of symmetric systems. A numerical example of solving the optimal control problem with phase constraints by the Adam gradient method and the evolutionary particle swarm method is given. In the example, a group of two symmetrical objects is used as a control object

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The Mathematical Model for Research of the UAV Longitudinal Moving

International Journal of Computer Network and Information Security ◽

10.5815/ijcnis.2021.05.03 ◽

2021 ◽

Vol 13 (5) ◽

pp. 29-39

Author(s):

Sergii Zhdanov ◽

◽

Natalia Kadet ◽

Valerii Silkov ◽

Mariia Zirka ◽

...

Keyword(s):

Mathematical Model ◽

Mathematical Models ◽

Frequency Response ◽

Unmanned Aerial Vehicles ◽

Control Systems ◽

Aerial Vehicles ◽

General Mathematical Model ◽

Logarithmic Frequency ◽

The Impact ◽

The Mathematical Model

The paper presents one of the perspective directions of the development to modern aviation, which is connected with designing and producing unmanned aerial vehicles (UAV) of various functionalities for applying in both military and civilian spheres. The syntheses of UAV control systems, regardless of their type and purpose presumes creation of adequate mathematical models, first of all adequate aerodynamic mathematical models. In the paper results that forms and justify the aerodynamic mathematical model and as well as the results of building a general mathematical model of the longitudinal movement of the perspective UAV are presented. Also factors that forms the mathematical model on given aerodynamic, geometric, mass and inertial data for a hypothetical perspective altitude long-range UAV are submitted. Assessment of the impact of these data on the dynamic, temporal, and logarithmic frequency response UAV also has been given in this paper.

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Improving the Efficiency of the Three-Stage Technique of Mathematical Model Identification of Complex Thermal Power Equipment

E3S Web of Conferences ◽

10.1051/e3sconf/202020903002 ◽

2020 ◽

Vol 209 ◽

pp. 03002

Author(s):

Vitalii Alekseiuk

Keyword(s):

Mathematical Model ◽

Mathematical Models ◽

Thermal Power ◽

Great Part ◽

Model Identification ◽

Identification Accuracy ◽

Model Parameters ◽

Power Equipment ◽

Operation Conditions ◽

The Mathematical Model

The problems of state estimation of thermal power system operation and identification of mathematical model parameters have not been acceptably solved due to the complexity of studied objects and their mathematical models, and the lack of effective methods, algorithms and computer programs to solve the required mathematical problems. The results of solving the indicated problems are of importance as such, and play a great part in the qualitative solution to the problems of thermal power equipment control, e.g., the problems of optimal load dispatch among thermal power plant units and optimal control of thermal power equipment operation conditions. The paper describes an effective three-stage technique of mathematical model identification of complex thermal power equipment. The technique allows us to more effectively detect gross errors in measurements of control parameters used for identification of the mathematical model of the studied equipment, to evaluate correctness and rectify errors in the mathematical model construction, and to improve identification accuracy. The article presents a new formulation of the optimization problem for more efficient identification of mathematical models of heat power equipment. An effective three-stage technique of mathematical model identification of complex thermal power equipment was tested on a detailed mathematical model of the present-day 225 MW generating unit that was constructed by the author. The paper presents results of solving the identification problem of mathematical model parameters of a generating unit.

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Spectral and integral methods of determining parameters in selected electric arc models with a forced sinusoid current circuit

Archives of Electrical Engineering ◽

10.1515/aee-2016-0007 ◽

2016 ◽

Vol 65 (1) ◽

pp. 87-103 ◽

Cited By ~ 3

Author(s):

Antoni Sawicki ◽

Maciej Haltof

Keyword(s):

Mathematical Model ◽

Mathematical Models ◽

Power Supply ◽

Electric Arc ◽

Dynamic Processes ◽

Model Parameters ◽

Static Characteristics ◽

Integral Methods ◽

The Mathematical Model ◽

Linear Shape

Abstract The paper discusses problems arising in attempts to accurately represent dynamic processes of an electric arc by means of simple mathematical models. It describes the properties of the universal Pentegov model, employing any shape of static voltagecurrent characteristics of an arc. Next, it presents spectral and integral measuring methods for determining arc parameters in the Mayr, Cassie and Pentegov models of the electric arc with a forced sinusoid current circuit, with the raising static characteristics of hyperbolic-flat and hyperbolic-linear shape. The influence is discussed of the random power supply disturbances on errors of determining the mathematical model parameters.

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NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

Criminalistics and Forensics ◽

10.33994/kndise.2020.65.43 ◽

2020 ◽

pp. 442-451

Author(s):

А.V. Batig ◽

A. Ya. Kuzyshyn

Keyword(s):

Mathematical Model ◽

Mathematical Models ◽

Computer Experiment ◽

Rolling Stock ◽

Software Systems ◽

Freight Car ◽

The Stability ◽

The Many ◽

The Impact ◽

The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

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Analysis on Present Mathematical Model for Predicting the Crop Production

International Journal of Innovative Technology and Exploring Engineering - Special Issue ◽

10.35940/ijitee.l7946.1091220 ◽

2020 ◽

Vol 9 (12) ◽

pp. 168-170

Keyword(s):

Mathematical Model ◽

Mathematical Models ◽

Real World ◽

Crop Production ◽

Ghg Emissions ◽

Data Set ◽

Factors Affecting ◽

The Government ◽

The Mathematical Model ◽

Government Website

India is a worldwide agriculture business powerhouse. Future of agriculture-based products depends on the crop production. A mathematical model might be characterized as a lot of equations that speak to the conduct of a framework. By using mathematical model in agriculture field, we can predict the production of crop in particular area. There are various factors affecting crops such as Rainfall, GHG Emissions, Temperature, Urbanization, climate, humidity etc. A mathematical model is a simplified representation of a real-world system. It forms the system using mathematical principles in the form of a condition or a set of conditions. Suppose we need to increase the crop production, at that time the mathematical model plays a major role and our work can be easier, more significant by using the mathematical model. Through the mathematical model we predict the crop production in upcoming years. .AI, ML, IOT play a major role to predict the future of agriculture, but without mathematical models it is not possible to predict crop production accurately. To solve the real-world agriculture problem, mathematical models play a major role for accurate results. Correlation Analysis, Multiple Regression analysis and fuzzy logic simulation standards have been utilized for building a grain production benefit depending model from crop production. Prediction of crop is beneficiary to the farmer to analyze the crop management. By using the present agriculture data set which is available on the government website, we can build a mathematical model.

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A mathematical model of common-cold epidemics on Tristan da Cunha

Journal of Hygiene ◽

10.1017/s0022172400021677 ◽

1971 ◽

Vol 69 (3) ◽

pp. 423-433 ◽

Cited By ~ 14

Author(s):

B. J. Hammond ◽

D. A. J. Tyrrell

Keyword(s):

Mathematical Model ◽

Common Cold ◽

Average Duration ◽

Model Parameters ◽

Epidemic Threshold ◽

Tristan Da Cunha ◽

Simulation Techniques ◽

Time Courses ◽

The Mathematical Model ◽

Computer Simulation Techniques

SUMMARYRecords of seven common-cold outbreaks on the island of Tristan da Cunha are compared with the corresponding time courses given by the mathematical model of Kermack & McKendrick (1927) and with an alternative model that directly involves a constant average duration of individual infection. Using computer simulation techniques the latter model is shown to be preferred and is then closely matched to the field data to obtain values for the model parameters. Consideration is then given to the intensity of epidemics predicted by the model and to the distribution of the actual epidemics relative to the theoretical epidemic threshold.

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BASIC MATHEMATICAL MODELS AND AN APPROXIMATE METHOD OF FILTRATION THEORY

UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES ◽

10.18522/1026-2237-2021-3-25-31 ◽

2021 ◽

pp. 25-31

Author(s):

Alla A. Mussina

Keyword(s):

Mathematical Model ◽

Porous Media ◽

Mathematical Models ◽

Heterogeneous Porous Media ◽

Effective Management ◽

Filtration Theory ◽

New Device ◽

Scientific Papers ◽

The Mathematical Model ◽

Inhomogeneous Liquids

The article defines the basic concepts of filtration theory and provides an overview of the existing mathematical models of inhomogeneous liquids in porous media. The paper considers the Stefan problem. The number of scientific papers devoted to the study of porous structures has recently increased. This is primarily due to the fact that the prob-lems of oil and uranium production have been identified, and the solution of environmental problems is overdue. Therefore, a new device is needed to develop models of liquid filtration. With the advent and development of computer technology, it has become easier to solve problems that require numerical methods for their solution. Understanding the movement of fluids and the mechanism of dissolution of rocks under the action of acids in heterogeneous porous media is of great importance for the extraction and production of oil and the effective management of these processes. The article examines the mathematical model of the theory of isothermal filtration. Possible variants of the solva-bility of the model are shown. The research scheme consists of the output of a mathematical model, the formulation of the problem, one variant of the solution of the problem, the algorithm of the numerical method of solving the problem.

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The generation of a mathematical model of the biogas production process from organic municipal solid waste

E3S Web of Conferences ◽

10.1051/e3sconf/202018002019 ◽

2020 ◽

Vol 180 ◽

pp. 02019 ◽

Cited By ~ 1

Author(s):

Marzhan Temirbekova ◽

Madina Aliyarova ◽

Iliya Iliev ◽

Aliya Yelemanova ◽

Saule Sagintayeva

Keyword(s):

Mathematical Model ◽

Municipal Solid Waste ◽

Solid Waste ◽

Anaerobic Fermentation ◽

Biogas Production ◽

Biogas Plant ◽

Model Parameters ◽

Biochemical Processes ◽

Biogas Plants ◽

The Mathematical Model

This paper justifies the efficiency of the biogas collection and utilization at the MSW (municipal solid waste) landfill in Almaty with the installation of several modern biogas plants. The optimal mode of processes occurring in a biogas plant is determined by computer generated simulations. Mathematical model parameters were identified to describe biochemical processes occurring in a biogas plant. Two approaches are used to resolve the mathematical model: the finite-difference method for solving the system of differential equations and simulation modeling by using the Any Logic package. A program is written in the algorithmic language C ++. Numerous calculations were carried out, the results of which are presented in curves and their qualitative picture is consistent with the ongoing processes. The created computer program allows to make a preliminary forecast of anaerobic fermentation occurring in the bioreactor depending on volume of the substrate, methane microorganisms and temperature conditions.

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