Mathematical modeling and parametric identification of a model using the example of a water-heating unit

2020 ◽  
Vol 42 (1) ◽  
pp. 103-109
Author(s):  
Sarsenbek Zhusupbekov ◽  
◽  
Laulasyn Abzhanova ◽  
Olzhas Nauryzbaev ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Mimo System ◽  
Control Object ◽  
Real Object ◽  
Water Heating ◽  
Heating Unit ◽  
The Mathematical Model

The article is devoted to systemic issues related to the principles of mathematical modeling of technological objects, and the degree of adequacy of certain mathematical descriptions to real processes in these systems. In the article using the least squares method (least squares), a model of a water-heating unit is constructed as a MIMO system. The analysis of the process as a complex multi-connected control object. Based on the experimental data, a mathematical model is obtained in the state space of the water path. The adequacy of the mathematical model to the real object was established by directly comparing the output values of the object with the output values of the model. The results of a comparative assessment of the transition characteristics of the constructed mathematical model and the control object are presented. From the transient characteristics of the object and the mathematical model, it follows that the mathematical model fairly accurately and qualitatively describes the properties of the modeled object, i.e., it is adequate to the modeled object. The material presented allows you to teach a student to study processes by the method of mathematical modeling, including the preparation of a mathematical description, the choice of a solution method, software implementation of the model and verification of the model’s adequacy to a real object.

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

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.

The Main Provisions of the Methodology for Assessing the Convergence of the Results of Mathematical Modeling of Continuous Processes of Avionics Devices and Field Experiments

2018 ◽  
Vol 19 (10) ◽  
pp. 680-688
Author(s):  
V. V. Slatin ◽  
M. A. Demkin ◽  
A. V. Golubkina
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Measurement Errors ◽  
Field Experiments ◽  
Least Squares Method ◽  
Regression Line ◽  
Flight Tests ◽  
Continuous Processes ◽  
Statistical Hypotheses ◽  
The Mathematical Model

The questions of estimation of convergence of the processes received in single flight tests of an aviation complex and at mathematical modeling are considered. This evaluation is performed based on the methods of analysis of variance and means of verification of statistical hypotheses in decision-making on the convergence of the compared processes. For each of the compared processes, the least squares method determines the regression lines. By methods of mathematical statistics the permissible proximity of regression lines of the compared processes is established and the average regression line equivalent to the mathematical expectation of the analyzed statistical processes is determined. With respect to this line, the variance of deviations of the compared statistical processes is determined and their belonging to the General sample of processes is estimated. This suggests that under normal laws of the distribution of measurement errors there is an adequacy of the processes of the mathematical model of the stages of operation of the aviation complex and the observed processes of these stages during flight tests of the aviation complex under study.

Research on Flatness Error Measurement of Revolving Body End-Face

2010 ◽  
Vol 44-47 ◽  
pp. 4002-4006 ◽  
Author(s):  
Peng Guan ◽  
Tian Biao Yu ◽  
Wan Shan Wang
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Sampling Method ◽  
Evaluation Method ◽  
Least Squares Method ◽  
Error Measurement ◽  
Measurement Evaluation ◽  
Revolving Body ◽  
The Mathematical Model ◽  
Flatness Error

According to problems of flatness error measurement of revolving body end-face, sampling method and evaluation method are studied in this paper. First, spiral sampling method is presented, in order to meet the needs of flatness error measurement sampling of revolving body end-face. Second, combined with least squares method, mathematical model applied to flatness error measurement evaluation of revolving body end-face is proposed. Finally, through the simulation, the mathematical model is proved to be correct.

Research on Self-Calibration of Circular Artifacts

2013 ◽  
Vol 475-476 ◽  
pp. 167-172
Author(s):  
Xin Mei Liu ◽  
Yun Chen
Keyword(s):  
Mathematical Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Random Noise ◽  
Poor Performance ◽  
Correlation Equation ◽  
System Error ◽  
Calibration Algorithm ◽  
The Impact ◽  
The Mathematical Model

In order to solve the problem of poor performance of the traditional calibration algorithm , the paper proposed a mathematical model under the constraints of nonrotating and nonscale error ,which solved the defects of inconvenience and expensiveness. Moreover, the mathematical model was obtained through the correlation equation based on the least squares method. Meanwhile , the paper discussed the impact of random noise on the model ,and it was simulated by Matlab. The result of the simulation shows that the model can separate the system error of circular artifacts accurately whether the existence of random noise or not. The result of this paper on expanding the application areas of selfcalibration is of great significance.

Research on Generator Excitation Parameter Identification - PSS Low-Pass Link Parameter Identification

2013 ◽  
Vol 805-806 ◽  
pp. 716-720
Author(s):  
Tao Xu ◽  
Tian Long Shao ◽  
Dong Fang Zhang
Keyword(s):  
Mathematical Model ◽  
Parameter Identification ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
National Standards ◽  
Matlab Software ◽  
Low Pass ◽  
Newton Iterations ◽  
The Mathematical Model

Combined with the contents of the study-PSS low-pass link parameter identification. Least-squares method is selected. Using least-square method for PSS low-pass link mathematical model are also deduced. For the results, because of the mathematical model is solving nonlinear equations, cannot used by the Newton method directly. So we choose to use Newton iterations, with this feature, choose to use MATLAB software to solve the equation. Identification of the use of MATLAB software lags after the PSS parameters obtained recognition results compared with national standards, identifying and verifying the practicability.

Methods of Mathematical Modeling of the Leaching Process of Cobalt-Containing Solutions

2021 ◽  
Vol 316 ◽  
pp. 661-666
Author(s):  
Nataliya V. Mokrova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Chemical Kinetics ◽  
Group Method ◽  
Data Handling ◽  
Multistage Processes ◽  
Leaching Process ◽  
Proposed Model ◽  
Simulation Results ◽  
The Mathematical Model

Current cobalt processing practices are described. This article discusses the advantages of the group argument accounting method for mathematical modeling of the leaching process of cobalt solutions. Identification of the mathematical model of the cascade of reactors of cobalt-producing is presented. Group method of data handling is allowing: to eliminate the need to calculate quantities of chemical kinetics; to get the opportunity to take into account the results of mixed experiments; to exclude the influence of random interference on the simulation results. The proposed model confirms the capabilities of the group method of data handling for describing multistage processes.

A prey–predator model and control of a nematodes pest using control in banana: Mathematical modeling and qualitative analysis

2021 ◽  
pp. 2150089
Author(s):  
Sudhakar Yadav ◽  
Vivek Kumar
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Local Stability ◽  
Detection Method ◽  
Initial Release ◽  
Pest Detection ◽  
Predator Model ◽  
And Control ◽  
The Mathematical Model ◽  
Theoretical Results

This study develops a mathematical model for describing the dynamics of the banana-nematodes and its pest detection method to help banana farmers. Two criteria: the mathematical model and the type of nematodes pest control system are discussed. The sensitivity analysis, local stability, global stability, and the dynamic behavior of the mathematical model are performed. Further, we also develop and discuss the optimal control mathematical model. This mathematical model represents various modes of management, including the initial release of infected predators as well as the destroying of nematodes. The theoretical results are shown and verified by numerical simulations.

scholarly journals Population Behavior in the Mathematical Model of the Spread of COVID19 Type SEIRS

2021 ◽  
Vol 6 (2) ◽  
pp. 83-88
Author(s):  
Asmaidi As Med ◽  
Resky Rusnanda
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Everyday Life ◽  
Applied Mathematics ◽  
Living Things ◽  
Simulation Results ◽  
Parameter Values ◽  
The Mathematical Model ◽  
Disease Free

Mathematical modeling utilized to simplify real phenomena that occur in everyday life. Mathematical modeling is popular to modeling the case of the spread of disease in an area, the growth of living things, and social behavior in everyday life and so on. This type of research is included in the study of theoretical and applied mathematics. The research steps carried out include 1) constructing a mathematical model type SEIRS, 2) analysis on the SEIRS type mathematical model by using parameter values for conditions 1and , 3) Numerical simulation to see the behavior of the population in the model, and 4) to conclude the results of the numerical simulation of the SEIRS type mathematical model. The simulation results show that the model stabilized in disease free quilibrium for the condition  and stabilized in endemic equilibrium for the condition .

scholarly journals Mathematical Modeling of Pollution Transfer in Open Channel

2019 ◽  
pp. 49-50
Author(s):  
Petro Martyniuk ◽  
Oksana Ostapchuk ◽  
Vitalii Nalyvaiko
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Numerical Solution ◽  
Boundary Problem ◽  
Water Flow ◽  
Numerical Experiments ◽  
Open Channel ◽  
Computational Algorithm ◽  
The Mathematical Model

The problem of pollution transfer by water flow in open channel was considered. The mathematical model of the problem was constructed. The numerical solution of the onedimensional boundary problem was obtained. The computational algorithm for solving the problem was programmed to implement. A series of numerical experiments with their further analysis was conducted.

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