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.

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.

Model Parameter Identification and Simulation of Ship Power System Based on Recursive Least Squares Method

2012 ◽  
Vol 220-223 ◽  
pp. 482-486 ◽  
Author(s):  
Jin Hui Hu ◽  
Da Bin Hu ◽  
Jian Bo Xiao
Keyword(s):  
Mathematical Model ◽  
Power Systems ◽  
Parameter Identification ◽  
Least Squares ◽  
Least Squares Method ◽  
Recursive Least Squares ◽  
Design Parameters ◽  
Model Parameters ◽  
Model Parameter ◽  
Model Parameter Identification

According to the lack of the part of the equipment design parameters of a certain type of ship power systems, the algorithm of recursive least squares for model parameter identification is studied. The mathematical model of the propulsion motor is established. The model parameters are calculated and simulated based on parameter identification method of recursive least squares. The simulation results show that a more precise mathematical model can be simple and easily obtained by using of the method.

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.

scholarly journals Identification of heat exchangers according to the criterion of energy efficiency

2019 ◽  
Vol 276 ◽  
pp. 06022 ◽  
Author(s):  
Vladimir Velichkin ◽  
Vladimir Zavyalov
Keyword(s):  
Mathematical Model ◽  
Energy Efficiency ◽  
Mathematical Models ◽  
Control Systems ◽  
Heat Exchangers ◽  
Control Object ◽  
Control Action ◽  
Model Parameters ◽  
Quality Of Control ◽  
The Mathematical Model

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.

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.

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.

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.

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