scholarly journals A Generalized Analytic Mathematical Model of the Electromechanical Converter as a Control Object

2016 ◽  
Vol 16 (4) ◽  
pp. 72-76
Keyword(s):  
Mathematical Model ◽  
Control Object ◽  
Electromechanical Converter

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.

scholarly journals Identification of Neural Network Model of Robot to Solve the Optimal Control Problem

2021 ◽  
Vol 20 (6) ◽  
pp. 1254-1278
Author(s):  
Elizaveta Shmalko ◽  
Yuri Rumyantsev ◽  
Ruslan Baynazarov ◽  
Konstantin Yamshanov
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Mathematical Model ◽  
Optimal Control ◽  
Neural Network Model ◽  
Software Package ◽  
Control Object ◽  
Robotic Systems ◽  
Object Model ◽  
Modern Machine

To calculate the optimal control, a satisfactory mathematical model of the control object is required. Further, when implementing the calculated controls on a real object, the same model can be used in robot navigation to predict its position and correct sensor data, therefore, it is important that the model adequately reflects the dynamics of the object. Model derivation is often time-consuming and sometimes even impossible using traditional methods. In view of the increasing diversity and extremely complex nature of control objects, including the variety of modern robotic systems, the identification problem is becoming increasingly important, which allows you to build a mathematical model of the control object, having input and output data about the system. The identification of a nonlinear system is of particular interest, since most real systems have nonlinear dynamics. And if earlier the identification of the system model consisted in the selection of the optimal parameters for the selected structure, then the emergence of modern machine learning methods opens up broader prospects and allows you to automate the identification process itself. In this paper, a wheeled robot with a differential drive in the Gazebo simulation environment, which is currently the most popular software package for the development and simulation of robotic systems, is considered as a control object. The mathematical model of the robot is unknown in advance. The main problem is that the existing mathematical models do not correspond to the real dynamics of the robot in the simulator. The paper considers the solution to the problem of identifying a mathematical model of a control object using machine learning technique of the neural networks. A new mixed approach is proposed. It is based on the use of well-known simple models of the object and identification of unaccounted dynamic properties of the object using a neural network based on a training sample. To generate training data, a software package was written that automates the collection process using two ROS nodes. To train the neural network, the PyTorch framework was used and an open source software package was created. Further, the identified object model is used to calculate the optimal control. The results of the computational experiment demonstrate the adequacy and performance of the resulting model. The presented approach based on a combination of a well-known mathematical model and an additional identified neural network model allows using the advantages of the accumulated physical apparatus and increasing its efficiency and accuracy through the use of modern machine learning tools.

Symmetric Control Systems

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

scholarly journals Fundamentals of Synthesized Optimal Control

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 21
Author(s):  
Askhat Diveev ◽  
Elizaveta Shmalko ◽  
Vladimir Serebrenny ◽  
Peter Zentay
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Control Method ◽  
Direct Method ◽  
Equilibrium Points ◽  
Control Object ◽  
Optimal Control Method ◽  
Optimal Value ◽  
New Formulation ◽  
The Mathematical Model

This paper presents a new formulation of the optimal control problem with uncertainty, in which an additive bounded function is considered as uncertainty. The purpose of the control is to ensure the achievement of terminal conditions with the optimal value of the quality functional, while the uncertainty has a limited impact on the change in the value of the functional. The article introduces the concept of feasibility of the mathematical model of the object, which is associated with the contraction property of mappings if we consider the model of the object as a one-parameter mapping. It is shown that this property is sufficient for the development of stable practical systems. To find a solution to the stated problem, which would ensure the feasibility of the system, the synthesized optimal control method is proposed. This article formulates the theoretical foundations of the synthesized optimal control. The method consists in making the control object stable relative to some point in the state space and to control the object by changing the position of the equilibrium points. The article provides evidence that this approach is insensitive to the uncertainties of the mathematical model of the object. An example of the application of the method for optimal control of a group of robots is given. A comparison of the synthesized optimal control method with the direct method on the model without disturbances and with them is presented.

scholarly journals A Mathematical Model for a Conceptual Design and Analyses of UAV Stabilization Systems

Fluids ◽  
2021 ◽  
Vol 6 (5) ◽  
pp. 172
Author(s):  
Vadim Kramar ◽  
Aleksey Kabanov ◽  
Sergey Dudnikov
Keyword(s):  
Mathematical Model ◽  
Transfer Functions ◽  
Mutual Influence ◽  
Complete System ◽  
Control Object ◽  
Stabilization System ◽  
Elastic Deformations ◽  
Dynamic Constraints ◽  
Control Actions ◽  
Analysis And Synthesis

This article considers the principle of constructing mathematical models of functionally complex multidimensional multiloop continuous–discrete UAV stabilization systems. This is based on the proposal for constructing a mathematical model based on the class of the considered complexity of the stabilization system-multidimensionality, multi-rating, and elasticity. Multiloop (multidimensional) UAV stabilization systems are often characterized by the control of several interconnected state elements and the existence of several channels for the propagation of signals and mutual connections between individual objects. This is due to the need not only to take into account the numerous disturbing factors (for example, wind) acting on the control object as well as the need to use several points of application of control actions. Additionally, an important point is the possible separation of the mutual influence of the roll and yaw channels of the UAV on its synthesis and analysis. For this purpose, a mathematical model has been constructed using a description in the form of transfer functions, and therefore, in the form of structural diagrams. The principle of obtaining transfer functions is shown to demonstrate additional dynamic constraints introduced by elastic deformations into the stabilization loop through gyroscopic devices and accelerometers. This will make it possible to formulate a methodology for analyzing the influence of aeroelastic constraints on the stabilization loop, which will allow developing approaches to formulate requirements for the effective placement of gyroscopes and accelerometers on the UAV. The proposed approach allows creating a complete system of analysis and synthesis tools for complex multidimensional continuous–discrete UAV stabilization systems.

scholarly journals IMPLEMENTATION OF THE METHODS OF IDENTIFICATION OF STATIC CONTROL OBJECTS

2017 ◽  
pp. 72-78
Author(s):  
Sergey Pachkin ◽  
Sergey Pachkin ◽  
Roman Kotlyarov ◽  
Roman Kotlyarov
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Automatic Control ◽  
Automatic Control System ◽  
Mathematical Description ◽  
Control Object ◽  
Parametric Identification ◽  
Identification Problem ◽  
Temperature Control System ◽  
The Mathematical Model

One of the main tasks solved in the development of automatic control systems is the identification of the control object, which consists in obtaining its mathematical description. The nature and type of the mathematical model is determined by the goals and tasks for which it will be used. In the present case, the aim of obtaining the model is the synthesis of an automatic control system. Proceeding from the requirements of control problems, the identification problem consists in determining the structure and parameters of the mathematical model that ensure the best similarity of the model and object responses to the same input action. The article considers the experimental method of obtaining a mathematical description of the control object based on the results of measuring its input and output parameters and then processing the obtained results. The control object is the EP10 emulator made by the Oven Company, which is a miniature furnace. The emulator is used in experimental research in the process of commissioning using thermostat controls, and also applicable for educational purposes as part of training and research stands. As a result of structural identification with subsequent adjustment of the coefficients with the help of parametric identification, a model of the control object in the form of a second order aperiodic link is obtained. Parameters and type of the mathematical model allowed to make calculations and determine the parameters of adjustment of the TRM251 PID-controller. The software implementation of the automatic control system in the MatLAB environment made it possible to evaluate transient processes in a closed system. Thus, the calculation and analysis of the automatic control system in the first approximation were made. The final result can be obtained at the stage of commissioning the automatic temperature control system in the EP10 emulator using adaptation algorithms.

scholarly journals MATHEMATICAL SIMULATION OF THE HEATING SYSTEM RADIATOR OF AS A CONTROL OBJECT

2021 ◽  
Vol 11 (3) ◽  
pp. 38-43
Author(s):  
Alexander P. MASLYANITSYN ◽  
Elena V. MASLYANITSYNA ◽  
Marina S. KRASNOVA
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Transfer Function ◽  
Heat Carrier ◽  
Block Diagram ◽  
Thermal Power ◽  
Control Object ◽  
Heating System ◽  
Structural Diagram ◽  
Transfer Processes

The problem of mathematical modeling of a heating system radiator as a control object is considered. The purpose of its development is to create a generalized mathematical model of thermal processes in a room heated by means of water radiators. A calculation scheme of heat transfer processes between the heat carrier of the radiator and the air of the room has been developed, on the basis of which the heat balance equations are writt en. This takes into account both steady and unsteady heat transfer processes between the coolant, radiator and room air. A block diagram of the mathematical model of a heating radiator has been developed. After the introduction of assumptions and transformation of the structural diagram of the nonlinear model, the structural diagram of the linear mathematical model of the heating radiator was obtained. On its basis, the transfer function of the heating radiator is derived, the output coordinate of which is the thermal power. The resulting transfer function can be used in a generalized mathematical model of a heated room. The analysis of the transfer function of the heating radiator is carried out and it is shown that its dynamics is determined not only by geometric parameters, but also by the fl ow rate of the heat carrier.

scholarly journals DEVELOPMENT OF A CONCEPTUAL MODEL OF A ROBOTIC COMPLEX FOR THE PRODUCTION OF RAVIOLI OF SPECIAL FORMS

2020 ◽  
pp. 32-41
Author(s):  
Oleg Burdo ◽  
Igor Bezbakh ◽  
Pavel Golubkov ◽  
Serhii Shyshov ◽  
Aleksander Gavrilov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Production Process ◽  
Conceptual Model ◽  
Raw Materials ◽  
Control Object ◽  
Automatic Process ◽  
Effective System ◽  
Objective Basis ◽  
The Mathematical Model ◽  
Functional Purpose

The article provides a substantiation of the conceptual model of the production process of special forms of dumplings. It is the first stage in the development of a model of this process as a control object. The purpose of which is to form an objective basis for the development of an effective system for automatic process control. The development of the conceptual model presupposes the specification and description of the properties of control channels and acting disturbances to the level of their mathematical model, which can be implemented in a simulation environment. Problems of identification of the mathematical model of the process of the production of dumplings, i. e. obtaining a mathematical description of processes based on the results of its purposeful experimental research, due to its complexity as a control object.The experimental approach, in this case, gives much more reliable results on the properties of the process. An attempt to obtain such general properties on the basis of experimental data would inevitably lead to the need for very complex and lengthy multifactorial experiments and nontrivial procedures for their processing. But this will leave open the question of the adequacy of the model for those conditions of the process and types of raw materials that were not covered by the experiments. Fundamentally important is the fact that the mathematical model of the process is developed as a model of the control object.Model can be used in two ways. This is due to the fact that in the closed circuits of the SAC, the discrepancy between the models can be considered as a manifestation of uncontrolled coordinate and parametric disturbances. It is in conditions of this kind of disturbances that the SAC must fulfill its functional purpose. The developed mathematical model of the production process of special forms of dumplings will be used by us only in the direction, when it is of great importance not so much quantitative as its qualitative correspondence to the original object.

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.

Automation of Concrete Heat Treatment in Thermoactive Formwork in Monolithic Housing Construction

2020 ◽  
Vol 897 ◽  
pp. 250-254
Author(s):  
Anatoly Fedorovich Tikhonov
Keyword(s):  
Heat Treatment ◽  
Mathematical Model ◽  
Control System ◽  
Transfer Functions ◽  
Block Diagram ◽  
Control Object ◽  
Housing Construction ◽  
Control Actions ◽  
Concrete Mix ◽  
Concrete Temperature

The block diagram and algorithm for concrete treating in thermoactive formwork is presented. Article presents parameters of the concrete mix, to enter in a command block before automated heating of the concrete mix in thermoactive formwork in accordance with the schedule of changes in concrete temperature in the process of obtaining desired strength. Article formulates mathematical model of the control object for thermal treatment of concrete with consideration of the specifics and general patterns, processes and technological requirements. Article determined control actions, transfer functions of the object and phase graph of the control system.

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