scholarly journals MATHEMATICAL SIMULATION AND STUDY OF CONTROL STABILITY OF THE CHEMICAL-ENGINEERING PROCESSES IN INDUSTRY

2020 ◽  
pp. 4-13
Author(s):  
G Abitova
Keyword(s):  
Mathematical Model ◽  
Chemical Engineering ◽  
System Analysis ◽  
Mathematical Formulation ◽  
Control Object ◽  
Formulation Development ◽  
Mathematical Methods ◽  
Unknown Parameters ◽  
Initial State ◽  
Sulphide Ores

In this work is consider study and analysis of dynamic system for simulation of the technological process under uncertainty and complexity. To study and simulate a complicated technology process we carry out for consideration the technology of the process of roasting in fluidized bed furnaces of polymetallic sulphide ores. The choice is justified by the fact that, operation line producing of polymetallic sulphide ores represents a complex process, is characterized by a big number of transient processes, presence of process variables and deviations from technical regimes. To study process characteristics of any system functioning by means of mathematical methods the process should be formalized. This means, that adequate mathematical model needs to be developed. The choice of mathematical model depends a lot upon the features of the object and its controllability as well as of technological scheme and complexity of processes. Chemical engineering processes are complicated physical and chemical systems. Substance flows, which are part of these systems, are, as a rule, multicomponent. Therefore, for the purpose of study and qualitative control over chemical-engineering processes it is essential to apply the method of mathematic simulation, based on system analysis strategy, analysis of its structure, mathematical formulation development and evaluation of unknown parameters. Controllability means that such system attribute as having control actions, which make it possible to transfer the system from a pre-set initial state to the required condition during finite quantum of time. Therefore, the developed mathematical model of the process or control object should be controllable and stability.

scholarly journals SIMULATION OF CONTROL SYSTEM OF THE CHEMICAL-TECHNOLOGICAL PROCESSES

2021 ◽  
Author(s):  
Gulnara Abitova
Keyword(s):  
Mathematical Model ◽  
Chemical Engineering ◽  
System Analysis ◽  
Mathematical Formulation ◽  
Control Object ◽  
Formulation Development ◽  
Mathematical Methods ◽  
Unknown Parameters ◽  
Initial State ◽  
Sulphide Ores

In this work is consider study and analysis of dynamic system for simulation of the technological process under uncertainty and complexity. To study and simulate a complicated technology process we carry out for consideration the technology of the process of roasting in fluidized bed furnaces of polymetallic sulphide ores. The choice is justified by the fact that, operation line producing of polymetallic sulphide ores represents a complex process, is characterized by a big number of transient processes, presence of process variables and deviations from technical regimes. To study process characteristics of any system functioning by means of mathematical methods the process should be formalized. This means, that adequate mathematical model needs to be developed. The choice of mathematical model depends a lot upon the features of the object and its controllability as well as of technological scheme and complexity of processes. Chemical engineering processes are complicated physical and chemical systems. Substance flows, which are part of these systems, are, as a rule, multicomponent. Therefore, for the purpose of study and qualitative control over chemical-engineering processes it is essential to apply the method of mathematic simulation, based on system analysis strategy, analysis of its structure, mathematical formulation development and evaluation of unknown parameters. Controllability means that such system attribute as having control actions, which make it possible to transfer the system from a pre-set initial state to the required condition during finite quantum of time. Therefore, the developed mathematical model of the process or control object should be controllable and stability.

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 APPLICATION OF SYSTEM APPROACH IN METHODOLOGY OF SOLVING ENGINEERING PROBLEMS

2021 ◽  
pp. 23
Author(s):  
A. PASICHNYK ◽  
V. PASICHNYK ◽  
Y. KUSHCHENKO
Keyword(s):  
Mathematical Model ◽  
Initial Data ◽  
Industrial Development ◽  
System Analysis ◽  
Mathematical Formulation ◽  
Engineering Problem ◽  
The State ◽  
Problem Statement ◽  
Functional Connections ◽  
Engineering Problems

The purpose of this article is to develop and improve systemic methods for constructing solutions to engineering problems. The article provides a methodological approach to solving complex engineering problems based on the application of the system analysis method. The need for a preliminary assessment of the completeness of the initial data for the construction of a mathematical model of the problem is shown. At the stage of the problem statement, the problem statement is concretized in order to establish the research goal. As a result of a systematic analysis of the functional characteristics of the object under study, the main parameters and their relationship are determined, and the values of these parameters characterizing the initial state of the object under study are established. It is necessary to clarify the essence of the problem and formulate it so that the solution found is effective and can be obtained using existing means and in real terms. Based on the data of the analysis, the goal of solving the engineering problem is determined and the corresponding formulation is formulated in the following form: initial data; parameters; quantities to be determined. The functional connections between the main parameters of the object and the factors acting on it are established, they are described by mathematical relations and equations included in the mathematical model, taking into account the determining influence of the parameters of the problem on the state of the object. Thus, we obtain a mathematical formulation of the problem, the construction of the solution of which allows us to establish the parametric dependence of the state of the object for various values of the parameters. The reliability of the results obtained and the suitability of the chosen method, the decision should be confirmed by their testing and careful analysis. On the basis of the formulated approach, assessments have been carried out and the corresponding technological operations have been proposed for solving the engineering problem of removing the tanker «Delfi» from the aground in the water area of the Odessa coast of the Black Sea. The expediency of further improvement of the technology of application of the proposed approach for design tasks and industrial development of software and hardware complexes has been determined.

Analysis and modeling of an inverted pendulum system

2021 ◽  
Author(s):  
Keyword(s):  
Mathematical Model ◽  
Nonlinear System ◽  
Inverted Pendulum ◽  
System Analysis ◽  
Dimensional System ◽  
Two Dimensional ◽  
System Operation ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Two Dimensional System

A nonlinear system, which consists of an inverted pendulum mounted on a cart with an electric drive, is considered. A mathematical model is created, its analysis and modeling of the investigated two-dimensional system operation is carried out. Keywords mathematical model; inverted pendulum; system analysis; state space

scholarly journals Economic-Mathematical Model and Mathematical Methods for Substantiating the Choice of the Company Innovation Strategy

2016 ◽  
Vol 9 (27) ◽  
Author(s):  
Aleksandr Mikhaylovich Batkovskiy ◽  
Pavel Andreevich Kalachikhin ◽  
Elena Georgievna Semenova ◽  
Yury Filippovich Telnov ◽  
Alena Vladimirovna Fomina
Keyword(s):  
Mathematical Model ◽  
Innovation Strategy ◽  
Mathematical Methods

scholarly journals THE WARSHIP ASSIGNMENT SCHEDULE USING INTEGER PROGRAMMING MODEL

JOURNAL ASRO ◽  
2019 ◽  
Vol 10 (3) ◽  
pp. 49
Author(s):  
Ahmadi Ahmadi ◽  
Benny Sukandari ◽  
Agus Mahrowi
Keyword(s):  
Integer Programming ◽  
Programming Model ◽  
Mathematical Formulation ◽  
Combinatorial Problem ◽  
Mathematical Methods ◽  
Alternative Scheduling ◽  
Integer Programming Model ◽  
Maintenance Schedule ◽  
Hard Constraints ◽  
Decision Variables

Scheduling is an assignment activity that deals with constraints. A number of events can occur in a period of time and location so that objective functions as close as possible can be fulfilled. In the hierarchy of decision making, scheduling is the last step before the start of an operation. Scheduling warship assignments in Kolinlamil are an interesting topic to discuss and find solutions to using mathematical methods. The process of the Kolinlamil warship assignment schedule was carried out to produce an annual shipbuilding schedule. This process not only requires fast follow-up, but also requires systematic and rigorous steps. Where the assignment schedule is a fairly complex combinatorial problem. While making the assignment schedule that is applied at this time is considered less accurate because it calculates the conventional method. The process of warship assignment schedule in this study using the Integer Programming model aims to obtain alternative scheduling operations. The schedule observed was 13 warships in carrying out N operations for 1 year (52 weeks). This research begins with determining the decision variables and limitations that existing constraints. Hard constraints include: maintenance schedule, time and duration of each task, warship class assigned to the task and the number of executing warships per task. While soft constraints are how long the warship performs its tasks in a row. The mathematical formulation of the Integer Programming model created consists of three indicator, one decision variables, two measuring parameters and five constraint functions. Furthermore, determining the best scheduling alternatives is completed using the Microsoft Exel Solver computing program.Keywords: Scheduling, Integer Programming, Solver.

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 Building lifecycle management based on 4D modelling as the main workspace for building risk assessment

2020 ◽  
Vol 224 ◽  
pp. 02023
Author(s):  
R Kazaryan ◽  
N Galaeva ◽  
R Avetisyan ◽  
Sh Aliev
Keyword(s):  
Information Technology ◽  
Life Cycle ◽  
System Analysis ◽  
Planning Process ◽  
Block Diagram ◽  
Labour Productivity ◽  
Development Trend ◽  
Basic Block ◽  
Mathematical Methods ◽  
Element Base

The use of information technology in the management of construction projects has become a decisive factor for the successful completion of projects, taking into account time, quality and financial costs. There are challenges in visualizing the planning process and integrating information between stakeholders. The paper considers some aspects of the development trend of information technology in construction. The element base, including the risks arising during the design and construction, associated with the direct use of computer and mathematical models of the object in the design is considered. The generated information models will provide basic information for the participants in the design process, which ultimately will be the basis of the element base of an effective tool for ensuring project life cycle management. The following methods were used: system analysis, logical-mathematical modelling, systems theory, economic-visual modelling, research methods of operations, economic and mathematical methods. A basic block diagram of 4D modelling is presented to minimize the occurrence of risks during design. The model allows considering the possibility of assessing the duration of the project, the level of labour productivity, as well as visualizing the construction process. The presented analysis indicates the importance of using 4D modelling in relation to the life cycle of the object in order to prevent the possibility of construction risks.

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.

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