До питання математичного опису динаміки типових сільськогосподарських об’єктів із розподіленими параметрами
Abstract
TO QUESTION OF MATHEMATICAL DESCRIPTION OF DYNAMICS OF TYPICAL AGRICULTURAL OBJECTS WITH DISTRIBUTED PARAMETERS
V. Hryshchenko
To date, the establishment of an effective control system for a technological process or an agricultural object is impossible without the use of mathematical models of the dynamic properties of the control object. Since a significant number of objects of energy consumption implies the presence of heat and mass transfer processes, which causes a significant inertia (which is characterized by a constant time, for reception of feedback and transport delay for the geometry of the influences of the physical environment), consideration of the problem of modeling within the framework of dynamic objects taking into account the distribution of parameters by coordinate is justified. Adequate prediction of the behavior of such an object at perturbations will allow to control the parameters with the use of simple, practical
The purpose of the research is to analyze approaches to the creation of mathematical models of objects with distributed parameters and to determine the most rational form of description of the dynamics of objects with distributed parameters.
The article determines the relevance of the existing mathematical model of a typical object agricultural purpose with biological content ("breathing products", plants, animals) whose technological parameters vary both in time and coordinates. The definite system of differential equations in partial derivatives, with certain assumptions, accurately describes the processes of heat exchange of the airflow with the elements of the object. In the example of the process of cooling the plant product in the mound by active ventilation with air with less than the temperature product, approximate analytic solutions of the system of equations in partial derivatives are given that determine the dynamics of the object with variables in the height of the mound by parameters. It is shown that when applying the step-by-step method for calculating continuous processes on the basis of the mathematical description of the process in the elementary layer it is possible to accurately describe the actual process of cooling the disperse product using the cell's principle of constructing a dynamic model. The simulation process model is developed in MATLAB / Simulink in the form of functional blocks.
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