Abstract
In order to develop previously performed work we consider the problem of constructing a dynamic mathematical model of heating devices and systems. The heating system at the same time seems to be equivalent heater. The output value of the model in this case is the power (heat capacity). Decision is executed by the "gray box", that is the structure of the model is determined by analyzing the physics of the processes occurring in heating devices and systems, and the numerical values of its parameters are found from the experimental data by parametric identification. The resulting differential equation is linear with respect to the unknown quantity-power heater(heating), input the same size-water inlet temperature of the heating system and the temperature of the indoor air are included in this equation in a linear fashion, and the flow is in non-linear manner. It is shown that a constant flow of coolant model can be represented by the transfer functions in the iso-mapping Laplace transfer function of the channel "coolant temperature at the inlet to the heater(heating system) – thermal capacity of the heater(heating)" is a inertia component of the first order, and the channel "indoor air temperature-heat capacity of the heater(heating)" - inertia-forcing component with a negative coefficient of transmission. The qualitative features of the model parameters, in particular, their dependence on the coolant flow are analyzed. Algorithmic block diagram of the control object, which includes the heating system and the thermal regime of the building itself is provided. The results of the parametric model identification from experimental data is described. The model can be used in the development of intelligent control systems heating buildings.
Highlights
Ключевые слова: динамическая математическая модель, тепловой режим зданий, отопительные приборы и системы, структурный синтез, параметрическая идентификация, алгоритмическая структурная схема, система управления
In order to develop previously performed work we consider the problem of constructing a dynamic mathematical model of heating devices and systems
Decision is executed by the "gray box", that is the structure of the model is determined by analyzing the physics of the processes occurring in heating devices and systems, and the numerical values of its parameters are found from the experimental data by parametric identification
Summary
Рассматривается задача построения динамической математической модели отопительных приборов и систем. Модель может быть использована при разработке интеллектуальных систем управления отоплением зданий. Первоочередной задачей, которую необходимо решать при создании высококачественных систем автоматического управления, является задача разработки необходимого математического и программного обеспечений, в частности, динамических математических моделей отопительных приборов и систем и алгоритмов их параметрической идентификации. Поэтому рассмотрим задачу построения динамической математической модели отопительных приборов и систем. Что средняя температура теплоносителя в отопительном приборе может быть выражена следующим образом: tТ (tВХ tВЫХ ) / 2 ,. Подставляя данное соотношение в (2) и переписав его соответствующим образом, получим, что структура динамической математической модели отопительного прибора будет иметь вид: 2Cm. Перепишем данное уравнение, используя стандартные для теории автоматического управления обозначения [2]: T k1tВХ k2tВ
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