On controllability of the temperature mode of heated buildings

The temperature of the internal air of different rooms of heated buildings often must be different. At the same time, the number of control actions applied in this case is rather limited - as a rule, they regulate either the temperature or the coolant flow rate at the individual heat point (IHP) of the building. Moreover, the coolant flow rate almost never changes due to the inevitability of hydraulic deregulation of the heating system, therefore, as a rule, only one control action is available to control the temperature regime of buildings - this is the temperature of the coolant at the IHP. In this regard, an issue quite naturally arises on the controllability of the temperature regime of buildings, that is, on the possibility of maintaining different temperatures in different rooms. To solve this problem, a mathematical description of the temperature conditions of various rooms in a building with a two-pipe heating system has been proposed. This description is a matrix system of first-order differential equations. The concepts of excess internal air temperature and excess coolant temperature are used. The conditions of complete controllability of the object were found. For this, the controllability matrix was calculated, it was shown that its determinant can be expressed in terms of the Vandermonde determinant. This circumstance greatly simplified the definition of the conditions of controllability. It was noted that for the complete controllability of the object, it is necessary that all its premises would differ either in heat-shielding and heat-inertial properties, or in the characteristics of the heating devices installed in them. In most practical cases, usually, there is no such distinction; therefore, the temperature regime of heated buildings, as a rule, is not fully controlled.