Non-stationary thermal mode of a room at integrated regulation of split systems

Due to the non-linearity of the propagation of temperature waves in massive fences, one of the most difficult control objects is an air-conditioned room equipped with automated microclimate systems, especially if complex algorithms are used for regulation. Therefore, the task of studying the non-stationary thermal regime of such a room still remains actual, despite the presence of a number of solutions describing the behavior of the air temperature in it with changes in heat supply. On the other hand, such objects are regularly found in the decision-making process to ensure an internal microclimate, so the results obtained can be used for a wide class of tasks. The proposed work presents a variant of a simplified mathematical formulation and solution of the task of calculating changes in internal temperature in a room in which a local split-system type cooling system is provided for the assimilation of heat surpluses, regulated by an integral law, in conditions when general exchange ventilation performs only sanitary and hygienic functions. The basic differential equation of the room thermal balance for this case is formulated, and it is shown that with the introduction of a fixed layer thickness of sharp temperature fluctuations over the considered time interval, this equation with feedback describing the action of the regulator is linear of the second order and is solved in elementary functions in the form of a damped sine wave. Using this solution, calculations were performed for a characteristic room and its validity and formal compliance with the classical results of the automatic control theory were proved by comparing the results with data from field measurements carried out in the same room, as well as with the results obtained for similar tasks by other authors. The obtained formulas are proposed to be used for estimated calculations of the indoor air temperature behavior in an air-conditioned room with the assimilation of heat supply by split systems regulated by an integral law, and for solving identification problems to determine the actual parameters of the room and the controller.