Improvement of the calculated dependences for indoor air temperature in the integrated control of climate systems

Abstract

Introduction. The paper indicates that the further development of methods for calculating the thermal regime of disturbances in the automation of microclimate systems is still relevant. The aim of the work is to find an approximate analytical dependence of the air temperature in the conditions of a jump in the heat flow in air-conditioned rooms on time for the integral law of regulation of compensatory heat exposure from the climatic equipment. As a scientific hypothesis, the position is put forward about the possibility of expressing this dependence through trigonometric functions with sliding parameters. Materials and methods. The work involves the use of the basic differential equation of the thermal balance of a room serviced by climate systems equipped with continuous integral regulators, with a sudden change in the thermal disturbance. The linearization of the equation due to the freezing of variable coefficients and the Heaviside operational method are used, as well as the normalization method to eliminate the influence of the solution feature on the possibility of taking into account the initial conditions. Results. Analytical expressions are found for the coefficients and parameters of the approximate dependence of the temperature change in the room during the integral regulation of air conditioning systems under conditions of a jump in heat supply. Simplified formulas for the maximum deviation of the air temperature and the sliding frequency for the trigonometric functions involved in the solution are obtained, and their error is estimated in comparison with the exact solution on the example of one of the rooms in a residential building for the climatic conditions of Moscow. Conclusions. It is shown that the dependence of the air temperature in a room serviced by climate systems regulated by an integral law on time can be represented in a simplified analytical form on the basis of trigonometric functions with variable frequency. Additionally, the validity of the previously obtained exact solution for temperature changes in the form of an infinite series in degrees of time since the beginning of the thermal disturbance is confirmed.