Calculation of the characteristics of the thermal regime of the room with proportional-integral regulation of climate systems

Introduction. Further development of methods for calculating the thermal regime of premises under different algorithms of regulating the equipment of microclimate systems is still relevant. The aim of the research is to find an approximate analytical dependence of air temperature on time in air-conditioned rooms with a jump-like thermal effect and combined proportional-integral regulation of central climate systems in the absence of local heating and cooling units. As a scientific hypothesis, the position is put forward on the possibility of expressing this dependence through formulas for integral regulation already obtained by the author using correction coefficients.

Materials and methods. The basic differential equation for the dimensionless excess temperature in the room, including the most significant components of the heat flux, is used, while taking into account the peculiarities of the temperature wave propagation in massive enclosures in the initial period of time. Linearization and small parameter methods are used for asymptotic analytical solutions, as well as well as Runge – Kutta method for finding a numerical solution.

Results. Expressions for the maximum deviation of the air temperature from the setpoint and for the time it is reached, depending on the magnitude of the heat surpluses and the characteristics of the room’s own thermal stability, as well as well as on the control parameters, including asymptotic ones at small moments of time from the beginning of the thermal disturbance and a small share of the proportional component of the controller, are obtained. A comparison of the results of numerical integration of the basic differential equation with the indicated asymptotic solutions is presented.

Conclusions. It is shown that the asymptotic expressions for the dynamic control error and the time of its achievement are obtained from formulas previously found by the author for purely integral control by introducing correction factors containing a dimensionless parameter characterising the ratio of the proportional and integral components of the controller. These correlations are confirmed by comparing different variants of analytical solutions, have a fairly universal appearance, require a minimum number of source data and are available for engineering practice.

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