Mathematical description of the static operational mode of the ceramic brick cooling zone in a tunnel kiln with distributed supply of cooling agent

The analysis of the technological process of cooling ceramic bricks in a tunnel kiln as a control object with parameters distributed along the longitudinal coordinate is performed. It is revealed that the process under consideration has a significant effect on the strength of the finished brick, while research in the field of developing effective methods and means of controlling this stage is practically absent. In the course of the work, the following were determined: a vector of output coordinates, including the temperatures of the brick and cooling air and their gradients along the longitudinal coordinate of the kiln, a vector of control actions consisting of the flow rates of the supplied cooling air and the extracted air, a vector of disturbing actions - the temperature of the brick at the entrance to the cooling zone, the air supplied to the cooling zone, and the environment. A calculation scheme for the process of reducing the temperature of ceramic bricks has been developed taking into account an arbitrary number of points of supply and extraction of air to the cooling zone, which determines the number and size of its sections. Taking into account the accepted assumptions and simplifications, a mathematical description of the static mode of operation of the cooling zone with distributed supply and selection of the cooling agent was performed in the form of a system of non-homogeneous differential equations with the corresponding boundary conditions, which is problem-oriented towards the synthesis of automatic control systems. Their solution made it possible to determine the mathematical operators that link the output coordinates with the control and main disturbing effects. In the future, the results of the work can be used to create effective control systems for the brick cooling process, which will improve the quality of products and reduce energy costs for production.