Наведено передатні функції й частотні характеристики циліндричної теплоакумулюючої стінки як об’єкта з розподіленими параметрами залежно від межових умов на зовнішній і внутрішній поверхнях. Отримані результати можуть бути використані для синтезу систем керування.

Almost all real objects control in chemical, food, metallurgical, oil and other industries, in fact in the entire field of human activity are objects with distributed parameters.

From mathematical modeling point of view a lot of plants in different industries can be considered as cylindrical heat storage walls with distributed parameters. Selected research path based on the following considerations: consider only heat objects with distributed parameters as the most common in the industry; Mathematical model objects with distributed parameters obtained in the form of the transfer function as the most suitable for further research in terms of analysis and synthesis of control systems using existing software. The aim of this study was to receive transfer functions and frequency responses as mathematical models of above mentioned plants. To solve this problem the main equation of heat conductivity was put in basis. In addition three kinds of boundary conditions on external and internal wall surfaces were taken into account. Different combinations of boundary conditions on external and internal wall surfaces result in different kinds of transfer functions and frequency responses. These functions are transcendental and perhaps must be simplified for practical using. It was proposed few nontrivial ways in order to calculate frequency responses of cylindrical heat storage walls. To implement this calculation it is necessary to have available a subroutine for computing certain functions. If necessary, these routines can create their own with the above formulas. You can also use the tables of the functions, forming the basis of their structure interpolation (polynomial, cubic splines or B-splines). But most appropriate looks above numerical integration of differential equations with appropriate boundary conditions on single stepped input signal with zero initial conditions.

Obtained results can be used for researching of plants, which can be considered as cylindrical heat storage walls with distributed parameters, and for control system synthesis.

КУБРАК А. І., к.т.н., проф.; ЖУЧЕНКО О. А., к.т.н., ас.


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