Discrete approximation of models with distributed parameters

The relevance of the study is due to the need to develop a mathematical apparatus of approximate mathematical description in the form of discrete transfer functions for solving problems of control of continuous systems with distributed parameters. Therefore, this article discusses the model of approximation of dynamic properties of systems. Approximation is performed in the static mode area by replacing derivatives with their differential analogues applicable to the difference model of the Carson discrete transformation, sequentially differentiating the transformation results over the complex variable and moving to the limit at the zero value of this variable. The leading approach to the study of the problem of management of continuous systems with distributed parameters is the method of analytical modeling, which allows to obtain a difference model with a high degree of approximation. In the article, the results of the transformation of the model in the form of a sequence of equations providing a recursive calculation of the moments of discrete weight functions, starting from the moment of zero order. The coefficients of approximate discrete transfer functions are determined by solving systems of linear algebraic equations, the coefficients of which depend on the moments of discrete weight functions. This is an example of a calculation for a system described by two differential equations with partial derivatives. Materials of the study are of practical value for specialists of chemical industry, non-ferrous metallurgy and a number of other industries, where methods of analytical modeling of objects are widely used.

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