Синтез еквівалентної математичної моделі для системного аналізу складної системи

Abstract

The paper proves why a mathematical model of a complex system with many inputs in the form of a multiple regression equation cannot be used in problems of predicting the original coordinate of this system if it is not possible to influence its input coordinates, and in problems of controlling the original coordinate of this system if it is possible to influence any of the input coordinates. It is shown that the results of the proof are fully consistent with the experimentally obtained dependences for a normally functioning industrial complex system, which is a diffusion apparatus for the extraction of sugar from beet chips. Using autoregressive models for each input coordinate of a complex system, a synthesis of such a mathematical model of this system, which can be used in predicting the output coordinate of the system in the absence of influence on its input coordinates and in the problems of controlling this output coordinate b to one of the input coordinates. A method for synthesizing an equivalent mathematical model of a complex system operating in a stationary mode, suitable for predicting and controlling one output coordinate of this system, depending on several input coordinates, each of which is given by an equivalent autoregressive dependence, which takes into account several previous values of this input transformed into a time series. The results of the synthesis of an equivalent mathematical model of a complex system are generalized to complex systems with several output coordinates, each of which depends on several input coordinates