Методи синтезу та ідентифікації еквівалентних математичних моделей багатовимірних динамічних об’єктів

Abstract

Thesis researches the creation of methods for synthesis and identification of mathematical models of minimum order for decreasing time when used in tasks of analysis and optimisation of processes in multidimensional dynamic objects. For the first time the research proves that the process in minimum phase dynamic objects with negative feedback which are described by the linear differential equation of the high orders, may be equivalently described within the scope of minimum phase ones by the differential equations of minimum order, which equals the sum of maximum order of the derivative in the right part and a three num. For the minimum phase linear multidimensional dynamic objects, that operate in the mode of the real time signal transmission and which do not have the derivatives in the right part of the differential mathematical model, there had been for the first time developed the method for identification of the processes by the mathematical models not higher than that of the third order, equivalent as for the cutoff frequency. The algorithm of the method is based on the system of the equations, one part of which shall be synthesised with the consideration of the boundary conditions, set by the minimum frequency and cutoff frequency, and the other part shall be synthesised using the standard procedure of the least squares method with the use of Bode magnitude plots. The suggested method of synthesis and identification of the equivalent models had been transformed into the multidimensional continuous linear minimum phase dynamic objects, described by the differential equations with the derivatives in the right part. Practical value of the results obtained is that, first of all, they complement to the theory of synthesis and identification of the mathematical models of dynamic systems with the conditions of using the equivalent mathematical models with the minimum allowed order instead of mathematical models of multidimensional dynamic objects, that is, objects of the high orders in the tasks of their analysis and optimisation, they also complement this theory with the methods for identification of the equivalent models, for which there had been created specific realisation algorithms and calculation correlations for the evaluation of the adequacy.