Information Technology of the Fourier-Integral Method Implementation for Dynamic Systems Identification

Abstract

Information technology has been developed for implementing the Fourier integral method of identifying dynamic systems using information about their input and output signals, created in the 1980s by B. I. Mokin and generalized by O. B. Mokin. The developed information technology is based on a computer program created in the Python language. The first part of this Python program, implementing the first stage of the proposed information technology for identifying dynamic systems, decomposes the experimentally obtained input and output signals of the dynamic system into truncated Fourier series. The second part of this Python program generates mathematical models of the real and imaginary frequency characteristics of the identified dynamic system using its a priori given transfer function, selected from a set of these functions, given symbolically with increasing number of symbols. The third part of this Python program calculates arrays of values of the real and imaginary frequency characteristics of the dynamic system being identified, using the Fourier coefficients calculated in the first part of the program and the calculated relations of the Fourier integral identification method. The fourth part of this Python program uses the sum of squares of deviations of the actual frequency response values of the dynamic system, calculated using the Fourier integral identification method, as the optimization criterion. from the values of the same characteristic calculated using its mathematical model, using the least squares method, determines the optimal values of the parameters of the a priori given transfer function according to the selected criterion. The fifth part of this Python program, using as a criterion the sum of the squares of the deviations of the values of the imaginary frequency response of the dynamic system, calculated using the Fourier integral identification method, from the values of the same characteristic calculated using its mathematical model, determines the error of identification of the parameters of the a priori given transfer function. At the next stage of implementing the proposed information technology, the next a priori specified transfer function is selected from a set of transfer functions specified symbolically, and the process of its identification using the developed Python program is repeated, starting from its second part. This process is repeated until the identification error decreases and ends at the stage where the identification error begins to increase. The transfer function, whose parameters are calculated at the previous stage of implementation of this information technology, is declared to be the optimal mathematical model of the dynamic system, and this mathematical model will be optimal not only in terms of parameters, but also in terms of structure.