IDENTIFICATION OF LINEAR DYNAMIC SYSTEMS IN THE ENVIRONMENT OF POLYNOMYAL SIGNALS

Abstract

A method for the structural and parametric identification of one-dimensional linear stationary dynamic systems, represented by differential "inputoutput" constraint equations, is proposed. The method is focused on both active and passive experiments. The method is based on a polynomialrepresentation of the input and output signals of the identified dynamic system. A compact vector-matrix representation of polynomials is proposed,which makes it possible to find the forced component of the solution of linear differential equations as a result of performing simple linear algebraicoperations. The vector-matrix representation of polynomials made it possible to quite simply solve the problem of inversion of linear dynamicalsystems and the problem of compensating the measured perturbation. The issues of representing time signals in polynomial form are not considered inthis paper. Based on the obtained linear representation of a one-dimensional dynamic system, which links the parameters of the input and outputsignals with the parameters of the differential equation of the identified dynamic system mathematical model, a linear system of algebraic equations forunknown coefficients of the differential process equation is obtained. In the general case, the resulting system belongs to the class of overdeterminedsystems, and therefore its solution can be obtained by the least-square technique and is reduced to finding a pseudoinverse matrix. A block diagram ofsoftware for solving the problem of structural and parametric identification in the environment of polynomial signals is proposed. The algorithmincludes the procedure of comparing the results of numerical simulation of the identified model with the output experimental signal and correcting thestructure of the model based on the results of the comparison.