QUASI-ANALYTIC METHOD OF LINEAR DYNAMIC SYSTEMS INVERSION

Abstract

The problem of inversion of dynamic systems has become widespread while solving the problems of control, identification, and measurement problems arising during the design and research of electrical and mechanical dynamic systems. Inverting is an effective way of implementing disturbance control processes, as well as in combined control systems with a predictive model. The analysis of information sources showed that in the practical solution of most inversion problems, a number of difficulties arise, which are associated with the high sensitivity of the results in relation to the accuracy of the parameters of the mathematical model of the control object, the instability of the inverse model of non-minimum-phase objects, and the violation of the conditions of physical feasibility. The work offers an effective method of inverting linear stationary dynamic systems, free from the mentioned shortcomings in many respects. The basis of the method is the presentation of input and output signals in the form of infinite linear combinations of their derivatives. A method of determining the sequence of matrix coefficients of linear representations of input and output signals is proposed. The main theoretical result is obtaining relationships between matrix coefficients of input and output signals. The work considers mathematical models of linear dynamic systems in the form of differential equations in the state space and in the equivalent "input-output" form. The considered systems must meet the conditions of asymptotic stability, as well as the condition of equal dimensions of the input and output vectors. Requirements for mathematical models of input and output signals are given, the fulfillment of which allows, instead of infinite sums representing signals, to be limited to a finite number of terms.