About the accuracy of assessment of stability of linear periodically time-variable circuits by the frequency symbolic method

Abstract

Introduction. In the paper considers the question the research of accuracy (reliability) assessment of the stability of linear periodically time-variable circuits by the frequency symbolic method and determining the ways of ensuring it. Assessment of stability is reduced to calculating the real parts of the roots of the denominator of the normal transfer function of a linear inertial part of parametric circuit. Main part. Should be noted that the frequency symbolic method involves determining the transfer functions of their approximation by the Fourier polynomial. Therefore, we can assume that the error of the results are determined by: a) the number of the first k harmonic components selected to expression approximating of the transfer function; b) the number of decimal digits r taken for representing numbers that defines accuracy of performance of arithmetic actions. Thus, the accuracy of estimating stability of circles in our case is determined by selected values of k and r, a decrease which can lead to deterioration of accuracy, but excessive increase - to unjustified costs of computer time and memory. Last is enough critical, since the analysis of real parametric devices with several parametric elements by the frequency symbolic method is carried on critical opportunities of symbolic processor of the modern versions of MATLAB, so at excess value of k and r possible occurrence of incorrect situations. Conclusions. To ensure the reliability of assessment of the stability of linear periodically time-variable circuits based on the frequency symbolic method necessary reasoned to choose the number of harmonic components in the approximation of the transfer functions by the Fourier polynomial and the number of digits taken for representing numbers that defines accuracy of performance of arithmetic actions.