Вычислительные алгоритмы исследования устойчивости динамических систем в задачах схемотехнического анализа

Abstract

The article presents efficient computational algorithms for analysis of the stability of the dynamical systems. The algorithms are based on the principle of modal approximation. A numerical algorithm for computing of the poles of the transfer function is proposed, which ensures determination of the poles located in the right half-plane. In order to detect the pole with the positive real part the suggested algorithm exploits the property of the damping factor ς i =- αi αi 2 + βi 2 for the obtained poles λi= αi+i βi . This factor is negative for the poles with positive real parts. The following sequence of the form ς1 α1 , β1 - ς0 < ς2 α2 , β2 - ς0 <...< ςk αk , βk - ς0 is constructed for the computed poles. The sequence is converged to the pole with the positive real part under ς0 <1 . The paper presents an algorithm for computation of the poles of the transfer function with the maximal sensitivity with respect to the circuit parameters. The suggested algorithm allows us to detect the parameters with the maximal impact on the shift of the poles and to determine the critical parameter values corresponding to the boundary of instability.