ANALYSIS OF SELF-OSCILLATIONS IN NONLINEAR TWO-DIMENSIONAL CONTROL SYSTEMS

Abstract

A simple method of investigation based on the harmonic linearization and the characteristic transfer function methods, of symmetric one-frequency self-oscillations in nonlinear two-dimensional control systems with identical transfer functions of separate channels and rigid cross-connections is proposed. As opposed to the general approach, in which the determination of all vectors of self-oscillations is required, with the subsequent examination of the harmonic balance condition for the one-dimensional characteristic syste­m­s, the approach presented in the article is based on the determination of those values of amp­li­t­u­des and frequencies of oscillations for which one of the two characteristic syst­e­m­s is on the stability verge and on the simple graphic test of the collinearity condition. At that, the procedure of investigation of self-oscillations is brought maximally close to the classical procedure of investigation of nonlinear systems with a single input and single out­p­ut. A nume­r­i­c­al example of self-oscillations’ investigation is given, as well as the results of dynamic simu­la­tion in the Simulink package environment that verify the calculated data are presented.