Estimation of stability of oscillations of linear time-varying systems with one time-varying parameter with calculation of influence of higher frequency motions

Abstract

The paper reveals a new method for estimation of stability of oscillations of linear time invariant systems with one time-varying parameter given by a harmonic function. The suggested approach includes building a matrix of transfer functions, which calculates interference of the highfrequency oscillations of the output of the linear time-invariant part of the system. Suggested approach makes possible to build equivalent of the Nyquist criterion for linear systems with a single time-varying parameter. The application of the suggested approach is shown by numerical examples. Results of the present article may be used for control systems of cranes and other lifting mechanisms.