Frequency analysis of parametrically controlled oscillating systems

Abstract

The study attacks the problem of the stabilization of linear time-invariant (LTI) system oscillations. The paper suggests a new type of parametrical feedback and reveals the characteristics of such feedback. The feedback contains simple units of time-delay, squarer, differentiator, sign function, and linear gain. Frequency analysis based on stationarization of the time-varying parameter proves the stabilizing properties. A numerical example shows dependence between the time-delay value set in the parametrical feedback and time constant of the envelope curve of oscillations. A classical spring pendulum case is analyzed.