Obtaining the frequency response characteristics of a nonlinear servomechanism from an amplitude- and frequency-sensitive describing function

This paper presents two general concepts which are very valuable in analyzing nonlinear servomechanisms. A graphical procedure is introduced by which the frequency response of a nonlinear closed-loop system can be determined from the describing function. The theory is valid for the general describing function which is both amplitude and frequency dependent. Second, an analytical method is developed for evaluating the describing function by Fourier analysis of that type of nonlinear component whose time constant and gain vary with the magnitude of the input signal. As an example of a nonlinear element which meets these specifications the 2-phase servomotor was selected. The closed-loop frequency response was then predicted by the graphical method and verified experimentally.