The frequency response of a certain class of non-linear feedback systems
J C West, John L. Douce · British Journal of Applied Physics · 1954
A method is described for predicting the frequency response of a certain class of non-linear feedback systems of any order. The restrictions on the feedback system are: (i) only one non-linearity is present, (ii) the output of the non-linear element is a single-valued function of the input, i.e. the non-linearity is of the "simple" variety, (iii) the output of the non-linear element is independent of frequency, i.e. it does not depend on the time derivatives of the input, (iv) the non-linearity is followed by an element of the system possessing a frequency-dependent transfer function of the low-pass type such as one or more integrators. Hence most electromechanical servo-mechanisms and many other cyclic control systems come within the scope of this analysis. The "jump" phenomenon, (4-7) or discontinuity in the gain-frequency characteristic which may arise under certain conditions of input amplitude and degree of damping, is evaluated. Some experimental work on a particular system is described and the results compared with those predicted.