Signal stabilization of self-oscillating systems

The hunt (self-oscillations) of a physical system may often be removed by the introduction of an appropriate stabilizing signal which changes the open loop gain of a closed loop system in a non-linear manner. The theory of stabilization developed in this paper explains experimental results reported by R. Oldenburger in 1957. With the aid of Fourier series the designer can determine the periodic signal to be inserted at one point in a loop to yield a desired stabilizing input to a nonlinear element in the loop. This is illustrated by sinusoidal and triangular inputs to a nonlinear element. An example where a limiter is the only nonlinearity, is employed to illustrate the theory. The input-output characteristics of non-linear elements are in practice always modified by the presence of extra signals such as "noise." Further, nonlinearities are always present in physical systems. The effect of extra signals on nonlinearities and system performance is thus of concern in the general study of physical systems, regardless of whether or not the problem of stability is involved. The results of this paper for the problem of stability extend readily to the problem of system performance for arbitrary disturbances. This paper is to be published in the Proceedings of the First IFAC Moscow Congress by Butterworth Scientific Publications, in 1960.