The Second Describing Function and Removal of Jump Resonance by Signal Stabilization

Abstract

A derivative of the output of a nonlinear element is taken with respect to the input. For commonly occurring nonlinearities which are piecewise linear, this derivative is sectionally constant with respect to the input. This property of the derivative is used to reduce the computational work required for deriving the describing function. The concept of this derivative is applied to the study of the effect of a high-frequency signal on the input-output relationship of a system containing a limiter with hysteresis. This signal may be regarded as an extra signal introduced into a system to improve the performance of the nonlinear component. The mathematical analysis of the effect is simplified if the extra signal is a triangular wave instead of sinusoidal. The extra triangular signal is applied to removing the jump phenomenon which exists in a feedback control system with a limiter with hysteresis.