Question

Describing function analysis of nonlinear systems hysteresis loop

Answer 1

A new method is given for evaluating the describing function of hysteresis-type nonlinearities. A circle of radius Ais constructed to represent a sinusoidal input A sin θ, where θ = ωτ.In the case of a single-valued nonlinearity, an output contour C with area A1 is sufficient to represent the output wave-shape. In the general case of double-valued nonlinearities, another output contour C′ with area B1 is required to determine the general describing function. The ratio of the second area B1 to the first area A1 determines the phase shift. It is to be noted that the second area B1 is directly related to the area of the hysteresis loop or the backlash