Jump resonance in a third order nonlinear control system

Abstract

An analysis is presented in which a graphical method is used to gain a better understanding of jump resonance. In the frequency range of interest the orthogonal components, u and v, of the steady state first harmonic approximation are plotted in a u-v plane. Constant angular frequency loci are drawn on the plane and intersected by a circle of radius F, the magnitude of the sinusoidal forcing function. These intersections determine the amplitude of the first harmonic solution. The locus of vertical tangents, normally associated with the amplitude-frequency curve, plotted on the u-v plane is used to determine the lower jump resonant frequency. The approximation reveals that jump resonance can be precluded if the forcing function does not exceed a calculable value referred to as the threshold value. The threshold value is determined from the system parameters. For a forcing function sufficiently large it is shown that real solutions in the immediate neighborhood of angles of lag of π 2 do not exist. A critical forcing function such that a maximum lag angle of π 2 is possible may be determined from system parameters.An electronic analog computer was used to verify the results of the study.