Jump resonance criteria of nonlinear control systems

It is known that jump resonance can occur in a non-linear control system if the vector locus of the linear part passes through a certain region which depends upon the nonlinear part only. This paper is concerned with further investigations of the boundary curves of such regions. It is revealed that by normalizing the non-linear characteristic and using the inverse-vector plane, the region occupied by the boundary curve can be localized in the domain near the origin. It is also revealed that there exists a limit to boundary curves under certain conditions. For nonlinearities written by nondecreasing functions, idealized saturation and dead zone have a limit boundary curve. Boundary curves for typical nonlinearities are given. Conditions where jump resonance occurs in the second-order servo system with idealized saturation are also investigated.