Static Bifurcation in Mechanical Control Systems

Feedback regulation of nonlinear dynamical systems inevitably leads to issues concerning static bifurcation. Static bifurcation in feedback systems is linked to degeneracies in the system zero dynamics. Accordingly, the obvious remedy is to change the system input-output structure, but there are other possibilities as well. In this paper we summarize the main results connecting bifurcation behavior and zero dynamics and illustrate a variety of ways in which zero structure degeneracy can underly bifurcation behavior. We use several practical examples to illustrate our points and give detailed computational results for an automobile that undergoes loss of directional and cornering stability.