A nonlinear study of the gain margin of a third order regulator system

Abstract

This thesis analyzes the dynamic response of a third order regulator system. Particular emphasis is placed upon the loss of stability of the nominal equilibrium state. The system utilized in this research models the fundamental turning dynamics of an autonomous vehicle. We make extensive use of bifurcation theory methods in analyzing the dynamics after initial loss of stability. The effective gain of the system is used as the main bifurcation parameter, since this is directly related to the gain margin for linear systems. It is shown that the nonlinear characteristics of the system may significantly affect the practical significance of its gain margin, as a measure of robustness to parameter variations, unmodeled dynamics, and external disturbances