A method for determining the stability of high-order nonlinear systems and the effect of system-controller parameter variations on system stability

This graduate project develops a method of analysis which determines the stability of high order nonlinear systems. The solution of the sets of differential equations of these high order nonlinear systems was accomplished by the use of a nonlinear analog model. This method of analysis uses no simplifying linearizations and hence yields results which are as accurate as the model describing the physical system. The results of the analog study are real-time trace solutions and are presented in the form of Stability Maps. Stabi1ity maps give a clear presentation of the relationship between the critical variables that govern the system; and thus yield a clear and simple method to make judgments en the effect of controllers on these systems. The design of a controller for a rocket engine combustion system was chosen as a motivating example to illustrate the method. This particular physical system was chosen since it is complex enough to fully illustrate the method. As in Liapunov's Methods, regions of stability for state variables are determined, except that this method gives the stability region which is largest in size. This ability to determine the complete region of stability gives this study a uniqueness not found in current methods of nonlinear analysis.