Robust stability of nonlinear hydraulic servo systems using closest Hopf bifurcation techniques

Abstract

A critical evaluation of current methods for analyzing hydraulic servo systems indicates a need for alternative methods that are better able to quantify robust stability, especially with respect to the existence of nonlinear oscillations. This paper addresses that need by examining a new analysis method that is capable of predicting stability robustness for nonlinear systems with high-dimensional parameter spaces. The method is based on the computation of "closest" Hopf bifurcations which correspond to the birth of limit cycle oscillations. A formal procedure that makes use of closest Hopf bifurcations for analyzing the robust stability of nonlinear systems is presented and applied. Practical implementation issues are addressed, with emphasis on interpretation of results to yield a meaningful quantitative measure of stability robustness. The new analysis method is validated via comparisons with previously published describing function results and new simulation results.