A bifurcation-based procedure for designing and analysing robustly stable non-linear hydraulic servo systems

Abstract

A critical evaluation of current hydraulic servo system analysis methods indicates a need for alternative methods better able to quantify robust stability. One promising method recently developed for analysing large-scale power systems determines stability robustness in a high-dimensional parameter space by computing the distance to the ‘closest’ Hopf bifurcation (which corresponds to the birth of a limit cycle oscillation). In this paper a procedure is developed for applying closest Hopf bifurcation theory in the design and analysis of robustly stable hydraulic servo systems. The procedure addresses practical implementation issues such as the impact of an inhomogeneous parameter space and the choice of a metric that yields a meaningful quantitative measure of stability robustness. Results from the new procedure applied to a common position control system compare favourably with published describing function results and new simulation results. Additionally, the new procedure is easier to apply and produces results which are easier to interpret and use. As a demonstration of the design procedure's ability to handle non-linear systems with high-dimensional parameter spaces, a hydraulic servo system with an inhomogeneous seven-dimensional parameter space is designed to meet a robust stability requirement.