Improved methods for robust stability analysis of nonlinear hydraulic control systems: A bifurcation-based procedure

Automatic transmission hydraulic systems designed using the current industry-standard analysis procedures sometimes exhibit unacceptably large pressure oscillations. The current simulation-based analysis procedures fail to predict these steady state nonlinear oscillations (limit cycles) because the inefficiencies associated with using simulation for stability analysis and parameter space gridding for robustness analysis severely restrict the size of the parameter space that can be analyzed, leading to an incomplete and sometimes inaccurate measure of a nominal system's stability robustness.; An alternate method for quantifying stability robustness with respect to limit cycle oscillations can be developed based on the following facts: (1) Hopf bifurcations correspond to the birth of limit cycle oscillations, and (2) a nominal system's stability boundary can be approximated by the boundary of its feasibility region which is generically composed of locally smooth codimension 1 bifurcation surfaces (Hopf and Saddle Node bifurcations). The Closest Bifurcation Method uses these facts to avoid the difficult process of completely defining the stability boundary by directly computing the points on the boundary that are locally closest to the nominal system by means of an efficient iterative procedure that finds the directions in parameter space that pass through the nominal system and are co-linear with the normal vectors.; A rigorous Stability Robustness Analysis Program (STRAP) based on the Closest Bifurcation Method is developed in this dissertation. The program is validated by comparison with experimentally verified simulation results. It represents a significant improvement over current analysis methods because it is capable of efficiently analyzing large systems with large parameter spaces, leading to a more meaningful measure of a system's stability robustness. Newly developed strategies for improving analysis efficiency via reduced state submodels and parameter space reductions enable the analysis method to better handle large systems. Other advancements include methods for normalizing non-homogeneous parameter spaces to produce meaningful distance metrics, and procedures for quantifying stability robustness with constrained parameters. The most important advancement is an extension of the local Closest Bifurcation Method to make it capable of quantifying global stability robustness with respect to both asymptotic stability and large amplitude oscillations.