Enhanced robust stability analysis of large hydraulic control systems via a bifurcation-based procedure

Because of their size and complexity, the initial design of many hydraulic systems is based primarily on steady state models. Nonlinear system dynamic characteristics are normally checked by simulation and/or prototype testing of the final design configuration, but even at this stage only the nominal system design and a limited number of other possible systems can be analyzed due to the excessive cost of each system analysis. Exhaustive parametric studies that verify the performance and stability of all possible systems are generally not practical. The deficiency associated with this analysis limitation is that hydraulic control systems that are predicted to be stable sometimes exhibit nonlinear pressure oscillations of unacceptably large magnitude. This paper documents the development and demonstration of a bifurcation-based analysis procedure that focuses on potential modes of oscillation rather than on analyzing all possible systems to yield a “practically rigorous” robust stability analysis of large nonlinear systems. Additional contributions of this research include: (1) proposed solutions to the main issues that complicate the robust stability analysis of large nonlinear systems, (2) demonstration of the use of the results from a bifurcation analysis to inform and enable an efficient nonlinear analysis, and (3) a detailed description of the possible nonlinear responses for a large automatic transmission hydraulic system with a 9-dimensional state space and a 24-dimensional parameter space.