Robust stability analysis of large-scale hydraulic control systems

Many large-scale hydraulic systems are so complex that their initial design must be carried out using only steady-state models-nonlinear dynamic characteristics are only checked for the final design configuration by simulation and/or prototype testing. This is due to the size and complexity of the models, the number of parameters, and the expense of each nonlinear analysis. This paper proposes a bifurcation-based procedure efficient enough to permit the consideration of system dynamics earlier in the design. The main obstacle to rigorous dynamic analysis of a large-scale system using bifurcation is the possibility of multiple response modes in the feasible parameter space. Each possible response mode has a different sensitivity with respect to the different system parameters, and the task of finding all possible response modes and determining which is the most likely to occur is daunting-but is feasible with an efficient analysis algorithm. The key advancement described in this paper is the development of an efficient global search procedure that combined with the closest bifurcation method produces a `practically rigorous´ result with respect to the identification of all possible response modes and a meaningful quantification of the relative probability of occurrence for each one. For demonstration, the global search procedure is used to rigorously analyze the stability robustness of a particular large-scale automatic transmission hydraulic system with a 9-dimensional state space and a 24-dimensional parameter space