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 testin g of the final design configuration, but even at this stage only the nomina l system design and a limited number of other possible systems can be analy zed due to the excessive cost of each system analysis. Exhaustive parametri c 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 stabl e sometimes exhibit nonlinear pressure oscillations of unacceptably large m agnitude. This paper documents the development and demonstration of a bifur cation-based analysis procedure that focuses on potential modes of oscillat ion rather than on analyzing all possible systems to yield a "practically r igorous" robust stability analysis of large nonlinear systems. Additional c ontributions of this research include: (1) proposed solutions to the main i ssues that complicate the robust stability analysis of large nonlinear syst ems, (2) demonstration of the use of the results from a bifurcation analysi s to inform and enable an efficient nonlinear analysis, and (3) a detailed description of the possible nonlinear responses for a large automatic trans mission hydraulic system with a 9-dimensional state space and a 24-dimensio nal parameter space. (C) 2001 The Franklin Institute. Published by Elsevier Science Ltd. All rights reserved.