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.

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

Nonlinear dynamic analysis of complex hydraulic driving processes

This paper studies the influence of the return and the valve spring rate on the stability of a four-way valve‐controlled double-acting actuator. A fully nonlinear model for this system is developed based on the orifice equation. The new model contains both the upstream chamber and downstream chamber for each orifice. The geometry of the return orifice and the valve spring rate has an impact on the stability boundary of the four-way valve‐controlled double-acting actuator. A larger return orifice requires using a stronger valve spring to ensure the stability of the system. It is shown that, for the nonlinear system, a stable limit circle can be born from an unstable origin as bifurcation occurs. [DOI: 10.1115/1.4024005]

The Impact of Return Orifices on the Stability of a Four-Way Valve–Controlled Double-Acting Actuator

A critical evaluation of current methods for analyzing hydraulic servo systems indicates a need for alternative methods that are better able to quantify robust stability, especially with respect to the existence of nonlinear oscillations. This paper addresses that need by examining a new analysis method that is capable of predicting stability robustness for nonlinear systems with high-dimensional parameter spaces. The method is based on the computation of "closest" Hopf bifurcations which correspond to the birth of limit cycle oscillations. A formal procedure that makes use of closest Hopf bifurcations for analyzing the robust stability of nonlinear systems is presented and applied. Practical implementation issues are addressed, with emphasis on interpretation of results to yield a meaningful quantitative measure of stability robustness. The new analysis method is validated via comparisons with previously published describing function results and new simulation results.

G.G. Kremer

Papers

Robust stability of nonlinear hydraulic servo systems using closest Hopf bifurcation techniques