Theoretical and numerical study on the PD controlling of a simple hydraulic system

摘要

The paper addresses the analytical and numerical study of a hydraulic positioning system with PD controlling. Two control valve types are considered; two-stage directional valve exhibiting relay-like behaviour and proportional valve, which is capable of controlling the flow continuously. The mathematical model consists of a set of four nonlinear ordinary differential equations with discontinuous right-hand side, which exhibit self-excited oscillations in a wide parameter range. By using novel analytical techniques, closed formulae are derived for stability conditions. To verify these results, the periodic orbits are also computed as the solutions of a two-point boundary value problem, with the help of the software AUTO. By using this numerical technique, not only the stability boundaries and the properties of the oscillations (amplitude, frequency, etc...) can be computed efficiently but also more realistic and complex systems can be analysed.