Stability and Step Response of a Hydraulic Servo with Special Reference to Unsymmetrical Oil Volume Conditions

Abstract

This paper reports a theoretical and experimental evaluation of the stability and response of a hydraulic servomechanism used to position a mass when the oil volumes on the two sides of the jack are substantially different. Application of small perturbation theory to the closed loop system shows that the loop gain for marginal stability is least when the oil volumes are equal and that when these volumes are unequal the response of the system is governed by a fourth order differential equation. Predictions of marginal stability gain and of the step response are in good accord with measurements made on an experimental rig. A system with unequal oil volumes is shown to be inherently more stable and to have a faster but less oscillatory response than when the oil is equally distributed about the jack piston. Coulomb friction is accounted for analytically by a viscous friction energy equivalent. When the response approximates to a damped sinusoid it is shown that it is necessary to base the equivalent upon this response.