Series Analysis of a Closed-Loop System Containing a Loaded Hydraulic Relay

Abstract

Analysis is made of a closed-loop system that contains a hydraulic relay. It is shown that the ramp response of a system with an error signal, velocity feed-forward, and velocity feedback, may be expressed as a rapidly convergent infinite series whose terms may each be determined as the response of a linear system in the presence of a forcing function. Inclusion of a small number of terms in the series is sufficient to provide excellent prediction of the error signal. Similar analysis and results are presented for the system subject to a Coulomb load.