Describing function-based analysis of a nonlinear hydraulic transmission line

This paper presents an analytical method of predicting and eliminating limit cycle conditions in hydraulic drive systems, where backlash in the actuator seal is the dominant nonlinearity. It is shown that limit cycle conditions are a strong function of certain plant parameters. The elimination of limit cycle conditions may thus be achieved by the alteration of certain inherent plant parameters. Fluid flow in a hydraulic pipe is modelled using transmission line theory. The sinusoidal-input describing function is used to indicate which values of the plant parameters would result in limit cycle conditions. The analytical results were verified on an experimental test bench