Application of the Theory of Complete Functions for the Stability Analysis of a Hydraulic System with Distributed Parameters.

A hydraulic balancing system for rolls is used to exemplify this application of the theory of complete functions. The equations of a pressure wave were selected as a mathematical model of the system. The boundary conditions are established by applying Newton's principle to the mechanical part and the continuity law to the hydraulic part of the problem. To simplify the mathematical model, one of the moving boundary cross-sections is fixed. Use is made in this connection of some properties of the Laplace-Carson transformation. By applying the generalized Routh-Hurwitz stability criterion to a certain quasi-polynomial, some stability relations are established between various parameters. The considerations are illustrated by a numerical example.