一つの制御弁を含む油圧系の安定性 Ｉ 安定判別法

Abstract

An oil-hydraulic system including a control valve often induces self-exciting oscillation and causes significant troubles. Especially, the oscillation caused by interference between the valve and passive elements (chambers, restrictions, pipelines etc. ) occurs easily and is difficult to prevent. As a rust step, the authors began their study using mathematical models for the control valve, the passive elements and a system consisting of them. The characteristic equation and a stability theory was derived from the model for the system. Stability discriminations were performed for a few simple systems. The results obtained from this research aye as follows; (a) A characteristic equation was derived for a system including a control valve with passive elements existing for both the upstream and downstream sides and withoug any branch lines. (b) A new stability criterion was derived from the Hermite-Hurwitz's theory. The advantage of this method is that, instead of solving to the characteristic equation to order m(assumed to be odd), one needs only to solve a few equations to order (m-1)/2. By this method, the approximate value of the natural frequency of the system can be easily estimated in the case where the real parts of the roots of the characteristic equation are very small compared to the imaginary parts. (c) As a limiting case, the characteristic equation for a valve-pipeline system (distributed system) was derived, and it was shown that the result coincides exactly with the solution of the wave equation.