Stability Analysis of Cross Beam System with Two Time Delays

The cross beam that is controlled by air-operated valve is a typical two time delays dynamic system involving unknown parameters in engineering. The paper handles a new method to research the stability of this system on the basis of generalized Strum theory. The analysis focuses on the stability switches of the system with increase of the time delay from zero to infinity. The crossbeam system has two unknown control parameters. By the discussion, the paper presents the conditions that these parameters must satisfy to make the crossbeam stable in time delay range. It is found that the system undergoes one stability witch as the time delay increases