Applying Hopf Bifurcation Theory To Research The Vehicle-Guideway-Coupled Elastic Vibration Control Of Maglev Train

The vehicle-guideway-coupled vibration limits the development of maglev train. So far, with the limit of external technology level, the mechanism and character of vehicle-guideway-coupled vibration are not clear to the engineers, and then how to restrain the vibration by control method has become an important problem.This paper discussed the character and shortage of the maglev model based on rigid guideway. The elastic guideway model which can describe the vehicle-guideway-coupled vibration roundly was built, and the controllability and observability and stability is analyzed. It has been proved that the vehicle-guideway-coupled vibration is corresponding to Hopf bifurcation problem of constant differential coefficient equation in mathematics; therefore, we can get the bifurcation point with the model to find the vibration frequency and self-excitated oscillation critical point of nonlinear system.In this paper, we selected 2 methods to carry on the research of the vehicle-guideway-coupled vibration, one is 3 states feedback and the other is 5 states feedback. It should be noticed that the traditional method to solve Hopf bifurcation problems is complex to calculate Jacobian matrix. So we can use Hurwitz determinants to transfer the Hopf bifurcation point into a resolve of a nonlinear equation and get an algebra criterion. We can theoretically calculate each coupled vibration point and frequency under the conditions of 3 states and 5 states feedback. Finally,from the view point of pole configuration and stability,we can conclude that the 5 states feedback method is more effective to restrain the vibration than 3 states feedback method.This paper has some creative achievements: First, we select variables suitably by a nonsingular matrix to build a single point elastic guideway model. Second, we carried on 5 states feedback research and proved that the ability of 5 states feedback is stronger to restrain the vibration than 3 states feedback by theoretical analysis, emulation and experiments.