STABILITY AND HOPF BIFURCATION OF THE MAGLEV SYSTEM
WU Jian-jun; SHEN Fei; SHI Xiao-hong
(1.Key Laboratory of Mechanics on Western Disaster and Environment of Ministry of Education, School of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China; 2. Xian Modern Chmistry Research Instiitute, Xian 710065,China; 3. Sichuan College of Architectural Technology,Deyang Sichuan 618000 ,China)
Abstract：The influence of feedback control gains on the stability of the nonlinear maglev system is investigated and the range of the design parameters maintaining the system stable is obtained. A test function for Hopf bifurcation is introduced to analyze the formation condition of the Hopf bifurcation. In this way, the time-consuming of eigenvalue computation in the process of analyzing system stability is avoided. With the velocity feedback control gain as the bifurcation parameter, the normal form theory and center manifold argument are applied to derive the explicit formulae, which determined the stability, direction and period of Hopf bifurcating periodic solutions of the maglev system. So, the asymptotically stable system can be achieved by adjusting parameters in the direction opposite to that of the Hopf bifurcation. Finally, the numerical simulation is performed to illustrate the validity of the main results.
2010, Vol. 29 
