Abstract
This study concerns the local and global bifurcation behaviors for the 5D magnetic levitation flex-rotator control system. A five dimension dynamic model of the system is constructed and appropriate equations of the nonlinear control system are developed. The co-dimension two local bifurcation is discussed. An analytical method was formulated and used to directly yield two dimension normal forms, and universal unfolding for the case with the non-semisimple double zero eigenvalue about the system; by Melnikov method, global homoclinic bifurcation behaviors are discussed. The conditions of bifurcation for various parameters, bifurcation curve, parameters plane, are obtained. A safe domain for selection of the parameters of the system is given. Finally, the theoretic analysis is proved by simulating for a 5D control system. Hopefully, the breath of the application will indicate the potential of the theoretic analysis.
