多维磁浮柔性转子控制系统分岔与控制器设计

讨论了多维悬浮柔性转子控制系统局部及全局分岔问题，首先建立了该复杂系统动力学模型，应用中心流形和求规范形综合方法，得到此系统非半简双零特征值问题的规范形及其普适开折，并进一步讨论了此控制系统的分岔 行为（余维二分岔）及稳定性；给出了为实现稳定控制，控制器参数、转子系统结构参数的相互关系及稳定控制域，即给出分岔 参数条件、分岔曲线、转迁集，最后，给出此柔性转子控制系统的数值仿真结果。

THE BIFURCATION BEHMIORS AND CONTROLLER'S DESIGN FOR A MULTIDIMENSIONAL MAGNETIC LEVITATION FLEX-ROTATOR CONTROL SYSTEM

Owing to its little mechanical friction, no pollution, smaller noise, low maintenance cost, et., magnetic levitation system is widely used in the aerospace, precision machine tool and other advanced technology fields and its structural characteristics have been extensively studied. However, the research deals with the overlapping subjects of the electromagnetic, electronics technology, control theory, rotor dynamic, et., so that the theoretic research is very difficult, and the most analysis was with regard to simulating and test. Recently, in the studying of dynamics, the case of low dimension magnetic levitation rotor-bearing system, has been discussed; But, up to now, the dynamic behaviors about multidimensional magnetic levitation control system, specially, its bifurcation behaviors and global dynamic stability have not been discussed. In this paper, the problem of the local and global bifurcation behavior for the multidimensional magnetic levitation flex-rotator control system is discussed. A dynamic model of the system with nonlinear magnetic force and feedback control is presented. The system's normal form and universal unfolding of the non-semi simple double zero eigenvalue are achieved. The complex dynamic behavior of the control system will be shown by the analysis (co-dimension two bifurcation, Hopf bifurcation, and heteroclinic bifurcation). By theoretical analysis, it is shown that the design of parameters has a close relation with the system's stability; the range of selected parameters are achieved when the control system is stable, based on the condition of bifurcation parameters, bifurcation curve, bifurcation set and phase portraits. From numerical simulating of system, the complex dynamic behavior is shown, and the result is in correspondence with the theoretic analysis.