ANALYSIS OF DYNAMIC STABILITY FOR MAGNETIC LEVITATION VEHICLES BY LIAPUNOV CHARACTERISTIC NUMBER
磁浮列车的动力稳定性分析与Liapunov指数

This paper is to give an analysis of dynamic stability of the dynamic control system ofa magnetic levitation vehicle moving over flexible guideways by means of the Liapunov characteristic numbers. In the dynamic control system considered here, the Bernoulli-Euler theory of beamsis employed for behaving deformation of guideways, and the negative feedback of displacement andits velocity of the gap bewteen the "maglev" and the guideways is employed. After the modaltechnique is taken in analysis of deform4tion of guideways, and small disturbance of the relativedisplacement in vertical direction is assumed in the study of dynamic stability, a system of ordinarydifferential equations with periodically variable coefficients are obtained to characterize the behavior of dynamic stability of the dynamic control system. Then, a conclusion on the dynamic stabilityof the dynamic control system is gained by means of the Liapunov characteristic numbers. Theresulted criterion for the dynamic control system is that when the Liapunov characteristic numbersof the system all are less than zero, the dynamic system is stablly controlled; otherwise, if there isone Liapunov characteristic number which is greater than zero in the system, the controlled system becomes unstable. Since the Liapunov characteristic numbers can be obtained by a numericalintegral to the dynamic system, this method for judging stability of the controlled system has themerit of small computation and simple of searching method to compare with the method based onthe Floquet theory to which one should search all characteristic values of matrix of basic solutionsof the dynamic system when it is of high dimension. Finally, some numerical examples are givento show that the method of Liapunov characteristic number is efficient.