STABILITY ANALYSIS OF MAGLEV VEHICLE WITH DELAYED POSITION FEEDBACK CONTROL

Because of the inherent instability, EMS maglev train requires the application of active control to achieve a stable suspension. In every suspension control loop, there is inevitable time-delay, which may affect the performance of the system. When the time-delay exceeds a critical value, the maglev train will become unstable. Previous studies have proved the existence of the critical time-delay. The relationship between critical time delay in control loop and vehicle parameters (including vehicle speed, position feedback control gains, guideway parameters, and suspension parameters) is studied in this paper. A dynamic model of a maglev vehicle/guideway coupling system is established. The 10 DOF vehicle includes a carbody and four maglev frames. Each maglev frame contains four electromagnets. The guideway is modelled as a series of continuous simply supported Bernoulli-Euler beams. The vibration equation of the guideway is obtained by a modal superposition method. In order to achieve vehicle/guideway coupling, a conventional electromagnetic force model which is linearized in the neighborhood of stable suspension position is adopted. The fourth-order Runge-Kutta method is used to obtain the dynamic response of the vehicle/guideway coupling system. A proportional derivative (PD) control algorithm is used for the feedback control of the electromagnet current. To facilitate the analysis, this paper assumes that all the time-delay occurs in the control loop, and that only the position feedback control loop exists. In order to analyze the motion property when critical delay occurs, we write a simulation program. Using the program, the dynamic responses of maglev vehicle considering different position feedback control delay are calculated. The delay value which results in motion divergence is defined as critical time-delay. Based on the calculations and analysis, following suggestions to promote the stability and weaken the effect of time-delay in position feedback control loop are provided: Enlarge bending rigidity and damping ratio of the guideway; Reduce position feedback control gain; Enlarge velocity feedback control gain; Enlarge second suspension damping. In addition, in view of that the critical time-delay of a stationary vehicle is always smaller than that of a running vehicle, hence, the critical time-delay of stationary vehicle shall be considered as safety limit value.