Research On Hopf Bifurcation And Sliding Mode Control For Suspension System Of Maglev Train

The vehicle-guideway vibration greatly influences the project price and ride comfort. It is currently attractive and difficult to study the vibration of the vehicle-guideway in the field of suspension control. Maglev suspension control is the core and key technologies. The appropriate control algorithm plays a vital role in maglev suspension control.This paper studies two aspects of the mathematical model of the maglev train control system:one is dynamic behavior and the other is control theory. The dynamic behavior study includes analyzing the stability and Hopf bifurcation of the delay feedback control maglev system to find the reason of vibration of the vehicle-guideway. And control theory research includes calculating the control input and stabilizing the suspension system of magnetic lev-itation train using the sliding mode control algorithms.We discuss the dynamical behavior of the delay state feedback maglev suspension sys-tem by choosing the time delay as the bifurcation parameter in Chapter three. Using the center manifold and normal form theory, in the first two sections we analyze the stability and Hopf bifurcation of rigid guideway and flexible guideway magnetic levitation systems with the delayed state feedback control, and determine the nature of Hopf bifurcation and the sta-bility of the limit cycle by calculating the normal equation. Comparing with the method of center manifold, which is classic but needs tedious calculation, the method of perturbation is more quickly and easier. In the forth Section, using the Pseudo-Oscillator analysis, we calculate the approximate expression of the amplitude of the periodic solutions, and verify its validity by numerical simulations.Delays are inevitable. Selecting appropriate control parameters in the delay state feed-back control of the maglev train system is also important. In the fourth Chapter, we discuss the relationship of time delay and velocity feedback control gain which influence the stabil-ity of maglev system. When time delay is fixed, choosing the velocity feedback control gain as the bifurcation parameter, we analyze the quality of the Hopf bifurcation and calculate the approximate expression of periodic solutions of the maglev system by using the method of multi-scale. The delay maglev system is stable when the velocity feedback control gain within a certain range, and would have two limit cycles even exist a double Hopf bifurcation by changing the value of the feedback gain. And then we analyze the existence and the sta-bility of the periodic solutions when double Hopf bifurcation occurs. In certain conditions, the maglev system would occur second bifurcation.Then we select the appropriate control strategy, from simple to complex, to control the suspension system of maglev train. In the fifth Chapter, using the sliding mode control algorithm, the control input is determined to ensure the maglev system stable. This Chapter includes two aspects:linear and nonlinear sliding mode control. First of all, combining with linear quadratic regulator, the sliding mode control is applied to the linear maglev train system; then we apply the modified tangent function to the adaptive sliding mode control of nonlinear system of maglev train, and verify its effectiveness through numerical simulations.