Study On Vertical Nonlinear Dynamics And Feedback Control Of Two Degree Of Freedom Maglev System

Maglev trains are becoming an important part of transportation because of their safety,speed and low noise.The maglev train system has nonlinear characteristics,such as the electromagnetic force and the non-linearity of the suspension of the second series.Meanwhile,the suspension of the second series will also produce viscoelastic characteristics due to friction,material and other reasons.If the system is stimulated by external excitation,it may produce complex dynamic characteristics.This paper mainly analyzes and researches the nonlinear characteristics of suspension of Maglev train II,viscoelastic characteristics of suspension of Maglev train II due to suspension material,friction and damping,suspension control of maglev vehicle,delay controller of maglev train,and other aspects.The main research contents are as follows:(1)The stiffness and damping of the secondary suspension of maglev system are adopted in polynomial form to study the dynamic characteristics of maglev system with nonlinear stiffness.The electromagnetic force of maglev system has open-loop instability,so firstly,the electromagnetic force is linearized at the equilibrium position and the feedback control is added.The stability boundary of the system is obtained by using Routh-Hurwitz stability criterion.On the basis of the stability of the system,the correctness of the calculated results is verified by calculating the numerical and analytical solutions of the system.Then calculate the Jacobi matrix of the system,and on this basis calculate the system Hopf bifurcation conditions,through the numerical solution including time domain diagram and phase diagram to verify.Finally,the influence of continuous parameter changes on chaotic motion is studied.(2)A fractional differential term is added to the two-system suspension equation of maglev system to describe the viscoelastic characteristics of the two-system suspension.The periodic excitation is applied to the system,and the iterative matrix of the incremental harmonic balance method is derived,and the correctness of the calculation results is verified by numerical simulation.By changing the parameters of fractional differential term,the amplitude-frequency response characteristics of the system are studied,the influence rule of fractional differential term on the system is obtained,and the influence of the change of the system’s feedback control parameters on the chaotic behavior of the system is studied.(3)The state feedback control method has disadvantages such as poor robustness.In this paper,considering the moving position of the system,two different control parameters are adopted to enhance the control of the system far from the equilibrium position.The amplitude-frequency response curve of the system is calculated by the incremental harmonic balance method and compared with the state feedback control method to verify the control effect of the new control strategy.By changing the piecewise control parameters,the variation law of the amplitude-frequency response characteristics of the system is obtained.Applying uneven amplitude excitation to the system verifies the effectiveness of the new strategy.(4)Considering the delay in feedback control of maglev system,a maglev system model with two degrees of freedom delay controller is established.Based on the Routh-Hurwitz stability criterion,the stability range of the system without time delay is obtained by using the dislocation-velocity delay controller.Then the critical value of the system delay is obtained by the condition of the characteristic root crossing the imaginary axis.By changing the feedback control parameters of the system,different time delay critical values are obtained,and the change rule between the feedback control parameters and the time delay critical values is obtained,and the time delay critical values are verified.