Non-resonant response, bifurcation and oscillation suppression of a non-autonomous system with delayed position feedback control

Abstract

The maglev system with delayed position feedback control is excitated by the deflection of flexible guideway and resonant response may take place. This paper concerns the non-resonant response of the system by employing centre manifold reduction and method of multiple time scales. The dynamical model is presented and expanded to the third-order Taylor series. Taking time delay as its bifurcation parameter, the condition with which the Hopf bifurcation may occur is investigated. Centre manifold reduction is applied to get the Poincare normal form of the nonlinear system so that we can study the relationship between periodic solution and system parameter. At first, the non-resonant periodic solution of the normal form is calculated based on the method of multiple time scales. Then the bifurcation condition of the free oscillation in the solution is analyzed, and we get the conditions with which the free oscillation has maximum and minimum values. The relationship between external excitation and the periodic solution is also discussed in this paper. Finally, numerical simulation results show how system and excitation parameters affect the system response. It is shown that the existence of the free oscillation and the amplitude of the forced oscillation can be determined by time delay and control parameters. So felicitously selecting them can suppress the oscillation effectively.