Effect of time delay in velocity feedback loop on the dynamic behaviors of magnetic bearing system

The effect of time delay in velocity feedback control loop on the dynamic behaviors of single degree of freedom magnetic bearing system is studied. The stability of trivial equilibrium point is discussed and the critical time delay where Hopf bifurcation may occur is obtained by analyzing distribution of the roots of the associated characteristic equation. Then an approximate analytical method is performed to determine the direction and stability of Hopf bifurcation and analyze the primary resonance of system. Given system parameters, the validity of above analytical method is verified and the effect of time delay on the forced vibration of system is studied by numerical method. It is found that the amplitude of stable period motion increases, some complex dynamical behaviors such as quasi-periodic motion may occur, and the system may get out of control with the increase of time delay. Therefore the effect of time delay should be taken into sufficient consideration in the design of system control loop.