Nonlinear oscillations in magnetic bearing systems

Nonlinear oscillations in magnetic bearings caused by gyroscopic effects at high speeds are analyzed. A nonlinear model for the magnetic bearing is set in state-variable form, using air-gap flux, gap displacement, and velocity as state variables. The system, which is unstable in nature, is stabilized locally around the equilibrium point at zero speed using an optimal robust servocontroller. It is shown that as the speed changes the system undergoes Hopf bifurcation to periodic solutions around some critical speed. The Hopf bifurcation analysis is done using a software routine called BIFOR2. The limit cycle is shown to be unstable, so the methods of nonlinear bifurcation control are used to stabilize it. An easily implemented nonlinear feedback control of quadratic order is derived to control the Hopf bifurcation occurring in the system. The transient response of the system with and without nonlinear feedback is obtained to show the effectiveness of nonlinear feedback