Title :
Nonlinear oscillations in magnetic bearing systems
Author :
Mohamed, Abdelfatah M. ; Emad, Fawzi P.
Author_Institution :
Dept. of Electr. Eng., Maryland Univ., College Park, MD, USA
Abstract :
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
Keywords :
control engineering computing; electric machines; feedback; limit cycles; machine bearings; magnetic devices; nonlinear control systems; optimal control; oscillations; servomechanisms; stability; transient response; BIFOR2; Hopf bifurcation analysis; air-gap flux; control engineering computing; electric machines; equilibrium point; gap displacement; gyroscopic effects; limit cycle; machine bearings; magnetic bearing systems; magnetic devices; nonlinear control systems; nonlinear feedback control; nonlinear oscillations; optimal control; optimal robust servocontroller; quadratic order; stability; transient response; velocity; Air gaps; Bifurcation; Cause effect analysis; Control systems; Feedback control; Limit-cycles; Magnetic analysis; Magnetic levitation; Nonlinear control systems; Robustness;
Conference_Titel :
Decision and Control, 1989., Proceedings of the 28th IEEE Conference on
Conference_Location :
Tampa, FL
DOI :
10.1109/CDC.1989.70175