Adaptive control of nonlinear vibrations of rotating shaft on a magnetic bearings

In this paper, a rotor system on a magnetic bearing isstudied. The nonlinear modeling of a rotor with activeabsorber is presented. In the modeling, geometry effect ofmagnets are considered and due to the nonlinear stiffness ofmagnetic bearings highly nonlinear coupling between therotor shaft and absorber exists. Elastic supports are modeledwith appropriate springs and dampers. The eccentricity ofthe rotor induces notable vibrations which should besuppressed, the Negative stiffness of the nonlinear bearingspermits to vanish the amplitude of vibrations at lowfrequencies. A complete dynamical model with fulluncertainty on the parameters is presented. A nonlinearadaptive active controller is designed to capture nonlinearcouplings and unknown parameters which vanish therotational vibrations. The simulation results are presented toshow suppressing the vibrations of the rotor by applying theproposed controller.