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

In this paper, a rotor system on a magnetic bearing is studied. The nonlinear modeling of a rotor with active absorber is presented. In the modeling, geometry effect of magnets are considered and due to the nonlinear stiffness of magnetic bearings highly nonlinear coupling between the rotor shaft and absorber exists. Elastic supports are modeled with appropriate springs and dampers. The eccentricity of the rotor induces notable vibrations which should be suppressed, the Negative stiffness of the nonlinear bearings permits to vanish the amplitude of vibrations at low frequencies. A complete dynamical model with full uncertainty on the parameters is presented. A nonlinear adaptive active controller is designed to capture nonlinear couplings and unknown parameters which vanish the rotational vibrations. The simulation results are presented to show suppressing the vibrations of the rotor by applying the proposed controller. .