Active Magnetic Bearing: The Influence Of PID Controllers On The Non-linear Vibration And Design Of The Robust Controller

The main purpose of this thesis is to discuss the influence of Proportion- Integration-Differential (PID) parameters on the non-linear vibration of Active Magnetic Bearings (AMBs) in the resonance areas. And considering the outside general uncertainties, the robust controllers are designed to satisfy the conditions.The nonlinear vibration of a mono-mass rotor supported by the AMBs, which are controlled by PID controllers, is investigated. For such a rotor-bearing system, the motion equation can be finally simplified to the generalized Van der Pol-Duffing equation. Therefore, when the parameters of PID controllers are changed, the non-linear phenomena such as softening/hardening spring characteristic, jumps and separation of the resonance curve can be observed and analyzed. According to the Lyapunov stability theories, the stable areas in the main resonance can be obtained. These conditions will provide the basis for the choice of the PID controllers.The similar nonlinear phenomena occur in the 3 times super-resonance and 1/3 time sub-resonance. When the PID controllers' parameters are changed, the relation between the amplitudes and frequency is also various. According to the relation, the appropriate parameters of PID controllers are selected to avoid the phenomena in these areas.The general uncertainties of the AMBs with single freedom are considered. According to the H?theory, the robust controller is designed and the results from the simulation show its validity.