Wide Area Stabilization of a Magnetic Bearing Using Exact Linearization

This paper deals with wide area stabilization of a magnetic bearing system via exact linearization method[Ishidori, 1989]. Feedback control is indispensable for a magnetic bearing, because it is essentially an unstable system. To design a feedback control system, a linear mathematical model of the plant is convenient, however, the force of electromagnet is highly nonlinear. Then usually a local linear approximation around the steady operating point is employed, but the obtained linearized model can not express the exact behavior of the system at any other operating points. In this paper, we apply exact linearization approach to a magnetic bearing to achieve wide area stabilization. At first, we derive a nonlinear mathematical model of a magnetic bearing system, then we show this system belongs to a class of exactly linearizable nonlinear systems. Using exact Unearization method, we transfer the nonlinear model of a magnetic bearing to a hnear time invariant state space model in spite of a change of the operating point and the rotational speed of the rotor. Then we construct the state feedback control system by conventional LQ method. Finally, we evaluate the validity of our proposed method especially concerned with the change of the operating point and the rotational speed by several experiments.