An Active Magnetic Bearing is an actuator acting without contact on a body using electromagnetic fields. AMB are essentially used to position without contact rotors of rotating machines with the following advantages: rotor speed increasing beyond 100 000 rd/m, maintenance reduction (no greasing system), and introduction in specific environments (high temperature, vacuum). The unbalance (du to non coincidence between the geometrical axis and the axis of inertia of the rotor) is a rotating acceleration which is applied to the geometrical center and modifies the desired trajectory. This point has not be almost treated in non linear. To solve this problem, we have proposed a new process modelisation where the perturbation is an intrinsic part of the model (owing to lagrangian formulation). This method has allowed to obtain several models: simulation model, analysis model, model for command. In the following part, we have developed a new technique to control the unbalance to obtain rotation either around the geometrical axis or the axis of inertia to reduce the energy consumption. The control of unbalance is obtained using the coupling of a control law in a fixed reference frame and a other in a rotating reference frame turning at the rotor speed. This two commands represent the desired accelerations required to stabilize the rotor. Knowing this accelerations, the used of a nonlinear transformation is then necessary to obtain a real current or voltage command. This transformation uses, in one hand input-state linearization and passivity, in the other hand sliding modes. In the last part can be found the simulations and the real experiments obtained on a experimental device we have building during the thesis.
