Optimal Control of the Gyroscopic Effects

On the rigid model of a rotating machine on active magnetic bearings (AMB), the gyroscopic effects appear as two derivative cross-coupling filters between the two planes of symmetry of the shaft, with a gain depending on the inertia and linearly varying with the rotational speed. Knowing that, we can add to the controller the opposite effect, under the form of two high-pass cross-coupling filters. After the presentation of the benchmark developed by the Societe de Mecanique Magnetique (S2M, Vernon, France), a complete model of AMB machine, combining a model for a rigid suspended rotor, to a modal model of the shaft, (reduced model built from the high-order nodal model extracted from an FEM software), is exposed. Our modeling approach presents several advantages: the model is simple to obtain, accurate and of a very reasonable order, so that it is easy to simulate. We use the model obtained in order to develop a control strategy for the gyroscopic effects. The method, based on the state-space model of the system, is a generalization of a another approach, also exposed, based on a transfer function model of the AMB machine. The advantage of the method is that the tuning of decentralized controllers is highly facilitated by the fact that the system, as seen by these controllers, is independent from the rotational speed