Autobalancing of AMB Systems Using a Differential Regulator Based Output Regulation Approach

High speed rotating machines are subject to unbalance forces caused by residue weight. When the rotor’s axis of geometry and its principal axis of inertia are not aligned, unbalance forces synchronous to the rotational speed cause the rotor to deflect from the geometric center and enter a whirling motion. To reduce the effects that the rotor unbalance has on high speed machineries supported by AMBs, the conventional approach has been to either generate counteracting bearing forces or to shift the rotating axis in such a way that the shaft is rotating force-free or performing auto-balancing. In this paper, a differential regulator based output regulation approach is presented to address the autobalancing of AMB systems for varying rotational speeds. After formulating the output regu- lation problem with a time-varying exosystem, it is observed that the compensator gains can be obtained based on the solution of the differential regulator equation (DRE) and the output regulation objective can be achieved approximately with a small bounded error in the regulated output. The proposed method is verified in simulation for autobalancing with both varying and constant rotational speeds on a flexible rotor AMB test rig.