Robust control of magnetic bearings in subcritical machines

Abstract

This publication deals with the robust control of active magnetic bearings (AMB). Methods are developed for the control system synthesis and analysis for subcritical machines.

A new synthesis method is developed for the position control loop. In the method, linearization is achieved using two rotation matrices, and two controllers are designed using SISO (single-input, single-output) methods. The controller structure is based on the H∞-optimal controller, which is the best solution with respect to the stated physical performance limits. A generalized Nyquist diagram, based on the numerical range, is used to analyze the system. This diagram gives highly nonconservative stability robustness estimates and is mathematically elegant. The effect of the most important nonlinearity, i.e. power amplifier saturation, is carefully analyzed.

For unbalance compensation a simple algorithm is proposed which has only one tuning parameter. By using the generalized Nyquist diagram, it is shown that this simple algorithm generally works in the case of subcritical machines, also at the rigid-body resonance speeds. The single feedback coefficient and robustness can be easily determined using the generalized Nyquist diagram. Finally, AMB is used in mechanical balancing of an elastic rotor.