DC Control Effort Minimized for Magnetic-Bearing-Supported Shaft

A magnetic-bearing-supported shaft may have a number of concentricity and alignment problems. One of these involves the relationship of the position sensors, the centerline of the backup bearings, and the magnetic center of the magnetic bearings. For magnetic bearings with permanent magnet biasing, the average control current for a given control axis that is not bearing the shaft weight will be minimized if the shaft is centered, on average over a revolution, at the magnetic center of the bearings. That position may not yield zero sensor output or center the shaft in the backup bearing clearance. The desired shaft position that gives zero average current can be achieved if a simple additional term is added to the control law. Suppose that the instantaneous control currents from each bearing are available from measurements and can be input into the control computer. If each control current is integrated with a very small rate of accumulation and the result is added to the control output, the shaft will gradually move to a position where the control current averages to zero over many revolutions. This will occur regardless of any offsets of the position sensor inputs. At that position, the average control effort is minimized in comparison to other possible locations of the shaft. Nonlinearities of the magnetic bearing are minimized at that location as well.