Reducing power loss in magnetic bearings by optimizing current allocation

Conventional magnetic bearings control current or flux by operating symmetrically about a bias current or bias flux. This approach is known to be much easier to control than operating without a bias but has the disadvantage of introducing additional power loss. Although one obvious way to minimize the power loss is to alternate activation of the two opposing electromagnetic actuators, this single actuator allocation strategy has not been successful in practical applications because it results in severe performance degradation. In this paper, we investigate the fundamental reasons behind the performance degradation under the single actuator allocation strategy. One major reason is voltage saturation in the circuit systems. On the basis of this result, we formulate the problem of minimizing the energy consumption by allocating the currents under the constraint of bounded voltages. We establish necessary conditions and properties for the optimal solution, which we use to determine the optimal allocation strategy for some common force signals. Since the optimal solution is very sensitive to the variation of the force signal, we propose a simple static allocation strategy to approximate the optimal solution.