Computational Cost Reduction of MIMO Controllers for Active Magnetic Bearing Systems

Generalized MIMO controllers such as H_∞ and µ have not been widely adopted in the magnetic bearing industry partially due to high computational cost relative to simpler SISO schemes. Computational cost is important to industrial magnetic bearing vendors as their controller hardware is based on embedded processors that have limited bandwidth.  Studies to mitigate the problem of high order controllers show the limit of the existing methods in order reduction while still maintaining satisfying robust performance. A novel method is proposed to reduce the computational cost of robust controllers by identifying the bounds on the controllers’ dynamic response, such that an implementation of a controller within those bounds results in the robust performance. The bounds are used to develop two computational cost reduction schemes for controller implementation, i.e., 1) identifying a dual-rate implementation of a single-rate controller which uniformly reduces the computational cost via interlacing technique, and 2) guided redesign of a controller by identifying negligible dynamics in the controller based on the identified bounds in the controllers’ dynamics response. The results of both approaches are demonstrated on two active magnetic bearing (AMB) systems, a model of a generator with permanent magnet biased AMBs and an experimental high-speed AMB machining spindle. A μ-synthesis controller is designed for both systems and the proposed method and schemes are applied. The comparison of standard implementation of the synthesized controllers and the proposed new implementations are compared. The results demonstrate considerable reduction in computational cost in terms of required number of multiply-accumulate (MAC) operations.