Computational Cost Reduction of MIMO Controllers for Active Magnetic Bearing Systems

Abstract

Generalized multiple-input-multiple-output (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 single-input-single-output 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 bounds in their 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) redesign of a controller by identifying its negligible dynamics based on the identified bounds in the controllers' dynamic response. The results of both approaches are demonstrated on two active magnetic bearing (AMB) systems, a model of a 300 kW turbine generator with permanent magnet biased AMBs, and an experimental high-speed AMB machining spindle. μ-synthesis controllers are designed for both systems, and the proposed method and schemes are applied accordingly. The comparison of standard implementations of the synthesized controllers and the proposed new implementations is presented. The results demonstrate considerable reduction in the computational cost in terms of required number of multiply accumulate (MAC) operations.