Exact Force Vector Regulation of the Three-Pole Magnetic Bearing

Abstract

The three-pole magnetic bearing is an attractive alternative to the conventional four- and eight-pole magnetic bearings because of its simple structure and ability to be operated with three-phase power electronics. However, accurately controlling the three-pole bearing is significantly more complicated. The conventional control implementations are prone to large force vector errors that can lead to instability in the magnetic suspension system. This article proposes a new control implementation for externally biased three-pole bearings that eliminates force vector error. This control implementation is based on solving a fourth-order polynomial in the form of a depressed quartic to determine coil current commands. An analytic framework and graphic techniques are developed to study the solution space for the bearing's coil currents and explain discontinuities that can arise in certain bearing designs. It is shown that bearings with either no bias or a normalized bias field in excess of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\frac{1}{3}$</tex-math></inline-formula> are preferred for suspension stability. The exact force vector regulator is experimentally demonstrated in a bearing prototype and shown to be advantageous over the conventional regulation approach.