Robustness Limitations in Self-Sensing Magnetic Bearings

Self-sensing magnetic bearings use measurements of voltage and current in electromagnets to estimate the position of a magnetically levitated object. By estimating position in this manner, explicit proximity sensors are eliminated, along with significant cost, weight, and hardware complexity. Motivated by early and discouraging experimental studies, several theoretical papers have concluded an inherent difficulty in employing self-sensing. In light of later experimental work that appears to avoid this difficulty, we argue that these conclusions may be attributed to an over-simplification in the model from which this apparent difficulty is inferred. Specifically, if a linear time-invariant (LTI) model is derived from the underlying nonlinear model by linearizing the system at a fixed equilibrium point, analysis of this LTI model leads to the incorrect conclusion that self-sensing cannot be robust. The present work establishes that, if essential features of the nonlinearity are retained by linearization along a periodic trajectory, analysis of the resulting linear periodic model predicts more acceptable levels of robustness.