Very small implanted permanent magnets guided by large electromagnetic coils have been proposed previously as a method for delivering hyperthermia to or guiding catheters through brain tissue. This procedure is termed "magnetic stereotaxis." Early efforts employed a single coil on a movable boom, a design that proved logistically difficult to use on human patients. The present work deals instead with a design where several stationary coils are employed to develop a force on the implanted magnet. The coil current-to-force relationship is developed for this type of machine, and several optimal solutions for realizing an arbitrary static force are presented for various constraints on the orientation of the implanted permanent magnet. Costs of the different solutions are compared in several examples using a mathematical model based on the Magnetic Stereotaxis System (MSS) developed by Stereotaxis, Inc.,
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.
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