Finite Element Analysis-Based Modeling and Feedback Linearizing Control of a Large Air Gap Magnetic Levitator

This paper summarizes a finite element analysis (FEA)-based modeling approach and nonlinear control synthesis for a large air gap magnetic levitator. The levitator consists of a 10 mm diameter heteropolar magnetic bearing used to control the position a 2 mm diameter ferromagnetic collar bonded to a flexible microcatheter. The unusually large air gap causes the system to exhibit strongly nonlinear behavior, which is attributed to significant leakage and mutual magnetic flux paths. FEA is used to model these nonlinear flux relationships and derive system state equations. Next, a feedback linearizing controller is designed, and closed-loop system simulations are performed using MATLAB. These simulations demonstrate stability and excellent tracking performance over a range of catheter positions. Steady-state performance is shown to depend on catheter position, with errors of up to 0.1760 mm in response to a 3 mm step input. The time-averaged error in tracking a 3 mm diameter circle is shown to be at most 0.0170 mm. Control strategies which are more robust to model uncertainties and discrepancies are recommended to improve the tracking performance.