Real-Time Data-Driven Force and Torque Modeling on a 2-D Halbach Array by a Symmetric Coil Considering End Effect

Halbach arrays have been widely implemented in magnetic levitation systems. They concentrate the magnetic field over one side, and their magnetic flux density in the central region can be modeled. This article proposes a novel lookup table-free data-driven method to model the force and torque on a 2-D Halbach array when the magnet array is above a stationary coil. One critical contribution of this article is the rapid and accurate force and torque modeling when the coil is located near the edge of the 2-D magnet array. First, the area under the 2-D Halbach array is divided into a central region, edge regions, and corner regions. Then, nonlinear force and torque components are identified and modeled with a modified third-order Fourier series for force and torque modeling. The proposed model is implemented on an industrial server, and the average computation time is measured to be
$2.3 ~\mu \text{s}$
. This model is universal for symmetric coils, verified through experimental measurements with circular and square coils of different sizes. The measurement result agrees well with the proposed modeling method, showing that the proposed method is suitable for real-time control of the ironless planar motor.