Modeling and Analysis of a Permanently Magnetized Sphere´s Motion Facilitated by Field Manipulation

A model describing the motion of a magnetized sphere in a fluid medium subject to an applied field is developed. The inspiration for this system is rooted in technologies and procedures being explored in the biomedical community. In these systems, the accepted approximation of Stokes´ flow about the sphere is discussed and limitations to this are identified with drag force relations accounting for wall effects presented. For this system, the sphere is approximated as a point dipole and the resulting electromagnetic force model is presented. For motion of the sphere using static electromagnets, a reduced coil set technique is proposed. The technique consists of utilizing the minimum number of coils for generation of the desired force on the sphere. This approach is in contrast to the existing solutions which use the full coil set for parallel and anti-parallel motion and single out a solution for the under determined system. A technique for determining the proper coil combination is developed from examining the definiteness of the geometric field functions. A coil array configuration consisting of a four coil assembly is investigated to facilitate planar motion of a magnetized spherical particle in a fluid medium. For this configuration, the reduced coil set consists of only two adjacent coils being active at any given time. The exact inverse current solution for the minimized coil set is derived and presented. The system dynamic model is formulated and represented in a nonlinear state space system