Magnetic Levitation and control using two solenoids with their axes in a vertical plane

Magnetic Levitation has found tremendous utility in fields like transport and tribology. It is also one of the classic experiments used in introductory courses in controls. This paper discusses a two-dimensional extension to this classic experiment. In this proposed setup, a diamagnetic object is to be levitated using the magnetic field strength of two solenoids with an iron core each located in two separate locations with their axes in the same vertical plane. The key feature of this new setup is the ability to levitate the object in any position within a portion of a plane as compared to a single line in the classical experiment. Using two currents in the coils as two inputs, the objective is to have a position and velocity control of the object. In order to do so, first, the analytical form of the magnetic field strength outside the two solenoids is determined. Then, the magnetic force acting on the sphere is evaluated. Using these expressions, equilibrium points are established based on the required position and the stability of these points is analysed. Further, a control system is implemented to achieve the aforestated objective.