Magnetic-bearing related chaotic electromechanical oscillator

The work deals with a switching mode control of a magnetic levitation system that possesses a symmetrical geometry similar to that usually found in magnetic bearings. The control depends on switching the current in two attracting electromagnets installed on both sides of the suspended object. The underlying idea is to use merely discrete (noncontinuous) position sensors for the control. It is unfortunate that relying merely on one such sensor cannot enable stabilization. We observe, however, that two such sensors (mounted symmetrically on both sides of the symmetry plane) are sufficient for stabilizing the system. The dynamic features of the system are considered theoretically and also investigated by simulation work. An interesting dynamics that is associated with chaotic behavior is revealed. Namely, the region of stability of the suspended object is characterized by being related to a strange attractor. It is shown that the chaotic dynamic behavior is closely similar to that exhibited by certain purely electronic oscillators where feedback is channelled through hysteresis. The main tool employed for assessing the present chaotic behavior is a discrete map constructed for the sequence of velocities exhibited at the switching instances.