We study the problem of controlling the position of a platen levitated using linear motors in three-dimensional space. We develop a non-linear six-state model of the system and provide two non-linear controllers solving the set point stabilization problem. The first controller is derived by decomposing the model in two subsystems, applying feedback linearization to one of them, and using the invariance principle to prove attractiveness of the origin of the second subsystem. The second controller is found by dynamic feedback linearizing the entire system dynamics. In both cases we provide a rigorous procedure to determine the operating range of the device.