Abstarct: Magnetic levitation systems have practical importance in many engineering systems such as in high-speed maglev passenger trains, frictionless bearings, levitation of wind tunnel models, vibration isolation of sensitive machinery, levitation of molten mextal in induction furnaces, and levitation of mextal slabs during manufacturing. The maglev systems can be classified as attractive systems or repulsive systems baxsed on the source of levitation forces. These kind of systems are usually open-loop unstable and are described by highly nonlinear differential equations which present additional difficulties in controlling these systems. Therefore, it is an important task to construct high-performance feedback controllers for regulating the position of the levitated object. In recent years, a lot of works have been reported in the literature for controlling magnetic levitation systems. In this thesis we use two control methods include sliding mode control and fuzzy- impedance control on a typical train magnetic levitation system and compare the performance of two controllers on it.