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This paper presents modeling and analysis of eddy-current damping that is formed by a conductive plate placed below the levitating object in order to suppress vibrations and ensure stability. It is demonstrated that vibrations should be damped to preserve stability and precision especially for stepwise motion. The levitated object is a small permanent magnet in our experiments. A magnetic drive unit is used for vertical motion of the magnet. Eddy-current distribution in the plate is calculated by solving diffusion equation for vector magnetic potential. The eddy force applied to the object is derived by a coil model representation. It is shown that if a 20 mm radius, 9 mm thick aluminum circular plate is used for eddy-current damping, the levitated object can closely follow a step input with a steady- state precision varying between 0.04 and 0.07 mm depending on the plate object distance. Eddy-current damping is a key technique that improves levitation performance to increase the diversity of applications of magnetic levitation systems in micromanipulation and microelectronic fabrication. [ABSTRACT FROM AUTHOR]