Micron-Scale Linear Actuation
What you're talking about is a high-resolution linear stage. You can get what you want, but it's not remotely in your price range if you're concerned with using a hobby board for control. Newport, for instance, carries a series of linear motorized stages which will give resolution of 1 nm and accuracies better than 1 um, and drive intervals up to 350 mm. Of course, a 100 mm throw unit will cost you 8k+, but they are available. 

If you're willing to take chances, eBay currently has a stage with 1 um resolution and +/- 5um accuracy for about 1/3 that.