I built a sharpening station last year and like it a lot.  It has one issue though.  The whole thing wobbles badly during use.  The casters and small base don’t make a good combination.  I came up with a solution in this video:

It took a bit of messing around with feet material, but felt will work just fine for now.  I might find some kind of heavy duty rubber feet for longer term use.  Until then, stay sharp my friends!