Even with DC servo motors you are not able to drive in the low velocity range in such a linear and smooth way
Figure_6 shows the measurement of a PLS-85 stage with linear scale (with encoder resolution of 0 nm). The speed of 100 nm/s was choosen, so 360 µm within one hour or about 10 mm per day. The movement is very smooth. Zooming the first 100 nm travel is shown
figure_7.
Here it is important to realize that the interferometer resolution is 5 nm which results in the step-wise diagram. These steps are not coming from the stage, the movement is much more smooth. But its very important to understand that the speed is linear and variations are in the 1 nm/s range which is amazing for a loaded stage with several mm travel range. Also here the results can be improved by using a better encoder resolution.
Figure_7 shows an open-loop result of a UPM-160 stage controlled with a speed 45 nm/s.
Figure_8 shows zoom-in of figure_7. The movement is very linear! The interferometer resolution is limiting the interpretation in the picometer per second scale.