I think that the Washington DC and BART San Francisco subway trains could drive themselves from the day the lines opened, or if not, within a few years after the lines opened. Then, the public was not ready for driverless trains so a driver sat in the cab anyway. There was at least one publicized instance where the operator got out of a BART train to inspect something and the train closed its doors and took off, doing a pretty good job of driving itself for several stations until another operator intercepted it and took control.
Even with no automation, the controller already accelerates the train smoothly and the maximum speed depends on what notch the controller was put in together with voltage and whether the train was going uphill, downhill, etc. The automatic control, in some cases, retrofitted, needs to monitor the speed, cut the power, coast, apply the brakes, and then apply power again as needed, If the controller was set in a low notch, the automation will still work although the maximum speed at any time could be less than the speed limit for the track section. If the controller was still in a high notch when the automation applied power or if the operator set the controller immediately into a high notch, the train will still accelerate smoothly from a dead stop. The Boston trains do not have the mechanism to open the doors, wait a predetermined time, close the doors, and (after all doors close fully) start up from a station.
(As mentioned earlier, the Boston trains require that the operator have the controller handle under his control for the train to move at all, automated section of track or not.)
Build something. Anything.