How to make a solenoid armature travel at a faster rate of speed?
You can drive the solenoid with a higher voltage.

As long as your duty-cycle is low enough that you don't have heating issues, it should work fine.

It's worth noting that 15 mm in 2 ms is pretty fast. That translates to 7.5 m/s, or 27 kph.



How big is your solenoid? Can you tell us more about the solenoids you are looking at?