DC motor constant acceleration
To control acceleration you need to measure one of two things: Current or Velocity.

Acceleration is the affect of torque being applied to some inertia &amp; torque is proportional to current. Thus if you measure current &amp; control current you will control acceleration.

Acceleration is the rate of change of velocity. Thus if you measure the velocity you can deduce acceleration.

to implement this you will need a controller to generate an error term (be it current or velocity) &amp; via a PI controller to generate a voltage demand to then generate the needed PWM to synthesis the needed voltage. 

I would suggest controlling based upon velocity simply because controlling acceleration via Torque (ie current) is extremely dependant on the load profile.  Equally if a DC motor is being used you can take credit for the velocity is proportional to the voltage applied &amp; while this "constant" isn't really constant, it variation with stator current maybe low enough that you could operate open-loop with just a voltage profile.