Remote pan a 2.7m carbon fibre camera pole
A PID controller may be more then what you need, but a PID controller can control the damping and overshoot of your motor. There is more on PID controllers at How to learn PID Control?

As for your motors, I think using a stepper motor will probably be your best option. There is some information about stepper motors at Arduino Stepper Motor

Using an Arduino or any other micro-controller should work just fine for you.