No i was never really sure of that. How do you smooth it out yourself? with a capacitor?
Resistor and capacitor, have a search on the forum for "low pass filter", there should be 100s of threads about this.
Do you think that 1 amp will be able to be supplied from 5 volt output of the Arduino?
Not a chance. But you need a current output not voltage don't you? That's a little too much in the linear domain for me.
How can avoid the "beat" situation?
I would sample at say 10x the frequency, take a 100 samples and pick the highest.
All this field coil stuff is out of my area I'm afraid, if you want 9v and you get 9v from 1A why not just rig up a current source that delivers 1A?
If it varies according to load or some such that's a different story and you need some control, something like
if monitoring_volts < correct_value
pwm_val += 5;
pwm_val -= 5;
But there's more to it than that, you need to add hysteresis, and some timing and probably a few things I haven't thought of.