Just some more information to either help or confuse.
heating and cooling is one of the absolute worst processes to attempt to control . if you measure an increase in heat, you are only measuring the BEGINNING of the avalanche of heat that will soon follow. oil burners, gas heater, hydronics, an the like heat up in a remote location and do not start to send the heat until the heat exchanger has reached a temperature. and once it has reached that temperature, it will run and send that heat, no matter what you do.
if you think of controlling heat, think more of managing a sluggish chaos of parameters.
as for damper control. forget all the fancy feedback, you really cannot use that in ducted air flow. if you move one damper partway, then the system pressures change and every other damper will have a new pressure and the flow will change in each.
some tips. first, do not try to turn your gas or oil heater on and off in any sort of fast duty cycle. you will wear out the motor, the blower, the gas valve or other parts. they are meant to operate about 3 to 5 times per hour at maximum and then only for a few weeks of extreme outside temperatures.
second. think of controlling half way. open a damper for a room that wants more heat and close the damper for one that has too much, but only move them half way to full open or full closed from where they are now. or move in 10% increments.
you can use a simple clock motor to move the damper. an AC synchronous motor is what the commercial HVAC companies use.
Since you really do not need to know the actual damper position, only if you need more or less heat, you can test your damper to get a speed of movement. then use a simple time-of-flight signal. if it takes 30 seconds to go from full open to full closed, then 3 seconds should move it about 10%
if you really want to get potions control, put a pot on the shaft.
also, the entire control system changes over the season. in the spring and fall you have occasional heat, in the deep freeze, you have continual heat. once you have data logged some of the operation, consider two different control strategies based on the outside air temperature.