Feedback for DC Motor Speed Control using PID
Can you instead make a tacho using a slotted opto switch and a disc with perforations. Alternatively you could get some kind of "once per rev" signal from a cheap inductive probe and a small magnet on the shaft.

Once you have this pulse waveform coming back you need to compare its frequency with a frequency that is equivalent to your demand. You mention you have a potentiometer as the "demand" - this could be used in a circuit such as a Voltage-to-frequency converter.

In effect, your demand has been translated to a frequency and that frequency is what you expect to get from your tacho (described above) when it has settled at the correct speed. Using a simple Exclusive or gate or the type II phase comparator as used in a 4046 phased lock loop would work - are you allowed to use logic chips?