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I'm working on a project in which I have to control the speed of a DC motor using an analog PID(using op-amps). The input will be provided with a potentiometer. The issue is that I can't figure out how to provide the feedback(a voltage proportional to the speed) for this system without using a microcontroller, which I'm not allowed to use.

I was told it could be done by somehow coupling a potentiometer with the motor, but fail to understand how this would provide velocity feedback.

Is there any, not too difficult way to get velocity feedback of a motor without using a microcontroller?

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Any device that provides information about rotational velocity is by definition a tachometer, so you're going to have to be more specific about that restriction. How about measuring back EMF or sensing commutation? –  Dave Tweed Apr 12 '13 at 13:03
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A poteniometer can be used for position feedback. You could differentiate that for velocity. But it would be limited to the mechanical range of the potentiometer - usually less than a turn, though some devices go up to 10 or 15 turns. Most would use a generator type tachometer, or frequency to voltage convert encoder pulses or commutation events. –  Chris Stratton Apr 12 '13 at 13:11
    
@DaveTweed : Sorry I seem to have misused the word. What I mean to say is, I can't use a tacho generator for this project because they're generally too expensive,unless there are more cost efficient options available. How would I go about using the back EMF? This is actually a project for my Control Systems course. –  Ammar Apr 12 '13 at 13:16
    
@ChrisStratton : It doesn't matter if the range is limited since it's only meant to be a proof of concept. So basically I could use a multi-turn pot and connect it to a differentiator op-amp? This would also give me an output voltage proportional to the velocity right? Thanks for the idea! –  Ammar Apr 12 '13 at 13:22
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You could use a interruptor disk mounted on the motor shaft, thereby obtain rotation rate as pulses using an optosensor, then do a frequency-to-voltage on that using op-amps. That is how pre-digital era remotely readable anemometers used to work. Also, since this is going into a PID, linearity against RPM is not essential - so a simple resistor-capacitor based F to V would work. –  Anindo Ghosh Apr 12 '13 at 13:57
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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?

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This is a great idea! I have a couple of questions though. Could I not do as Anindo Ghosh mentioned in a comment and use a frequency to voltage converter instead? Then I could invert the output voltage for negative feedback. On the other hand, if I use v to f conversion, I understand how the phase comparator would work but how would a XOR gate work? Logic chips are allowed and thank you for your help! –  Ammar Apr 13 '13 at 5:28
    
Well I don't think I'm going to get any more answers and I've decided to go with an optical encoder. I appreciate your help on the matter! –  Ammar Apr 15 '13 at 14:40
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