If I have a small PM DC motor fed with a PWM voltage is there an approximately linear relationship between motor speed and average DC voltage?

 

Yes.

 

I don't think so.... The PWM driven motor will be running at the RMS value of the PWM so I doubt it'll be linear..

Roman Black has a ton of info on PWM voltage relationship... Feed it with a sine curve to make it linear..

 

With PWM control, the current wave form is quite different from the Voltage W.F. It is a mean varying level and it is this combination of voltage square wave and sinewave looking current that decides the RPM.
Max.

 

For a DC motor, current is proportional to torque and, speed is proportional to voltage. The voltage being the "generator" voltage (back EMF according to Lens's law), i.e. the supply voltage less current*resistance.
For the same motor supplied with a PWM signal, one has to take into account the large series inductance. Current will vary with the PWM signal, but only by a small amount if the inductance and PWM frequency are large enough. dI/dt=V/L, where V is the difference between the instantaneous input voltage and the generator voltage. The current falls slightly on the LOW part of the PWM cycle and rises slightly on the HIGH part.
The net DC current flowing for a 50% mark:space 12V input, will be exactly the same as if it were supplied by a steady 6V DC, provided that the inductance and PWM frequency are high enough to keep the current continuous. That means that the "generator" voltage must be the same, and so must the speed.
Exactly the same thing would happen if an LC filter were placed between PWM signal and motor.
RMS calculations don't apply as RMS applies to the power supplied to a resistive load.

 

Roman Black has a ton of info on PWM voltage relationship...

I did find this which might be useful: https://www.romanblack.com/encoder.htm

 

Also depends upon the characteristics of the motor load.

 

Also depends upon the characteristics of the motor load.

Its a water pump.

 

What type (nature of) the pump?
Max.

 

It's a small pond pump being used for a pebble pool, powered by a solar panel. It is a bit too energetic in full sun and with some wind the water eaily misses the pool. So I want to control the speed independent of sun strength (providing there is enough).

 

If I have a small PM DC motor fed with a PWM voltage

So you have some kind of controller already?
If so what are the present results.
Or are wishing to modify/override the present automatic control by sunlight?
If it does have a present automatic controller, should not be difficult to reverse-engineer and modify?
Max.

 

No existing controller. Just the solar panel connected to the pump. In any kind of wind with good sunlight it will just empty the reservoir, but I do want to make the best use of available sunlight so some control rather than simply restricting the power.

 

So I want to control the speed independent of sun strength (providing there is enough).

Won't a standard voltage regulator do that?
To get fancy you could also control the speed dependent on wind strength .

 

I was concerned because it will need to run quite a bit slower than its full speed and then it might not even start and I think that PWM might alleviate that problem.

 

So what was the mention of 'PWM voltage' in the OP?
I assume whatever system you come up with it needs to be automatic dependent on sun light?
Max.

 

So what was the mention of 'PWM voltage' in the OP?

??

I assume whatever system you come up with it needs to be automatic dependent on sun light?

Yes. A super system might include measuring the wind but I'm not going there.

 

I have a small DC motor fed with a PWM voltage

??
Max.

 

??
Max.

OK, if it would make you happier, put an 'if' in front.

 

Makes all the difference!
Maybe something like a simple PWM controller and a LDR (light dependent resistor) auto control.?
http://www.stephenhobley.com/blog/2010/09/17/light-controlled-pwm-generator/
Max.

 

I was thinking that the solar panel voltage would be a good measure of sunlight.

I am thinking of using the Roman Black idea I linked to earlier to measure the actual motor speed and then control that by changing the voltage fed to the motor. For this to work I believe the motor would need smooth DC, but if the motor stopped the controller would see this and increase the voltage until it started again.