# PWM control of small PM DC motor

#### AlbertHall

Joined Jun 4, 2014
12,293
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?

#### Ian0

Joined Aug 7, 2020
8,947
Yes.

#### Ian Rogers

Joined Dec 12, 2012
1,134
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..

Joined Jul 18, 2013
28,056
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.

#### Ian0

Joined Aug 7, 2020
8,947
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.

#### crutschow

Joined Mar 14, 2008
33,361
Also depends upon the characteristics of the motor load.

#### AlbertHall

Joined Jun 4, 2014
12,293
Also depends upon the characteristics of the motor load.
Its a water pump.

Joined Jul 18, 2013
28,056
What type (nature of) the pump?
Max.

#### AlbertHall

Joined Jun 4, 2014
12,293
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).

Joined Jul 18, 2013
28,056
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.

#### AlbertHall

Joined Jun 4, 2014
12,293
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.

#### Alec_t

Joined Sep 17, 2013
14,009
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 .

#### AlbertHall

Joined Jun 4, 2014
12,293
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.

Joined Jul 18, 2013
28,056
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.

#### AlbertHall

Joined Jun 4, 2014
12,293
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.

Joined Jul 18, 2013
28,056

#### AlbertHall

Joined Jun 4, 2014
12,293