Is there any formal treatment of PWM and DC motors that covers the following points:

1. The frequency of the PWM​
2. The shape of the PWM waveform​
3. The shape/frequency optimality as a function of desired motor speed​
4. How does the type or weight or inertia of the motor influence these parameter's​
5. Feedback options (like perhaps an optical or hall effect sensor)​
6. Motor startup factors​

 

1/ Generally keep the PWM frequency as low as possible without audible noise, Microchip suggests starting at 5.5khz.
2/ The PWM waveform is usually aimed as square as possible.
5/ For RPM control, feedback can be a typical low frequency optical/inductive sensor. For positioning, a high pulse/rev encoder of some kind is often used.
6/ What start up factors?

 

Not that I am aware of.
But there are "general-rules".

The Frequency has much to do with avoiding the
creation unwanted Electrical-Noise, and Audible-Noise.
Generally, higher than ~20khz is preferred o avoid Audible-Noise.
There is usually little, or no advantage to exceeding ~20khz.
Very low Frequencies ( ~50 to ~100hz ) may be useful in
cases where extremely high start-up Torque is desirable, or
very low RPM operation is expected.

A Square-Wave is usually used for maximum Circuit, and Motor-Efficiency.

RPM-Feedback is optional, and must be tailored to the application.
.
.
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1/ Generally keep the PWM frequency as low as possible without audible noise, Microchip suggests starting at 5.5khz.
2/ The PWM waveform is usually aimed as square as possible.
5/ For RPM control, feedback can be a typical low frequency optical/inductive sensor. For positioning, a high pulse/rev encoder of some kind is often used.
6/ What start up factors?

Thanks, this is a start.

I'm really asking about the empirical or theoretical basis for these PWM designs, like 5KHz, how was that established? are there any graphs about performance etc vs frequency.

As for startup, I mean if the motor is stopped, no applied voltage, what is the best way to start the motor, just instantly apply the PWM to it or perhaps apply full power for a brief time until its rotating and then switch to PWM, these are the kind of questions I'm curious about.

 

I'm really asking about the empirical or theoretical basis for these PWM designs, like 5KHz, how was that established? are there any graphs about performance etc vs frequency.

It's about loss in the magnetic materials. It will depend on the grade of silicon-iron used, and the thickness of the laminations.
Higher frequency = more iron loss. Lower frequency = more annoying noise.

 

The best way is to ramp the PWM width up from start, especially if large motor and or under a load.
You use the frequency that is not a problem from the audible point of view.
I have used 6khz with no audible noise, but mine are "Old" ears!!
Every application is a little different from another, so many factors have to be considered, depending on the application.

 

The best way is to ramp the PWM width up from start, especially if large motor and or under a load.
You use the frequency that is not a problem from the audible point of view.
I have used 6khz with no audible noise, but mine are "Old" ears!!
Every application is a little different from another, so many factors have to be considered, depending on the application.

So isn't applying a square wave to an inductive load, more or less asking for electrical noise?

 

Yes it can, but there are many factors involved, The construction of a motor is typically is not an ideal way to amplify a audio signal, there are features which change and absorb many of the frequencies, In designing a drive for a particular motor, the PWM frequency can be tested in order to decide on a final minimum frequency.