PWM question

[2ndThermoLaw]

Hi

With the clark/park control strategy for a permanent magnet motor, what is the relationship between the commanded phase voltage to PWM and applied phase voltage. is that a simple gain of (Amp of Railvoltage/Amp of pulse)? thanks

 

[cswilson]

Simply put, PWM works by creating a time-averaged voltage value by admitting the full supply voltage for a fraction of the PWM period and not admitting any voltage for the rest of the period. The basic equation is:

V(time-avg) = V(supply) * %on-time/100

In a first-cut model, you can often ignore how the modulation scheme works and just assert that the time-averaged voltage is what is provided to the motor phase.

A couple of notes:

Note that this is a voltage modulation scheme (we live in a world of voltage sources). The relationship to current is indirect and depends on motor resistance, inductance, and speed.

You have to be careful in analyzing multi-phase motors, especially the Y (star)-wound motors most common in motors controlled with field-oriented techniques that use park/clarke transforms. The period of actual applied voltage is the time overlap when matching (top/bottom) transistors on "both ends" are on simultaneously. And current "splits" where the phases are joined.

 

[2ndThermoLaw]

hey thanks for replying

Now i dont want to model the high frequency switching. thus i'm unable to find %on time.

http://i2.photobucket.com/albums/y50/hondaAudio/motor.jpg

i belive this describes the modulating. now what i would like to find out is the relationship between command signal and the output/applied voltage (averaged 1str harmonic). I know the phases should be equal, but what about the amplitude?
This must be a function of Vdc(rail voltage), carrier frequency..etc correct?
cheers

 

[2ndThermoLaw]

oh and ignore the summer, it should be a comparator

 

[cswilson]

I think you're making it too complicated. What I am proposing for you is to ignore the inner workings of the modulation (at least first cut) and pretend you directly command the phase voltage, as you would for a linearly modulated amplifier.

Your algorithm will compute a desired phase voltage numerical value. In a real PWM scheme, this value as a percentage of the available voltage is encoded as a PWM duty cycle. But at this point you do not need to care about the actual modulation mechanism, as you said you are not interested (yet) in any effects that modulation scheme would produce (i.e. high-frequency current ripple). So for the purposes of the modeling, you can assume that you can produce that phase voltage directly, without worrying about the mechanism.

 

[2ndThermoLaw]

oh ok.. let me get this right..
So in a real PWM scheme command voltage computed will then be converted to percentage of duty cycle by another algorithm.. so say at the sampling instant of PWM, if (commanded voltage/rail voltage)=0.8, then the duty cycle for that period is 80%.
This gives a one-to-one (or near) relationship between commanded volatge and applied voltage? This would mean the gains have tuned for this case correct? I have no desire to tune them myself.

You are right I'm not interested in torque ripples, I'm looking at the mechanical system and need to drive it. I'm trying to build a base motor model, as i see further use for this in the future with refinements(to be done by an electrical engineer)

thanks cswilson

 

[cswilson]

Yes, you've basically got it now. The PWM generation circuit (virtually always a hardware circuit, not a software algorithm) produces a duty cycle proportional to the number value (assuming you are feeding it from a digital algorithm, which you would be with any Park/Clarke algorithm). The circuit, in turn, produces a time-averaged voltage equal to the duty cycle times the DC supply voltage.

For your purposes, you can gloss over the internal details and just assume your phase voltage command number results in a proportional voltage. The only "gain" terms I see here are the DC supply voltage (which you may or may not treat as constant, depending on the sophistication of your model) and any scaling factors that convert your internal numbers to real-world voltages or percents of the supply voltage.

 

[2ndThermoLaw]

hello cswilson

the gains i was referring to were the quadrature and direct PI controller gains in the algorithm.

supply is a constant voltage source.

>> just assume your phase voltage command number results in a proportional voltage.
is the resultant volatge then Vdc*(commanded number/maximum command number), where the maximum is maximum possible command value limited by no of bits?

And is the hardware circuit (not going to model this) a comparator?

thanks for your help

 

[cswilson]

You've got it now. A couple things to remember: In your formula

Vout = Vdc*(commanded number/maximum command number)

commanded number has a range of +/-maximum commanded number so you can source current into the phase or sink current out of it. In operation, a positive command turns on the top (sourcing) transistor, between Vdc and the phase, and a negative command turns on the bottom (sinking) transistor, between the phase and the return voltage (0V, or GND).

And yes, the PWM circuit is fundamentally a comparator, either analog or digital. In the analog scheme, your command number is put through a D/A converter, and the resulting voltage is compared to the voltage out of a high-frequency sawtooth generator (which must be of a significantly higher frequency than that of the analog signal your algorithm will produce -- this wasn't really the case in the drawing you put up).

In the digital scheme, the sawtooth generator is an up/down counter whose numerical value is compared to your command value.

 

[baltic]

I would say that voltage gain of 3-phase inverter with Y-connected motor winding is A=0.5*Vdc/Vtm, where:
- Vdc - DC bus voltage;
- Vtm - voltage command scanning triangular wave amplitude.

For Vdc=300V, Vdc=10V A=15. Suppose phase voltage command instantaneous value is v=4V. Then actual phase voltage generated by PWM amplifier is 4*15=60V.

There are many different aspects associated with PWM amplifiers - maximum voltage range utilization, additional motor loss induced by PWM etc. Some of them are addressed at

http://www.drbrushless.com

.

 

[cswilson]

Baltic brings up a good point. You can apply a voltage to each phase from 0V to Vdc. It is the relative voltage between the phase leads that matters for motor operation. Mathematically it is easiest to treat this as commanding each phase between -Vdc/2 and +Vdc/2. For your purposes, you don't even need to include the next step of offsetting all 3 phase voltages by +Vdc/2.

 

[2ndThermoLaw]

yep guys

i take the ground reference to be half of battery voltage, makes it easier