Excerpt from the course manual for Digital Control of Power Electronics - Why Power Converter Modelling Wastes Your Time

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Why Power Converter Control Transfer Modeling wastes your time?
And what to do about it?
I remember back to control engineering class and recall seeing large numbers of rational polynomials in s. I was
young and naïve and believed that they were actually useful. Then I got to look at power converter control and
found things that just did not fit with the “rational function of s approach” that had been presented. This annoyed
me and so I spent the next ten years looking for ways to deal with real power converter control transfers. I found
that every modeling method I looked at relied on the model being validated by a measurement and so I got to the
point where the model was something where I’d spend lots of time getting the mathematics right only to find that
it did not in any way accurately predict the converter transfer in all operating conditions. So now I just do the
measurement.
It is, hopefully, obvious from the first part of this course that measuring transfers are the best way to get them for
any system including any power converter. It can be a frustrating and actually pointless exercise designing
controllers for power converters if the power converter transfer is not available or is inaccurate.
A “design first, measure second” approach leads to compensators that work most of the time but maybe do not
work when the input voltage is high or when the load is low. Murphy’s or Sod’s law makes it clear that this type of
Ad hoc controller design will be stable in all operating conditions except for the last one you test.
There has been and is significant effort to model power converters using averaging or small signal linearization.
These models are useful and are suitable for design. The key issue in using them is that they may not be accurate.
Verification of accuracy is done by measuring the transfer frequency response of the actual operating power
converter and comparing it to the model. In true empirical evidence fashion it is typical to say that when the
model matches the measurements then the model is accurate. The conclusion from this is that the measurements
confirm the model as accurate. A follow on conclusion is that the measurement is necessary. In the event that the
measurement does not match the model then the measurement is repeated. If the results are consistently
different from then it is the model that is typically declared inaccurate. At this point the measured response is
used in the design process in place of the model.

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www.elmgdigitalpower.com 805 764 2027
Figure 29 Problems with power converter model with bad estimate of capacitor ESR

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www.elmgdigitalpower.com 805 764 2027
Figure 30 Model problem fixed after measurement
Figure 31 Typical power converter model inaccuracy

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www.elmgdigitalpower.com 805 764 2027
In effect a measurement is considered more accurate than the model. The suspicion is always that there is
something missing from the model. This means that the way to get accurate converter transfers is to measure
them. It may be useful to have a model but that model needs to be verified by measurement.
Overall the time spent verifying the model is probably better spent measuring frequency responses of the transfers
and using these in the design of the compensator.
The solution to modeling inaccuracy is measurement.
The measurement of control transfers is not difficult and is not overly time consuming. It is extremely valuable
and the insight gained from doing it is instructive and informative.
So how do you make the measurements?
14. How to make Manual Measurements
If there is the possibility of measuring the frequency response of a power converter manually then it is always best
to do this. The insight into the power converter that comes from hands on manual measurement is invaluable.
One way to do this is to use a signal generator and an oscilloscope as an analyser.
Figure 32 Requirements for a network analyser are a signal source with variable signal frequency and magnitude and the
ability to measure the input and output.

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www.elmgdigitalpower.com 805 764 2027
Figure 33 Simple control transfer measurement tools. (The human brain provides the interface to the computer.)
This approach is best for power converters or other plants with analogue inputs. The signal generator is connected
into the controller through a capacitor with the feedback loop open and the controller bypassed or set to 1. It may
be that the point in the circuit where connection is best has a low impedance from the stage before. If this is the
case then it may be necessary to disconnect the previous stage.
It will be necessary to supply a DC voltage to set the base duty cycle or operating point. This is typically done using
a potentiometer.
It is usually useful to have some idea of the expected gain of the power converter and if you do then this will give
some indication of the size of the signal needed at the input. If you do not have an estimate of the gain set the
signal generator amplitude to zero. Set the signal generator frequency to 109 Hz. Put one scope probe on output
voltage and set that channel to AC couple. Make sure that the scope probe is rated for the DC voltage. Put the
other scope probe on the capacitor lead that is not connected to the signal generator. Run the power converter
and slowly increase the signal magnitude from the signal generator keeping an eye on the converter output
voltage and the signal from the signal generator. The 109 Hz will be apparent on the output as a sinusoidal
voltage. Adjust the scope vertical scale so you can see the 109Hz signal and increase the input signal also. Look at
the difference between the phase of the input and the output. This is the phase angle of the power converter
transfer at this frequency. The ratio of the output to the input is the gain of the converter transfer.