On Mon, 21 Aug 2000, Andrew Kunz wrote:

> Thanks, Scott.
>
> That'll be interesting reading.  I'm working the PLL from the angle of changing
> time between steps rather than amplitude in order to keep phase locked (my only
> input is a zero-crossing detector).  I also have to generate multiple waves,
> since I'm generating "real" power not just a 110V household socket.

Perhaps, however I don't discuss the PLL part of it at all. I'm not sure how
your system is implemented. On one design I had to phase lock to a ~50-60 power
sine wave too. I found that zero-crossing information was unreliable. The reason
was that this was part of a power quality instrument and (almost) by definition
the "sine wave" is suspect. The jitter in zero crossing could be very large. So
instead, I wrote a single frequency 'DFT'. In other words, I did something like
this:

Assume f = f0

for one cycle's worth (delta t = 1/f)  of sine wave samples compute the
quadrature components:

sine_power = sum of (sine samples * sin(t*i))
cosine_power = sum of (sine samples * cos(t*i))

In other words, the integral of the unknown waveform multiplied by sine and
cosine functions was computed. You may also view this as two narrow FIR band
pass filters center about the frequency 'f'.

Now you can find the arc tangent of the ratio:

phase ~= arctan(sine_power/cosine_power)

to find the phase. This can then server as the control input to a PID algorithm.
The control output of course being the frequency. A simple proportional
algorithm could go something like:

If the phase is positive
  decrease the frequency slightly
else
  increase the frequency slightly

But beware, this can (will) have trouble locking. At the minimum, you'll need a
little part of 'D' in PID.

As you might expect, computing the division and then following that by arctan is
expensive (but doable...). So instead, I might suggest using the raw sine_power
and cosine_power terms. You may be lucky to just get away with only the
sine_power term. However, if your sine wave amplitude varies then the cosine
computation can help normalize the calculation.


Scott

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