Hi Erik,
A few comments and suggestions on the way.
Please note that for a PLL, a PID is equivalent to a PI regulator. Turns
out that the P and D factors of the PID sums to form the P of the PI
regulator, while the I transfer right over. I have seen no benefit in
real implementation of adding the D factor, it did not add any magic to
convergence.
Also note that P is proportional to f0*d and I is proportional to f0^2
where f0 is the PLL resonance-frequency/cut-over-frequency and d is the
damping factor. This is trival to derive and I usually do it on a white
board or a single sheet of A4 paper. I strongly advice you to use f0
and d as your steering parameters rather than P and I, it will make the
work better. Also, I recommend to keep d at least to 3 to avoid jitter
peaking issues.
The actual formulas contain a little more details with a few constants
here and there, but those can be lumped into a single aggregate constant
for each of the P and I, and knowing the basic relationship allows for
quick test and tweak. I've taught this to several colleagues and they
ended up testing their way to production values without too much effort,
they simply tweak them until they are satisfied with all the tests readings.
The gpsdo simulator tool is very fun and educational to learn from. I've
written several similar simulation tools and they have proven very
useful. I recommend to do tests to validate that the model and the
actual implementation match up.
One technique to decide f0 (or it's reciprocal the timeconstant) is to
plot the phase-noise of the reference and the controlled oscillator and
simply choose f0 to be at the intercept point of the two graphs. A
similar approach have been used on ADEV plots, in which case it is
called the Allan intercept point. The Allan intercept point is maybe a
little less well founded than the phase-noise variants, but try both and
see how you end up, it will be a learning experience.
For a PI PLL, you can usually test overshot reaction to a phase or
frequency step. The amount of overshot is directly related to the actual
damping factor, so that is easy to validate. Further, forcing it into a
low damping factor, you get a high Q so if you stress the loop with a
phase or frequency step, the period of the resulting ringing will
disclose the actual f0 of the loop. Using these two measurements, you
can fairly trivially establish the actual constants of this equation system:
P = Kp * f0 * d
I = Ki * f0^2
Anyway, knowing the actual f0 and d for your implementation and being
able to control those through the above equations will be of immense
help as you then aim to optimize performance.
Notice that scaling factor includes EFC input sensitivity, so if you
have different oscillators, break out that as the Ko factor and set it
properly for each oscillator. It is actually fairly simple to measure
the actual sensitivity by intentionally steer the EFC and see how much
frequency change, and you will trivially calculate the steering factor
Ko. With a little bit of work, one can make it self-calibrate this for
the oscillator.
As for your question, for your simulation and your implementation to
match up, you need to validate that your model of your implementation
match up and have know scale factors. Spending time to make sure things
work as you expect then saves you tons of work and you can use this
knowledge to simulate and then verify in actual implementation (which
tends to be slow) only a few times.
Cheers,
Magnus
On 2022-02-25 16:18, Erik Kaashoek wrote:
Inspired by the gpsdo simulator written by Tom Van Baak I am trying
to use simulation to validate the PID loop parameters for a cheap and
simple GPS referenced timer/counter I'm building.
The following one hour measurements where done using a Rbd reference
as input to the timer counter(see Timelab.gif plot attached)
1: Open loop (P=0, I=0) VC-TCXO versus the Rbd reference (green trace)
2: PPS of the internal GPS versus the Rbd reference. (PPS trace)
3: Rbd reference versus the closed loop (P=0.02, I=0) VC-TCXO (dark
blue trace)
4: Rbd reference versus the closed loop (P=0.01, I=0,00005) VC-TCXO
(red trace)
All .tim files also attached.
The performance of the TCXO was remarkably good for a sub 1$ device,
great care went into a stable, low noise, Vtune. The noisy supply did
not have a big influence
The open loop TCXO frequencies where divided by 1e7 (SW PICdiv)and
together with the raw PPS frequencies loaded into an Excel speadsheet
(see attached)
An identical PID controller (P=0.01, I=0.0005) was implemented in
Excel that took as input the frequency difference between the PPS and
the TCXO and calculated a correction for the TCXO frequency. The
corrected TCXO frequencies was exported from excel (PID output) and
imported in Timelab (PID, light blue trace)
As can be seen in the Timelab plot the controller implemented in Excel
did a better job then the controller in the timer/counter but the two
actual closed loop measurements used difference GPS and TCXO data (I
do not own sufficient good frequency counters to measure all
frequencies at the same time).
The timer/counter was open on a table with minimum thermal isolation
and during the measurements some draft through door opening/closing
could occur
My question: is the difference between the measured loop performance
and the simulated loop performance to be expected or am I making a
big mistake somewhere?
Feel free to ask more info or more measurement data
Erik.
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