[time-nuts] Re: Validating GPSDO control loop with simulation and measurement. Is this amount of difference between measurement and simulation to be expected?

[Magnus Danielson]

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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