[time-nuts] Re: GPSDO Control loop autotuning

[Markus Kleinhenz]

Hi Tobias,

I was looking into Kalman filters as well, albeit some time ago. But I
think i got some pointers that can put
you on your path.

1. The Kalman filter is an estimator not a controller. It gives you an
estimate of your current system state but no controll law.

2. Time and the Kalman Filter by Lorenzo Galleani et al
<https://ieeexplore.ieee.org/document/5438294> is a great article on the
topic.

3. There are control schemes which are designed for the state space like
Linear–quadratic–Gaussian control
<https://en.wikipedia.org/wiki/Linear%E2%80%93quadratic%E2%80%93Gaussian_control>

4. Comparison between Simulation and Hardware,Realization for Different
Clock Steering Techniques
<https://elib.dlr.de/127013/1/LQR_PP_Metrologia_paper_revised.pdf>Â  is
another paper on the topic

5. A Practical Approach to Optimal Control Problem for Atomic Clocks
<https://ieeexplore.ieee.org/document/8922770> claims to use a Kalman
filter and LQG control to achieve better ADEV than the used WPN reference.

I hope these are helpful.
Unfortunately i haven't had the time to implement these myself.

Regards
Markus

Am 09.04.2022 um 18:13 schrieb Pluess, Tobias via time-nuts:
> Hi all,
>
> My reply to this topic is a bit late because I have been busy with other
> topics in the meantime.
>
> To Erik Kaashoek,
> You mentioned my prefilter. You are absolutely right, I looked again at my
> prefilter code and decided it was garbage. I have removed the prefilter.
> Thanks to your hint I also found another mistake in my PI controller code,
> which led to wrong integration times being used. I corrected that and the
> controller is now even more stable. I made some tests and the DAC output
> changes less than before, so I guess the stability is even better!
>
> To all others.
> I discussed the topic of improving my GPSDO control loop with a colleague
> off-list and he pointed out that, on this list, there was a while ago a
> post about Kalman filters.
> I totally forgot about this, I have looked at them at university a couple
> years ago, but never used it and therefore forgot most of it. But I think
> it would be interesting to try to implement the Kalman filter and compare
> its performance with the PI controller I currently have.
>
> I guess the first step before thinking about any Kalman filters is to find
> the state space model of the system. I am familiar with the state space,
> but one topic I was always a bit struggling with is the question which
> variables I should take into account for my state. In the case of the
> GPSDO, all I can observe is the phase difference between the locally
> generated 1PPS and the 1PPS that comes from the GPS module. On the other
> hand, I am not only interested in the phase, but also in the frequency, or,
> probably, in the frequency error, so I think my state vector needs to use
> the phase difference (in seconds) and the frequency error (?). So my
> attempt for a GPSDO state space model is:
>
> phi[k+1] = phi[k] - T * Delta_f[k]
> Delta_f[k+1] = Delta_f[k] + K_VCO * u
>
> y[k] = phi[k]
>
> u is the control voltage that is applied to the VCO, Delta_f is the VCO
> frequency error and T is the sampling period, which is 1 second in this
> case because the control loop is executed once per second, triggered by the
> 1PPS pulse from GPS. Note that with "VCO" I actually mean the combination
> of the OCXO plus the clock divider that produces the 1PPS signal, which we
> want to control in both aspects, phase and frequency. So this VCO outputs
> just 1 Hz signals, plus or minus some deviation that depends on the control
> voltage of the OCXO.
>
> Assume for a moment the GPS module has no jitter and outputs a perfect 1PPS
> pulse. Also assume the whole thing is nicely locked and the VCO has no
> frequency and phase error. In this case, the model yields the right
> behaviour, that is, the phase (actually the time interval) between the two
> 1PPS signals is always 0. Also, Delta_f stays 0. (The linear VCO model
> assumes the VCO is at nominal frequency for zero voltage).
> Now if we assume we apply a VCO voltage u that sets the VCO high by 0.1 Hz.
> At the beginning, the 1PPS pulses are perfectly aligned, but one second
> later, the VCO is around 100ms too early and therefore the phase is now
> -100 ms and so on. It is not 100% correct because a 0.1 Hz frequency
> increase gives a 909 ms period and therefore the phase should be actually
> -91 ms, but it's sort of close. Since we are dealing with small frequency
> errors only, the approximation is probably good enough?
> Is that a useful state space model, would it make sense to try to proceed
> with this? or is this complete garbage and I am thinking too far.
> Or would it make sense to use the Kalman filter with only one state
> variable, which is the phase? In that case the calculations would probably
> be simpler.
>
> Thanks for any hints,
> best
> Tobias
> HB9FSX
>
>
>
>
> On Mon, Mar 21, 2022 at 9:08 AM Erik Kaashoek <erik at kaashoek.com> wrote:
>
>> Hi Tobias,
>>
>> I'm very new to all this GPSDO stuff and going through similar learning
>> but maybe I have some remarks/questions that could be relevant for you.
>> - Developing control algorithms is an extremely long process unless done
>> on a simulator. Tom Van Baak has an excellent simulator and several
>> realistic data sets for testing.
>> http://www.leapsecond.com/pages/gpsdo-sim/
>> - Use Timelab to look at the ADEV, the frequency error and the phase
>> error to evaluate the performance.
>> - Why do you prefilter? In my experience this only adds a time delay in
>> the input data for the loop and makes it harder to do a good job. Test
>> if the prefilter works by taking one of the GPS data sets from Tom and
>> run it through the prefilter and test using the simulator if the results
>> improve.
>> - In my GPSDO temperature changes and supply voltage variations where
>> the largest source of variations. You can simulate this with the
>> simulator by creating LO data sets with artificial changes in frequency.
>> Add a drift and test if the loop can keep up, add a jump and see how
>> fast it recovers
>> Erik, PD0EK
>>
>> On 20-3-2022 21:46, Pluess, Tobias via time-nuts wrote:
>>> Hi Bob,
>>>
>>> I see your point on quickly moving the OCXO. However of course this is
>> NOT
>>> what I do. To be precise, my GPSDO does this exactly once after powerup,
>> to
>>> quickly align the PPS. After that, the control loop takes over and steers
>>> the OCXO according to the error signal.
>>> I also have already implemented the algorithm that switches the control
>>> parameter sets: just after powerup, a "quick" set is used, that quickly
>>> brings the OCXO to the right frequency but also lets the DAC work quite
>>> hard. If the time error stays below 100 ns for a couple minutes, an
>>> "intermediate" control set is used with longer loop time constants. If
>> the
>>> time error stays below 100 ns for a couple minutes, the "slow" control
>> set
>>> is used which, currently, has a loop time constant of one hour. The DAC
>>> ouput changes very rarely, about one count up or down every couple
>> minutes.
>>> What I wanted to achieve with this autotuning is to find out whether 1
>> hour
>>> is a good time constant. Should it be longer? shorter? what would be the
>>> best value?
>>>
>>> Since the GPSDO already has a TIC built in, that measures the time
>> interval
>>> between the two PPS, I thought it must be, somehow, possible to assess
>> the
>>> current performance of the GPSDO. Lets say by estimating the ADEV. Based
>> on
>>> that value, it should then be possible to adapt the loop time constant,
>>> until some sort of optimum is found. No?
>>>
>>> Best
>>> Tobias
>>> HB9FSX
>>>
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Kleinhenz Markus
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