# [time-nuts] Finally, Success

Magnus Danielson magnus at rubidium.dyndns.org
Mon Sep 15 15:48:25 EDT 2014

```Bob,

On 09/15/2014 06:23 PM, Bob Stewart wrote:
> My daughter and I were discussing what she does for a living with time and phase as a geophysicist and relating that to what I'm trying to do with my GPSDOengine.  I explained that I was trying to keep the frequency accurate and stable, while also keeping the phase near a target of 180 degrees.  And suddenly, I realized that that's not what I was actually doing.  For the "I" term of PID, I was integrating on phase position, which was never going to work.
>
> So, I made a change to start integrating on the phase change from second to second (i.e. frequency error), and I think this is finally performing correctly.  The DAC is now very flat, and the phase is moving around as would be expected from Bob's and Tom's comments on the LEA-6T.  Here's an ADEV of the GPSDO's OCXO vs the 10811 in my 5335A.  It covers a timeframe from about 11:00PM last night to about 11:00AM this morning.  This is with the PID running as a PI controller with very small P and I gain values.
>
>
> http://evoria.net/AE6RV/TIC/GPSDO.vs.HP10811.png

For a PID PLL you need to build the phase error properly one way or
another being

PE = phase_ref - phase_out

If you use a TIC, the time difference is simply a variant of the PE
value (phase_out to start and phase_ref to stop channels). It may be
useful to have a offset value that can be subtracted numerically.

A PID on this then becomes
f = (PE - PE_prev)/t0
PE_prev = PE
Vi = Vi + I*PE
Vf = Vi + P*PE + D*f

Integrating on the derivate of PE helps in one particular case, when the
frequency error is so large that it doesn't lock up easily. This is done
like this:

f = (PE - PE_prev)/t0
PE_prev = PE
Vi = Vi + I*PE + F*f
Vf = Vi + P*PE + D*f

As you increase the F factor, the rate of frequency learning of I goes
quicker, and steers the exponential relaxation of the frequency error
before the beat frequency becomes so low that the phase-lock takes over.

As we (me and Warren) had a long thread before, turning up F is the same
as turning up P.

P is proportional to the damping factor
P is proportional to the PLL bandwidth
I is proportional to the square of the PLL bandwidth

Sounds like you had too low P value.

I could write the exact formulas up, they are easy to derivate with
paper and pen. It is also textbook material.

Make sure you have a damping factor of at least 3.

Hope it helps.

Cheers,
Magnus
```

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