Re: [Linuxptp-devel] Optimal P, I constants

[Miroslav L. <mli...@re...>]

On Wed, May 01, 2013 at 07:52:03AM +0200, Richard Cochran wrote:
> Please go ahead and see what you come up with. I am interested to see
> how you do it and what the results are. The servo parameters involve
> trade offs, and so there is no one right answer. Even if the software
> ends up with a tabular approach (one PI pair per sync rate), still we
> can always include your results in table form.

I tried to find which PI constant give the best RMS time error in the
simulation results when the jitter/wander ratio and update interval
change and run lines through the points. I guess it could be done
accurately by mathematical analysis, but that would be much more
difficult, at least for me. Similarly, it should be possible to get
constants which minimize the RMS frequency error or a combination of
the two.

Here is what I found, u is the update interval in seconds, a is the
Allan intercept in seconds and jw is the jitter/wander ratio. The
clamping constants were chosen so P+I ≈ 1/u and P*u ≈ (I*u)^0.5.

jw ≈ (a / 2)^1.5
P_min_rms_time ≈ min(10^0.2 / (u^0.3 * jw^0.5), 0.62 / u)
I_min_rms_time ≈ min(10^0.1 / (u^-0.4 * jw), 0.38 / u)

Here are calculated constants for some selected Allan intercepts and
update intervals.

 u\a |               1 |              10 |             100 |            1000 |
2^+4 | 3.9e-02 2.4e-02 | 3.9e-02 2.4e-02 | 3.7e-02 1.1e-02 | 6.5e-03 3.4e-04 |
2^+3 | 7.7e-02 4.8e-02 | 7.7e-02 4.8e-02 | 4.5e-02 8.2e-03 | 8.0e-03 2.6e-04 |
2^+2 | 1.5e-01 9.5e-02 | 1.5e-01 9.5e-02 | 5.6e-02 6.2e-03 | 9.9e-03 2.0e-04 |
2^+1 | 3.1e-01 1.9e-01 | 3.1e-01 1.5e-01 | 6.8e-02 4.7e-03 | 1.2e-02 1.5e-04 |
2^-0 | 6.2e-01 3.8e-01 | 4.7e-01 1.1e-01 | 8.4e-02 3.6e-03 | 1.5e-02 1.1e-04 |
2^-1 | 1.2e+00 7.6e-01 | 5.8e-01 8.5e-02 | 1.0e-01 2.7e-03 | 1.8e-02 8.5e-05 |
2^-2 | 2.5e+00 1.5e+00 | 7.2e-01 6.5e-02 | 1.3e-01 2.0e-03 | 2.3e-02 6.5e-05 |
2^-3 | 5.0e+00 1.5e+00 | 8.8e-01 4.9e-02 | 1.6e-01 1.5e-03 | 2.8e-02 4.9e-05 |
2^-4 | 6.1e+00 1.2e+00 | 1.1e+00 3.7e-02 | 1.9e-01 1.2e-03 | 3.4e-02 3.7e-05 |

What do you think?

-- 
Miroslav Lichvar