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

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

On Wed, May 29, 2013 at 11:53:42AM +0200, Miroslav Lichvar wrote:
> On Tue, May 28, 2013 at 07:16:15PM +0200, Richard Cochran wrote:
> > 	# method B at 2^-4
> > 	# pi_proportional_const  3.2
> > 	# pi_integral_const      0.05
> 
> Hm, doesn't the method B give at 2^-4 kp=0.2 and ki=0.8?

Well, it doesn't. It seems I was using a wrong formula for the method
B the whole time. I had not noticed it was written with multiplication
instead of division. The previous comparisons I made are invalid, I'm
sorry.

When I use the correct (hopefully) formula, the difference is much
less dramatic. This comparison is with the original method A (with jw
set correctly) vs the original method B (which doesn't have a jw
parameter).

u\jw |  1e0      |  1e1     |  1e2     |  1e3     |
2^-7 |   -1   -2 |  -4  -13 | -10  -23 | -14  -33 |
2^-6 |   -2   -1 |  -4  -11 |  -8  -22 | -13  -31 |
2^-5 |   -1    0 |  -3  -10 |  -8  -20 | -14  -30 |
2^-4 |   -2    2 |  -3   -9 |  -8  -19 | -13  -29 |
2^-3 |   -2    4 |  -2   -8 |  -7  -18 | -12  -28 |
2^-2 |   -2    5 |  -2   -7 |  -7  -18 | -12  -28 |
2^-1 |   -2    4 |  -2   -6 |  -7  -17 | -12  -27 |
2^+0 |   -1    0 |  -2   -5 |  -7  -17 | -13  -28 |
2^+1 |    0    0 |  -0   -1 |  -6  -13 | -11  -24 |
2^+2 |    1    0 |   0   -1 |  -3   -8 |  -9  -20 |
2^+3 |    1    0 |   0    0 |  -1   -3 |  -6  -15 |
2^+4 |    0    0 |   1    0 |   0   -1 |  -4  -10 |
2^+5 |    0    0 |   1    0 |   0   -0 |  -1   -4 |
2^+6 |    0    0 |   1    0 |   1    0 |   0   -1 |
2^+7 |    1    0 |   0    0 |   1    0 |   0   -0 |

Now, as I'm writing the patch for the extended servo configuration,
I'm looking for some defaults I could put into it. The most imporant
difference between the method A and B is in the exponents. If I set
the scale and the limiting coefficients identically and in such a way
that it gives the same defaults with 1 sec interval as the current HW
time stamping default, this is what I get.

method A':
kp = min(0.7 * u^-0.3, 0.7/u)
ki = min(0.3 * u^0.4, 0.3/u)

method B':
kp = min(0.7 * u^-0.5, 0.7/u)
ki = min(0.3 * u^0.5, 0.3/u)

u\jw |  1e0      |  1e1     |  1e2     |  1e3     |
2^-7 |   -0   -8 |  -3   -8 |  -3   -8 |  -2   -8 |
2^-6 |   -0   -7 |  -2   -7 |  -2   -7 |  -2   -7 |
2^-5 |    0   -6 |  -2   -6 |  -1   -6 |  -1   -6 |
2^-4 |    0   -4 |  -1   -5 |  -1   -5 |  -1   -5 |
2^-3 |    0   -3 |  -1   -3 |  -1   -3 |  -1   -3 |
2^-2 |    1   -2 |  -0   -2 |  -0   -2 |  -0   -2 |
2^-1 |    0   -1 |  -0   -1 |  -0   -1 |  -0   -1 |
2^+0 |   -0   -0 |  -0   -0 |  -0   -0 |  -0    0 |
2^+1 |    0    0 |   0   -0 |   0    0 |   0    0 |
2^+2 |   -0   -0 |   0    0 |  -0    0 |  -0    0 |
2^+3 |    0   -0 |  -0   -0 |   0    0 |   0    0 |
2^+4 |   -0    0 |  -0    0 |   0    0 |   0    0 |
2^+5 |   -0   -0 |   0    0 |  -0    0 |   0    0 |
2^+6 |    0    0 |  -0    0 |  -0   -0 |  -0   -0 |
2^+7 |   -0    0 |  -0   -0 |  -0   -0 |  -0   -0 |

The difference is small, but it seems the -0.3 and 0.4 exponents are
slighly better in minimizing both time error and frequency error. The
limiting coefficients could be increased to allow more aggresive
setting with longer intervals and reduce the error, but I think we can
focus on that later.

Thanks,

-- 
Miroslav Lichvar