[time-nuts] First success with very simple, very low cost GPSDO
WarrenS
warrensjmail-one at yahoo.com
Sun Apr 13 05:44:16 UTC 2014
Magnus wrote
>It may appear so, but the derivate, scale-factor F and integrate does not
>make the scale-factor F equalent to P, since you are forgetting that the
>derivate removes the DC term
We don't quite agree on that point yet.
I can not find anything different or special that your code example is doing
"at it's output",
It seems to produce the exact same results as a standard PI controller.
Also in your code and all PI code the FLL function you talk about is
provided by the P term, Don't need to add the derivate, scale-factor F and
integrate term.
The derivate & integrate function could remove (or change) the signal's
offset if it was coded to do so,
But in your code, DC offset removal is not shown, so it would appear that
**no** DC offset is being removed.
The DC Offset that is removed depends on what value that Vdp_pre is
initialize to, before the first cycle thru the code.
If Vdp_pre and Vi are both initialized to zero then there is no offset
removed,
and derivate, scale-factor_F then integrate exactally equals the same as
scale-factor_F only.
If vdp_pre is initalized to the first input value Vdp(0) instead of zero, as
is often the case, then the offset removed would be scale-factor_F x Vdp(0)
either way the code (with Vdp_pre & Vi pre-initialized to zero)
>
> Vdf = Vdp - Vdp_pre
> Vdp_pre = Vdp
> Vi = Vi + I*Vdp + F*Vdf
> Vf = Vi + P*Vdp
>
appears to produces the exact same output as the simpler code:
(when Vi is initalized to zero)
Vi = Vi + (I * Vdp) ;
Vf = Vi + (P+F) * Vdp
(To add offset removal, Initialize Vi to - F * First_Vdp_reading )
Also get same results from: (where Dc = 0)
or for offset removal set Dc to F*First_Vdp_reading
Vi = Vi + (I * Vdp)
Vf = Vi + (P+F) * Vdp - Dc
>F and P is not equivalents, as P will not contribute to the state of
>Vi, which is evident in the weak pull-in of a standard PI loop
We're going to have to disagree on that also.
The output is the sum of the P term and the I term, You end up with the
exact same results if you take something away from one of then and apply it
to the other.
That is what my two code examples are doing.
If you want faster pull in just increase the product of F*P, it does not
matter which, They both give the same exact results for DC and AC.
Tom, do you want to program Gpsim1 to break this standoff?
ws
*****************************
Warren,
On 12/04/14 21:09, WarrenS wrote:
> Magnus
>
> Interesting, Am I missing something or is there an error in your code or
> logic.
>
> Looks to me like the code is a PI controller with a added "D" term
> (Vdf) of input,
> and the "D" is then Integrated with a scale factor of "F" at Vi = Vi +
> F*Vdf ...
> An integrated derivative is exactly equal to a P
I may appear so, but the derivate, scale-factor F and integrate does not
make the scale-factor F equalent to P, since you are forgetting that the
derivate removes the DC term and the integration forms it's own DC term.
This DC-term as scaled through oscillator gain and added to the
oscillators offset is then subtracted from the reference frequency and
thus the error frequency is input to the integrator stage.
The FLL variant model can be understood if the differentiation is pushed
to both inputs of the phase comparator, where the reference frequency
and oscillators frequency will be subtracted rather than their phase and
the only remaining integrator in the loop is that holding the Vi term.
The frequency error term will exponentially decay with the time-constant
as set by the F coefficient.
So, F and P is not equivalents, as P will not contribute to the state of
Vi, which is evident in the weak pull-in of a standard PI loop.
However, F and P will for the AC behaviour of the loop be equivalents,
so care must be taken into setting P with regard to F in order to get
the expected damping of the loop.
Anyway, this is a FLL-aided PI-loop, which looks like an incorrectly
wired PID-loop. Quite minimalistic.
> Looks to me like the code is still just a standard PI controller where
> Vdp is the phase error;
> Vi = Vi + I*Vdp
> Vf = Vi + (P+F) * Vdp
>
> This can be simplified by dropping the F scale factor and increasing the
> P a little
>
> What am I missing?
I think I covered that above.
> One thing for sure that the code is missing is a pre-filter, which is
> very helpful because of the GPS phase noise.
It is missing a whole deal, but I wanted to illustrate the core.
One thing which is not covered is the un-wrapping of the phase detector
in the case that it does not wrap around binary. Another thing, the
frequency detector phase history may need to be unwrapped prior to
subtraction in order to make sure the frequency estimate becomes correct.
> Turning on the "D" term in a PID with a prefilter is mostly not
> recommended, They tend to just cancel each other.
I avoided the "D" coefficient name as it will be confusing to a normal
PID naming, when it will in fact does not do the normal "D".
Cheers,
Magnus
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