Frequency domain calibration: using DARM_CTRL

(This document is in cvs: calibration/timedomain/docs/derr_cal_vs_darm_cal.html)

Here I show a comparison between a the usual frequency domain calibration and
a frequency domain calibraiton that uses DARM_CTRL.  Both should be identical
except at calibration line frequencies.

I.e., I am comparing,

h(f)=DARM_ERR(f) * R(f)

with

h'(f) = DARM_ERR(f)/C(f) + (DARM_CTRL(f)/W(f)) * A (f)

where R, C, A are the response, sensing, and actuation, and W(f) is the whitening filter used on DARM_CTRL.
I can derive the equation for h' starting from the one for h (except for the excitation which is added to
DARM_CTRL).

So this is why they sould be identical to 7 significant figures (floating point precision) except at calibration
line frequencies.  This is not the case. I find differences at the 1% level.  For the Hanford instruments I
find large (10%) differences at 35Hz. At this frequency there is a sharp feature in the H1 and H2 servos. 
So I think the discrepancies are coming from the servo.

Livingston



Hanford 4k

Hanford 2k