Jeff K., Hang
After Jeff balanced the ETMX L2 stage coils, we fitted the L2A filters based on the measured transfer from LHO:42662.
The first attached plot showed the L2A decoupling results. The left panels were for L2P, and right ones for L2Y. From top to bottom, the panels showed the magnitude, phase, and coherence from measured L2 longitudinal drive to L3 oplev response. The black traces were results without L2A filters, and the red ones were the ones after we engaged the L2A decoupling.
For pitch, we could reduce the length coupling by about a factor of 2 in the 0.3-1 Hz band. Further improvement in the amount and frequency range of cancelation was limited by extra low pass applied to avoid injecting noise above 10 Hz.
For yaw, the reduction was less significant, and the filter actually made the coupling in the 0.1-0.3 Hz band worse. However, the L2Y coupling (though much higher than the sus model's prediction) was already a factor of ~10 below the L2P. Thus this might be okay. Or maybe we don't even need to engage the L2Y feeding forward.
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The new filters are loaded the H1:SUS-ETMX_L2_DRIVEALIGN_L2P/Y filter bank under FM6, 7, 8 (for L2A, plant inversion, and extra lowpass, respectively). The fitted TFs (orange traces) are attached as the second and third plots. The blue dots are measurement results from Jeff. The fitting is done with Lee's iirrational.
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Note: this only reduces the L2A coupling due to the actuation. The seismically induced motion of individual mirror is not zeroed and it will still cause angular motion due to the suspension L2A (especially L2P) coupling. To reduce the amount of arm cavity alignment control, it would be nice to have some local seismic L2A feeding forward.
I didn't pay enough attention to the DC position of the ETMX oplev, which had drifted quite off-centered at the time I did the measurements (LHO:42695). Thus the results above need to be revalidated. I will redo the measurement after centering the oplevs.
We tried to examine the effects of ETM L2 stage L2A decoupling using O2 data, and the results are attached.
The first plot showed the ASD of ETMY L3 PIT oplev. The blue trace is the total asd, the orange one is the projection of L2 longitudinal drive using coherence projection, and the green trace is the projection of L2 drive due to local L2A cross coupling. The local L2 stage cross-coupling seems to be a small contribution to the total RMS.
This might be better seen in the second attached figure. The blue trace was still the total oplev pitch signal, and the orange trace is the one after removing the L2 longitudinal drive. The rms only improved by a small amount.
A caveat is that the L2 stage L to L3 stage P transfer function was taken from the ETMX (not ETMY!) result AFTER the new coil balancing. Nonetheless, it seemed unlikely that the L2 stage L2A would significantly reduce the total pitch RMS. Will examine the contributions from upper stages in the future.