Summary:
Quantization error in QUAD suspension L1, L2 and L3 DAC channels are almost negligible except for ETMY L1 (which is only used for tidal).
ETMY L1 quantization noise is ~8E-3cts/sqrtHz per coil below 200Hz (as opposed to uniformly distributed error of 1.6E-3cts/sqrtHz), and this is just about a factor of 4 below the DARM feedback applied to EX L1 coils at 40Hz or a factor of 6 to 7 at 80Hz. Since the noise is incoherent between coils, there's another factor of 2, so overall this is about a factor of 8 at 40Hz or a factor of 12 to 14 at 80Hz.
It's not clear how much this matters to DARM (unless we apply the suspension model), but since EY L1 is only used for tidal, this noise is unnecessarily applied anyway. We should be able to enable any one of 3 stages of LPFs to mitigate this by a factor of 10.
Details:
I started checking if each DAC has an appropriate level of output such that the quantization noise is negligible. I looked at QUADs as the starting point.
Turns out that the only DAC that could matter is EY L1 OSEMs which receive only tidal as the input. Since tidal is just some really low frequency signal, digitization error power is concentrated to lower frequency.
In the first attachment, to the left is the ETMY L1 stage coil ouputs (the most downstream of the user model) and the corresponding IOP outputs (that are the same as coil outputs but after upsampling, low-passing and then casting to integer) during the observation.
In an ideal uniformly distributed error, the digitization error spectrum will be sqrt(1/12) /sqrt(32768Hz)= 1.6E-3 cts/sqrtHz, but in the case of EY L1 it's about 8E-3cts/sqrtHz below 200Hz or so. The noise go down as the frequency becomes higher.
OTOH, the middle left panel is ETMX L1 stage coil outputs and IOP channels. High frequency noise in IOP is roughly consistent with the uniformly distributed error.
This is already a useful comparison, but I wanted to know how much of ETMX L1 stage output is coming from DARM feedback (other components are LSC feedforward and tidal), so I looked at the DARM_OUT and ETMX L3 ISC_INF (middle right). As you can see a funny bump between 20 and 100Hz is from LSC FF.
Finally I propagated DARM_OUT through the filter chain in EX to one of L1 coils (right, yellow-ish) and plotted with EX and EY IOP output (orange and blue).
In the second attachment, other DACs in the QUADs look OK. Though we don't have a window to peek into the noise, the quantization noise at high frequency looks consistent with uniform distribution (1.6E-3) and the signal level of any of those channels seem to be large enough.
I'll check other suspensions.
Performing a similar study as was done for the PUM (see LHO aLOG 53482), I've gathered DAC requested data from H1SUSETMX UIM (L1), UL coil and used that and a model of the coil driver filters to estimate the DAC requested if we applied one stage of analog low pass -- which would require a the addition of a amplifying filter with one zero at 1.0 Hz, and a pole at 10.5 Hz. Conclusion: we have plenty of head room. We will only marginally decrease the amount of safety factor to saturation. I attach three plots: (1) the same amplitude spectral density and RMS study as in LHO aLOG 53482. (2) A several-day trend of the requested drive to all coils for ETMX UIM, such that one can see the true impact of tidal control (3) A several-day trend of the requested drive to all coils for ETMY UIM. Note, that this data goes to much lower frequency than the PUM data (and was taken in the middle of a 40 mph wind storm), so it is nicely representative of a "bad environment" scenario. The size of the drive as a result of the wind-storm is clearly visible at the tail end of the trends. We don't have a ramping EUL2OSEM matrix on the UIM, so we can't engange State 2 (LP1 ON) in the LOWNOISE_COIL_DRIVERS state. Thus, we'll have to just request state 2 before lock acquisition tomorrow during maintenance, and accept in SDF, such that all subsequent observation ready segments will have state 2 engaged (until otherwise noted). Hopefully the lock acquisition sequence doesn't require several more orders of magnitude of > 0.5 Hz UIM actuation... A reminder of the options for the UIM coil driver, from LHO aLOG 4495 Driver Type Circuit Iso. Stages State Switch State Freq. Resp DC Transconductance ACQ | LP (z):(p) [Hz] [mA/V] UIM D070481-v4 QUADL1 1 n/a | OFF OFF OFF (50):(300) 0.15 2 n/a | ON OFF OFF (10.5 50):(1 300) | 3 n/a | ON ON OFF (10.5 10.5 50):(1 1 300) | 4 n/a | ON ON ON (10.5 10.5 10.5 50):(1 1 1 300) V The templates from which I exported the data into matlab live here: /ligo/svncommon/SusSVN/sus/trunk/QUAD/H1/ETMX/ SAGL1/Data/2019-11-25_H1SUSETMX_Actuator_DAC_L1_Output_LFZoom.xml # new data from 2 mHz to 10 Hz SAGL2/Data/2019-11-25_H1SUSETMX_Actuator_DAC_Output.xml # exported "high frequency" data that was taken any way for PUM study and the script to process the data lives here (where among other analysis, I merged the ASDs at 9 Hz, where they're clearly no different between pre-wind-storm "high frequency" data and during-wind-storm "low frequency" data): /ligo/svncommon/SusSVN/sus/trunk/QUAD/H1/ETMX/SAGL1/Scripts/ estimate_coildriverstate_impact_UIM_20191125.m
I checked the M0 F1, F2 and F3 coils for all QUADs and they were good.
I also checked BS, PRM, PR2, PR3, SRM, SR2 and SR3. For most of the channels the signal was much larger than the quantization noise. For PR2 and SR2 M3 stage the quantization noise is large but there's no more coherence between IOP channels and DARM nor PRCL/SRCL than between user channels and DARM.