I made an update to the quad matlab model to account for these mystery features. See CSWG log 11197.

I describe my use of the Frequency Domain System Identification toolbox (FDIDENT) to fit this transfer function in CSWG elog #11205. FDIDENT is a third party Matlab toolbox which provides tools for identifying linear dynamic single-input/single-output (SISO) systems from time response or frequency response measurements. The toolbox is free for non-profit use.

https://www.mathworks.com/products/connections/product_detail/product_35570.html

http://home.mit.bme.hu/~kollar/fdident/

A stable, but non-minimum phase, model without delay – compatible with a Linear Time Invariant (LTI) representation -- results in a best fit for a 22 order numerator and 28 order denominator model, m2228. The model is compared to the measurement data in the attached bode plot.

I attach several new parts of this high frequency characterization in order to facilitate incorporating the uncertainty in any future transfer function fitting. 

I attach three new text files:
    "..._tf.txt" -- a copy of the originally attached text file, columns are 
        [freq re(A) im(A)]
    "..._coh.txt" -- an export of the (prefiltered) coherence, columns are 
        [freq iEXCCoh PCALCoh]
    "..._relunc.txt" -- an export of the combined relative uncertainty on the transfer function, columns are 
        [freq sigma_A]

Computing the uncertainty on this actuation strength was a bit of a challenge. 
Remember, the above measure of the actuation strength of the UIM stage, A, is a combination of two transfer functions, as described in P1500248, Section V. In this aLOG they're referred to as "PCAL2DARM" where we use the photon calibrator as a reference actuator, and "iEXC2DARM" where the suspension stage under test is used as the actuator. Typically, the iEXC2DARM transfer function has the lowest coherence. 
Even worse, I've combined many data sets of both transfer functions covering different frequency regions each with a different number of averages.
Thus form the uncertainty, I've taken each frequency region's data set, and 
    - Filtered both iEXC and PCAL transfer functions for data points in which the iEXC TF has coherence greater than 0.95,
    - Created a relative uncertainty vector for each iEXC and PCAL transfer functions using the standard B&P equation,
        sigma_TF(f) / TF = sqrt( (1-C(f)) / (2 N C(f)) )
    where C(f) is the coherence, and N is the number of averages (N was 10 for swept sine TFs, 25 for broad band TFs)
    - Concatenated the data sets to form the overall transfer function, A,
    - Combined the two uncertainty vectors in the standard way,
        sigma_A / A = sqrt((sigma_iEXC / iEXC)^2 + (sigma_PCAL / PCAL)^2)
    - Sorted the collection of 
        [frequency complextf iexccoh pcalcoh sigma_A]
    by frequency.
    - Exported the uncertainty.

Note that one only needs one column of uncertainty, for the absolute uncertainty in magnitude is just
    |sigma_A| = abs(A) * (sigma_A / A)
and the absolute uncertainty in phase is
    /_ sigma  = 180/pi * (sigma_A / A)

I attach a plot of the magnitude and its uncertainty for demonstrative purposes, so that when the files are used, you can compare your plots of this against mine to be sure you're using the data right. Note that I've multiplied the uncertainty by a factor of 10 for plotting only so that it's visible.

I've updated and committed the function that's used to process this data, and it can be found here:
    /ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/ER10/H1/Scripts/FullIFOActuatorTFs/
    process_H1SUSETMY_L1_HFDynamicsTest_20161117.m

For the record: The GraceDB trigger used to do this test, https://gracedb.ligo.org/events/view/G262286 , is a fake trigger (and clearly labeled as such in the log) inserted into GraceDB by Mina Cho and Peter Shawhan with group="Burst" and pipeline="CWB2G".  That's the same we we did periodic testing of control-room audio alerts during O1.  In this case the H1OPS and L1OPS labels were added by hand.

The attached plot shows that the noisy behavior around the frequency of this line persists after it was turned off.

1083.7 Hz calibration line restored just after the lock loss at 2016-11-18 23:30 UTC.

The high-frequency dynamics measurements quoted in this aLOG have been analyzed. See results in LHO aLOG 31603.

J. Kissel, K. Izumi, D. Tuyenbayev,

Overview

Actuation strengths [N/ct] for all three stages have been calculated with MCMC method. In In this analysis we used data from last set of measurements taken on Nov 17 (see above), together with measurements from Nov 7, 8, 10 and 12 (see LHO alogs 31303, 31371, 31403, 31433). The calculated actuation coefficients are:

K_U = 8.1648^-8 N/ct

K_P = 6.844^-10 N/ct

K_T = 4.395^-12 N/ct

The H1DARM model parameters were updated using these values, particularty:

UIM_NpA = 1.739; [N/A]
PUM_NpA = 0.0334; [N/A]
TST_NpV2_y = 1.612e-10; [N/V^2]

We will double check the overall DARM loop model, with the updated sensing and actuation, by comparing it to DARM loop TF measurements.

Notice that TST actuation coef came out as a negative quantity, we believe that there is a "-1" missing in the model of this stage.

Details

For this analysis we took each actuation stage to DARM TF and PCALY to DARM TF measurements at the same frequency vector and used only data points with coherences above 0.9, we adopted a Matlab script used at LLO for this part of the analysis (see EvanG's LLO alog 29438). For each actuation stage i, the test point excitation to DARM TF is

iEXC2DARM = Ai,meas * C / (1 + G)

and PCALY to DARM is

PCALY2DARM = C / (1 + G)

The ratio of the two gives:

iEXC2DARM / PCALY2DARM = Ai,meas

Then we divided this my the model of the given stage without the N/ct coefficient, A_i,model / K_i,model = F_i,model, gives measurement of the frequency-independent N/ct coefficient:

A_i,meas / F_i,model = K_i,meas

Then, we used GWMCMC library (https://github.com/grinsted/gwmcmc) for fitting amplitude and phase of the N/ct coefficient for each stage (if the frequency dependent part of the model is correct, then the phase should be 0 deg). The log likelihood function used for fitting is

logLike = log( ∏( 1 / sqrt(2πσ_i²) exp( - (K_i,meas - K_fit)²/(2σ_i²) ) )

Fit results for magnitudes are given above and the phases are at the order of 10^-3 deg.

The K_U, K_P and K_T coefficients calculated from multiple-frequency transfer function measurements differ from earlier estimations from single line (LHO alog 31344) by 1.7%, 5.3% and 3.1% for UIM, PUM and TST stages. Possibly some unaccounted systematics in the frequency reponses of the DARM model near 35 Hz (the previous analysis was done with the DARM model for ER9).

Izumi K, Kissel J, Tuyenbayev D,

We used ER10 model to re-run an earlier actuation strength analysis using calibrartion line data from Nov 3 - Nov 8 (LHO alog 31344). The original analysis was done with the DARM model in which the positive N/ct sign was used for TST stage actuation, the correct K_T sign must have been negative. Below we list the updated results from this single-line analysis, the values are taken from GPS time interval [1162369920 1162413500]:

K_U = 8.613 × 10^-8 ± 3.204 × 10^-10 N/ct
K_P = 6.802 × 10^-10 ± 2.254 × 10^-12 N/ct
K_T = -4.341 × 10^-12 ± 1.339 × 10^-14 N/ct

Notice this analysis is used as an additional check of the multiple-frequency analysis (see above). The DARM model parameters for ER10/O2 will be based on the multiple-frequency analysis results (refined numbers and comparison results are coming soon).

Izumi K, Kissel J, Tuyenbayev D,

Overview

We calculated the actuation coefficients for the H1 DARM reference time model. For UIM (L1) and PUM (L2) stages the N/ct coefficients were fit based on actuation TF measurements on Nov 7, 8, 10, 12 and 15. These numbers have been reported earlier (see above). The TST actuation strength will have a trend over long time period due to charge accumulation, thus for TST stage it is better to estimate the coefficient based on measurements taken within a short period of time. Since we set the reference sensing function parameters based on measurements taken on Nov 12, for estimation of the TST (L3) stage actuation we decided to use measurements around that date, particularly measurements from Nov 10 and 12.

Contributions from each of the actuation stages to the overall DARM response drops as 1/f⁶, 1/f⁴ and 1/f², for this reason MCMC (and LSQ) fitting were restricted to [0 10] Hz, [0 200] Hz and [0, 200] Hz for UIM, PUM and TST stages respectively.

Below are the resulting N/ct values, these values:

K_U = 8.1648 × 10^-8 N/ct (±  0.074% 1-σ)
K_P = 6.844 × 10^-10 N/ct (± 0.018% 1-σ)
K_T = -4.389 × 10^-12 N/ct (± 0.031% 1-σ)

And the H1DARM model were updated in the following way (only the N/V2 for TST stage is different from LHO alog 31649):

UIM_NpA = 1.739;         % [N/A]
PUM_NpA = 0.0334;        % [N/A]
TST_NpV2_y = 1.6097e-10; % [N/V^2]

New EPICS values used for DARM time-dependent parameters have been calculated with the updated H1 DARM model for ER10/O2 (see attachment 1).

Comparisons

MCMC and LSQ methods gave consistent results, fractional discrepancies between the two were at the order of 10^-5 (LSQ fit was done only for magnitude).

Discrepancies between the new values and the ones currently installed in the CAL-CS front-end model are:

UIM: 0.05% (compared 8.1689 × 10-8 N/ct, the currently installed, old value)
PUM: 0.05% (compared to 6.8407 × 10-10 N/ct)
TST: 3.42% (compared to 4.239 × 10-12 N/ct)

Discrepancies between these values and an updated single-line analysis results (see LHO alog 31668 above) are 5.5% (UIM), 0.6% (PUM) and 1.4% (TST). A larger discrepancy between MCMC and the single-line analysis for UIM, we believe, is mostly due to 5-10% systematic errors in the UIM suspension model at ~36 Hz (see a residual plot attached to Kiwamu's LHO alog 31427).*

Although, the TST stage coefficient was calculated based on Nov 10th and 12th measurements, discrepancies between the values estimated for each of the 5 measurements (Nov 7 - 17), are within 0.5% (see attachment 2).

*Check out Jeff's LHO alog 31603 for more UIM HF investigations.

Details

TST stage fitting plots are attached below (see attachments 3 and 4). UIM and PUM fitting results did not change (see previous report above, LHO alog 31609).

The new EPICS values for DARM time-dependent parameters are committed to

${CalSVN}/Runs/ER10/H1/Scripts/CAL_EPICS/D20161120_H1_CAL_EPICS_VALUES.m

The up-to-date H1 DARM model parameters are commited to CalSVN:

${CalSVN}/Runs/ER10/Common/params/IFOindepParams.conf              r3752
${CalSVN}/Runs/ER10/H1/params/H1params.conf                        r3826
${CalSVN}/Runs/ER10/H1/params/2016-11-12/H1params_2016-11-12.conf  r3786

DARM model scripts (SRC detuning TF was modified to include Q-factor at r3814):

${CalSVN}/Runs/O2/DARMmodel/*  r3814

Actuation coefficient fitting script was uploaded to

${CalSVN}/Runs/ER10/H1/Scripts/FullIFOActuatorTFs/fitActCoefs_Npct.m  r3829

And the results are at

${CalSVN}/Runs/ER10/H1/Results/Actuation/2016-11-20_H1_SUSETMY_*.pdf

These channels should probably be re-monitored.  You've unmonitored the L2Ps, when it's actually the P2Ls (and Y2Ls) that will change when we run A2L.  The P2L and Y2L gains are already not monitored for all the test masses.  I have re-monitored the L2P gains.

Doh! Smackforehead.

When you say a2l, do you mean the trio of them or just the one original, main one?

Ya just the main one: a2l_min_LHO. Thanks Ed.

General comment for operators:

when you run a2l make sure you take the observatory mode to commisioning first, then you can put it back when the script finishes.  This way we can avoid confusing people.  Once we have SDF tied into the intention bit this would automatically drop us out of observing. 

I think these should be re-monitored in the safe.snap file.  These values (the ones that are the setpoints in the safe.snap screenshot) are written in the ISC_LOCK DOWN state.  If they are not correct, we may have trouble locking.  They are then changed by guardian to the values in the Observe.snap screenshot when we reduce the modulation depths of the 9 and 45 MHz.  So, the values that we want will be different in the safe and observe snap files, but we probably want to be monitoring them in both.

Actually, rethinking on it, Hugh's not-monitoring of these channels in the safe.snap file is totally consistent with everything we've been doing lately (not-monitoring channels that are written explicitly by guardian).  Whether our current strategy makes any sense is a larger conversation, but these channels are probably fine not being monitored.

The 1083.7 Hz calibration line was turned OFF for a brief period (~1-2 hours) during this current 4501.3 Hz stretch. See LHO aLOG 31610 for details.

1083.7 Hz calibration line restored just after the lock loss at 2016-11-18 23:30 UTC.

The one channel remaining in the LSC SDF was H1:PSL-POWER_SCALE_OFFSET, which is changed by the LASER_PWR guardian as it changes the PSL power into the vacuum.  This will be different every lock, so I have un-monitored it in the Observe.snap file.  Also, TJ has changed the guardian to round it to 4 decimal places, which is more than plenty of precision.

Looking right now, everything left in the ASC SDF is stuff that is actively being worked on (SOFT offsets, input matrix for PRC2, etc), so we don't know yet what we'll run with for O2.  These should all stay monitored.

All of the filters in the DC loops were notches that were turned on for a sensing matrix measurement, and should have been turned off.  When I turned the notches off, the diffs went away, so we already had the correct settings accepted.

Thanks for the fine-tuning and details--just what we need for good control--Thanks Jenne--H

Current damping status of this now > 25 hour 32 W lock: no damping required after the first 2 hours. Attached plots again show damping loop output over the past 26 hours and HOOM spacing for reference. 

A. Staley (posted by J. Kissel on her behalf)

Alexa -- still looking out for us -- had sent me an email about the above trend. Thanks Alexa (and Zsuzsa for prompting her to look)! I quote it below:


The fiber polarization controller drifted quite a bit -- Sheila, Evan, and I would post alogs about it keep track of the drift. There are a couple of things worth noting:

We discovered that the fiber polarization controller creates a peak in the green locking noise at 27 kHz (LHO aLOG 10275). So we decided to keep the polarization controller off. We didn't spend time characterizing how much the wave plates would drift with the controller off. We ensured the drift/hysteresis of the polarization wasn't drastic over a period of a day or so, but were still expecting some drift over time.

We also know that the fiber polarization drifts with temperature in the MSR (LHO aLOG 7023, LHO aLOG 11509) and the temperature is not very well controlled in that room.

A bit unrelated, but I had also seen funny behavior with the motorized polarization controller (MPC) upon turning it off and on (LHO aLOG 11505). 

I am not sure if anyone went into more detail than that to characterize this drift or mitigate it -- it was always pretty trivial to adjust. The DCC has the manual (T1200496), which states the expected rotational drift of the wave plates over time--this is very small. Between that variation, temperature drifts, and drifts in the laser out SOP, I would expect some drift in the polarization. Again, I don't think this has been characterized or quantified and compared with the trends we've seen.