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