Jeff K., Evan G., Lilli S.

Summary:
The suspension actuators which are used to control the differential arm degree of freedom are calibrated from measurements using the Pcal as a fiducial. Currently, DARM feeds back to L3 on ETMX, L2 on ETMY, and L1 on ETMY. Our measurements are within ~5% of the nominal O2 values. 

Details:
This is to explain the SUS actuator calibration measurements from LHO aLOG 44507 in more detail. We processed the measurements using the pyDARM code which lives here:
/ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/O3/H1/Scripts/process_actuationmeas_20181010.py

Results and comparison with O2:

Parameter                              | Quantiles (0.15, 0.50, 0.84)      | Nominal O2 value | % change
--------------------------------------------------------------------------------------------------------
EX TST Actuator gain, H_c (N/ct)       | 4.502e-12, 4.505e-12, 4.508e-12   | 4.357e-12 (ETMY) | +3.4%
Residual time delay, tau_A (usec)      | 4.794, 5.896, 7.014               |                  |
                                       |                                   |                  |
EY PUM Actuator gain, H_c (N/ct)       | 6.484e-10, 6.508e-10, 6.531e-10   | 6.768e-10        | -3.8%
Residual time delay, tau_A (usec)      | 71.18, 79.91, 88.83               |                  |
                                       |                                   |                  |
EY UIM Actuator gain, H_c (N/ct)       | 8.513e-08, 8.535e-08, 8.557e-08   | 8.091e-8         | +5.5%
Residual time delay, tau_A (usec)      | 102.3, 112.2, 121.9               |                  |

Note that the residual delay is poorly characterized on the L2 and L1 stages because we didn't go to high frequencies and we made so few measurement points. Further characterization is necessary in order to better determine the residual delay. While the MCMC is able to precisely determine a residual time delay value, it is skewed by our lack of data (in O2, we used the L3 stage only to establish this delay, which was consistent with zero, and we don't expect that it has changed). Unfortunately, we have to pay attention to the different delay in different stages because we are actuating on different test masses that have distinct computers.

We drove at a new excitation point (see LHO aLOG 44459) that is parallel to the calibration lines at the input to the DRIVEALIGN bank. This new location captures any potential changes in the DRIVEALIGN bank gain (e.g., when the ESD bias sign is flipped) and allows us to back out measurements to a reference model time by using the time varying "kappa" values derived from calibration lines.

Attached are several figures to show the analysis:
1) All three actuation stages and residuals where the measurement is from the input to the DRIVEALIGN bank to meters DARM where we have removed the frequency shaping of the DRIVEALIGN filters but left the gain in place. This is the traditional "actuation strength" measurement and comparable to O2 measurements at the TEST excitation point.
2-4) Each actuation stage with the frequency dependence divided out, leaving only the gain of the actuation path (N/ct). The gain measurements and residuals (measurements/model) are shown.
5-7) Corner plots showing MCMC results which determine the gain and delay with uncertainties (shown in the above table)
8-10) Gaussian process regression fits to the residuals. With further measurements (expanded frequency bands, higher precision measurements, etc.) we can easily refine the unknown systematic errors. For example, if we better characterize the UIM suspension dynamics, then we can remove this systematic effect and utilize more frequency points from the UIM above 50 Hz.

We have put together a schematic diagram showing the sign conventions along the actuation paths. Just along the three SUS actuation paths and Pcal paths there are >30 possibilities for sign flips. You can't just flip signs and guess to get the right answer because we are making injections at several different points in the control loop. We actually have to understand and validate each one in the loop. We are confident that the actuator signs are correct because they match O2 measurements (see LHO aLOG 44691). #BookkeepingNightmares

Although the actuation strengths are roughly comparable to the O2 values, when we install these into the front end for control room calibration, we find that the DARM spectrum is incorrect by a factor of ~2.6 at 37 Hz (see LHO aLOG 44507). We need more time with the instrument in order to sort out what could be going wrong.