J. Kissel, P. Fritschel

After all the investigations into the SUS loop performance to find the source of the excess motion Pitch and Longitudinal motion at 0.43 (, 0.56, and 1.0) [Hz], Peter suggested perhaps it's merely the expected coupling between L and P, with the large not-yet-awesome input motion from the BSC-ISIs. So, following the same prescription used to generate the curves in G1200712, I produced the predicted QUAD test mass motion due to the measured (BSC8-ISI, ITMY) motion on June 26th, i.e. E1200668, in both L and P.

Attached are the results.

We see that indeed, given the (BSC8-ISI, ITMY) input motion, the predicted motion is on the order of 2.4e-6 [m RMS] and 5e-6 [rad RMS], with the expected first L and P modes at 0.43 Hz and 0.56 Hz, which have (modeled) damped amplitudes of 1e-5 [m/rtHz] and 2e-5 [rad/rtHz], reasonably consistent with results reported in LHO aLOG 3363, LHO aLOG 3302, and LHO aLOG.

There are several ways in which this model isn't perfect:
- The input motion is representative of BSC8-ISI (ITMY), which has been commissioned further than BSC6-ISI (ETMY), so one might expect the input motion to ETMY to be somewhat worse (It only has damping, No HEPI, No Level 0 Isolation Loops). Fabrice is working on getting me BSC6 data.
- I took the input motions in X, Y, Z, RX, RY, and RZ -- which are defined about the center (in X and Y) of the ISI, and at the lower-zero-moment-actuation-plane of ST2 of the ISI -- as direct inputs to the suspension point of the QUAD: (Y->) L, (X->) T, (Z->) V, (RY->) R, (RX->) P, (RZ->) Y, which means that the estimate for P does not account for the ~0.5 [m] lever arm between the ISI ST2 origin and the SUS point origin. See T1100617 for details (B. Lantz, C. Kucharcyzk, and I are working on getting the correct transform.)

The bonus attachments, relevant to the discussion, are as follows
- [2012-07-09_testmassmotion_bscinput.pdf] A plot of the motion used as input (identical to what is shown in E1200668)
- [2012-07-09_modeltf_*toP.pdf] The rarely-looked-at transfer functions between all degrees of freedom input to pitch in [rad/m] or [rad/rad].
- [2012-07-09_testmassmotion_P_resgndbudget.pdf] A break down of the predicted residual P motion from all degrees of freedom.

One VERY interesting revelation from these bonus plots: 
- T @SUS point transmission to P @ test mass becomes comparable to L to P in [rad/m] above ~1 Hz
- R @SUS point transmission to P @ test mass becomes roughly a factor of 10 greater to P to P in [rad/rad] above ~0.5 Hz
These mean we'll have to focus on reducing the T and R motion *just as much* as reducing the L and P motion.