J. Kissel, R. Mittleman

Another day, another dollar's worth of ISI problems. This morning, I received reports of more than 0.1 [urad] RMS motion of the arm cavity BSC-ISIs -- now ISI-ETMX. As I've done every day this week, I'd resolved to just install improved QUAD damping filters with higher damping gain. However, the first step in this process is to use the current performance of the ISIs as input motion. As soon as I gathered the data, I found that the performance of the ETMX was polluted by a -- you guessed it -- ~0.5 [Hz] spike feature / oscillation / resonance in the X DOF (aligned with the SUS ETMX's L DOF), which rings up the 0.44 [Hz] and 0.56 [Hz] modes of the QUAD. The worst part about it is that this particular feature had appeared over-night. 

Long story short, we did NOT find the source of the problem in the days worth of investigation, but it DID go away while we were investigating. Along the way, we've discovered several things that were poorly done on this chamber, which I'll detail below. However, now that feature is gone, I'll once again start the process of designing more beefy QUAD damping filters.

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The Story, in brief (each bullet corresponds to the attachments, in order):
- Took performance spectra of X direction (ST1 T240s, ST2 GS13s, and QUAD Optical Lever Pitch), at 2014 Jan 30 15:00 UTC (before the morning meeting, local time). Found feature at 0.51 [Hz] (with a resolution 0.01 [Hz]). 
     - HEPI Isolated (Level 1 isolation filters, Position-Only Blends), 
     - ISI Isolated (Leel 1 isolation filters, ST1 XY T100mHz_N0.44Hz, all other DOFs, and ST 2 with 750mHz blends), 
     - QUAD Damped (Level 2.1 damping filters.) 
- Looked at all Cartesian degrees of freedom on ST2 and ST1, only saw spike in X.
- Suspecting individual sensor flaws again, looked at raw T240 and raw CPS with only damping loops on. Saw nothing suspicious in any DOF.
- Closed loops again, tried blending ST1 without T240s (i.e. All DOFs on ST1 and ST2). Spike disappears, but the amplitude of the residual seismic noise is higher than peak amplitude of the feature. In-conclusive test. 
- Suspecting loop instabilities, completely characterized X DOF isolation loop in both 750 mHz configuration and T100mHz_N0.44 configuration, measuring open loop gain transfer functions, closed loop gain transfer functions, plotting blend and isolation filters, etc. etc. While we found several problems, none of which would cause any instability.
- Remeasured performance of ETMX at 2014 Jan 30 21:00 UTC (during lunch / journal club local time), and feature disappeared. Good flippin' grief.
- Measured plant with isolation loops open to assess signs, appear to be self-consistent, though they don't match the conventions in T1000388. 

The problems we found (which again, won't explain the ~0.5 [Hz] peak):
(1) Both sets of blend filters installed have flaws (see the first 2 pages of the "LoopChar" attachments):
     - 750 mHz: The L4C Highpass has way too much gain at low-frequency. Now, as discussed earlier, the filter has to include the L4C response, but the roll-off of the complementary filter should start at a much higher frequency, say 200 mHz. Further, the displacement sensor low-pass should fall off (in frequency) faster than the L4C, they're currently both falling as 1/f (as indicated by the matching phase of -90 [deg]). I know these are supposed to be the "robust, OK performance" filters, but c'mon. 
     - T100mHz_N0.44Hz: The displacement sensor low-pass filter should fall off at-least faster than the L4C, if not faster than the T240. It current returns to flat in frequency, re-injecting displacement sensor noise above 100 [Hz]. 

(2) Though we measured matrix signs of the plant to be self-consistent (see 2014-01-30_1500_H1ISIETMX_Plant.pdf): at "DC," (the bottom of our band of interest)
     - CPS = Flat in magnitude, and 0 [deg] phase, i.e. in phase, and in the same direction as the actuators
     - T240 = Rising as f in magnitude +90 [deg], i.e. with the response to velocity flat above 4 [mHz]
     - L4C = Rising as one factor of f in magnitude (+90 [deg] in phase) from being a velocity sensor, as well as two more factors of f (and another +180 [deg] in phase) from the inertial sensor response not yet compensated, for a grand total of what's shown: rising as f^3, with a phase of -90 [deg]
Comparing against the new document on conventions (T1000388), the individual elements are bonkers, and some coefficients are off by ~10-20%. 

These ISIs really need some TLC.