J. Kissel, A. Pele

On the Thursday of the week before last (2013-06-20), Arnaud took some measurements of the H1 SUS ETMY's damping loop, open and closed loop gain transfer functions (i.e. DAMP IN1 / DAMP IN2 = G and DAMP IN1 / DAMP EXC = G / (1+G)). The goal of these measurements was to confirm that I'm modeling the loops correctly -- because, according to the model alone, we should (a) be getting *plenty* of 0.43 [Hz] L/P damping, and (b) increasing the gain by factors of ~3 should cause the loops to go unstable. I mention factors of ~3 with regards to stability because fellow commissioners have successfully run in that configuration to get what cavity motion they need for locking the cavity (I think -- I've only heard via word-of-mouth, I haven't seen any aLOG detailing so), yet my modeling suggests that the L loop would be unstable with this gain increase, with a phase margin of less than ~15 deg.

During the measurement, the loops were in the configuration that Arnaud had put together in early May (i.e. my Level 2.0, 2013-05-01 design but with the extra 0.43, 1.0 [Hz] boosts in L, and the 0.56 [Hz] boost in P). This is the configuration that we continue to run currently (with an overall gain of 1 or ~3). 

I've since compared the 2013-06-20 data against what I had modeled, and the results are attached.

The conclusions are quite interesting.

Let's focus on pg 1, the L Open Loop Gain transfer function comparison. There are four curves on the bode plot:
(1) BLUE The open loop model of the filter scheme. This is the 2013-05-01 filter design, with the extra boosts at 0.43 and 1 [Hz] for L as modeled on 2013-06-14.
(2) GREEN The down sampling filter used to down sample from 16k to 256 [Hz] before the channel is stored in the frames. (The low pass corner in magnitude is up at ~120 [Hz], so it's not visible in the current x limits.)
(3) RED The measurements Arnuad took *without* correcting for this down-sampling filter (though multiplied by -1, because IN1 / IN2 = - G if one defines G = + P * K, i.e. the feedback minus sign is left explicit in the loop math and *not* absorbed in G, as per the convention I've used in my model).
(4) CYAN The measurements Arnaud took, divided by the known down-sampling filter.

These same curves are shown for the Pitch loop on pg 2; Pg 3 is the ratio of model / measurement for both L and P; and pgs 4 and 5 are the closed loop gain transfer functions (which don't reveal any more information than the the open loop gain transfer functions, but I show them because Arnaud took the time to measure them).

Things to notice:
(1) Up to 10 [Hz] the magnitude scale, based solely on known calibration coefficients (no fits or scaling!), is really quite close. (Pg 3 reveals that the model over-estimates the measurement by ~25%.)
(2) From 1 - 10 [Hz], the magnitude and phase in general, are dead-on. This means that the loops are in fact as border-line stable as we had modeled.
(3) The down-sampling filter explains the huge phase loss we see in the measurement. In fact, I had seen this phase loss many times before (see, e.g. pg 5 of G1201258, or pg 8 of G1300621), but only this past week surmised out what it was, found the filter deep in the guts of the RCG code, and plotted it.
(4) The discrepancy at ~30 [Hz] is the OSEM cross-coupling that's the cross-talk between the drive and response. So, it's an artifact of the measurement, and not real. (HOW CAN WE FIX THIS?)
(5) Notice that the 0.56 Hz mode doesn't line up with the model. We should measure more suspensions to see if this is true (I think it is), and then tweak the model so it better matches. Regardless, it seems there's still enough loop gain in P (i.e. the boost filter has a low enough Q), that the mode still gets damped.
(6) Most importantly -- the lowest L mode, at 0.43 Hz, for some reason, has an "inverted" resonance. Unfortunately, it's only one data point, but the coherence for that point is ~0.85, and the phase looks pretty darn smooth, so I'm pretty sure it's real.
	- Is this mode-splitting from over-damping?
	- Is it rubbing?
	- Do we see this feature in the undamped Phase 3b testing?
        - Do we see this effect in other fiber QUADs?
This (we'll, for now call it) mode-splitting results in little-to-no loop gain on that resonance, which is most likely why we're not getting nearly as much damping as the model predicts we should on this mode. In fact, looking at the manifestation of the mode in the P to P TF, there's hardly any at all -- hence the cavity's spot moving so much.

Confusingly, undamped, Phase 3b transfer functions and spectra of this SUS reveal no such feature of the 0.43 [Hz] mode, so unless something has happen to the SUS since then, we can pretty much rule out rubbing. Unfortunately, the H1 ITMY is a wire-rehang suspension, whose modes are at different frequencies (at least as different as the fiber model is to the H1 SUS ETMY's measurement), so the filters interacts with the modes differently, so we can't make a direct peaches-to-peaches comparison.

So, we've still got some work to do on the loop design. 

Action Items:
- Measure the OLG TF of H1 ETMY with high resolution around the 0.43 [Hz] mode, such that we can really resolve what's going on.
- Gather up all the current Phase 3b fiber QUAD measurements we have (i.e. H1 ETMY, L1 ITMY, L1 ITMX), see if these 0.43 and 0.56 [Hz] L/P modes are consistently lower than the model in frequency, and if so, tweak the model to better match the data.
- Get similar measurements from the L1 ITMs, to see if the same sort of mode splitting is happening.
- Get measurements of H1 ITMY, and model the loop using the wire-rehang parameter set. See if these boosts are doing any good there.
- Install Level 2.1 filters -- which are *modeled* to be much more stable, but yielding the same reduction in Q of the low-frequency modes, and remeasure the loop. 


Measurement and Analysis Details
---------
The templates for the measurements can be found here:
${SusSVN}/sus/trunk/QUAD/H1/ETMY/SAGM0/Data/
2013-06-20_0800_H1SUSETMY_M0_openloop_P_WhiteNoise.xml
2013-06-20_0900_H1SUSETMY_M0_openloop_L_WhiteNoise.xml
Note that the measurement was taken with all loops closed, such that it accurately represents the MIMO Open and Closed loop gain transfer functions. Hence, the excitation was driven through the damping loop filter bank's excitation point.

Which have been exported to the text files:
${SusSVN}/sus/trunk/QUAD/H1/ETMY/SAGM0/Data/
2013-06-20_0800_H1SUSETMY_M0_P_WhiteNoise_IN1EXC_tf.txt  # Closed Loop Gain TF
2013-06-20_0800_H1SUSETMY_M0_P_WhiteNoise_IN1IN2_tf.txt  # Open Loop Gain TF
2013-06-20_0900_H1SUSETMY_M0_L_WhiteNoise_IN1EXC_tf.txt  # Closed Loop Gain TF
2013-06-20_0900_H1SUSETMY_M0_L_WhiteNoise_IN1IN2_tf.txt  # Open Loop Gain TF
where each file's columns are 
[freq Re{L} Im{L} Re{T} Im{T} Re{V} Im{V} Re{R} Im{R} Re{P} Im{P} Re{Y} Im{Y}]
of either the IN1 / EXC (closed loop gain, G / (1+G)) or the IN1 / IN2 (open loop gain, G) transfer functions.

The model of the design is produced by
${SusSVN}/sus/trunk/QUAD/Common/FilterDesign/
design_damping_QUAD_20130501_withArnaudBoost.m

I then compared the boosted 2013-05-01 design against those measurements with the script
${SusSVN}/sus/trunk/QUAD/Common/FilterDesign/
compare_olgtf_model_vs_meas_20130501_withArnaudBoost.m

That produces the attached plots, which can also be found in
${SusSVN}/sus/trunk/QUAD/H1/ETMY/SAGM0/Results/
2013-06-20_H1SUSETMY_dampingloopcharacterization_20130501_Filters_withArnaudBoost.pdf