J. Kissel, M. Evans

As mentioned in LHO aLOG 3312, the previous measurements of the open loop gain TFs of the L P and Y loops for H2 SUS ETMY with the loops open. This method of getting the open loop gain would be fine if these degrees of freedom were entirely independent. However, L and P are fundamentally cross-coupled (and sounds like there may be some non-fundamental cross-coupling between L and Y). Further, if we want to obtain not only the open loop gain ( -G ), but the suppression ( 1/(1+G) ) and closed loop gain ( -G/(1+G) ), the loops need to be closed. If you're interested in the math behind these truths, as well as derivations of each of these figures of merit from the available excitation and test points, check out T1200336.

And so it goes. 

The attached measurements show the open loop gain (for the diagonal degree of freedom; L to L, P to P, Y to Y) and the closed loop gain for both the diagonal and off-diagonal terms. The plots compare three different data sets:

- 2012-06-29, Loops Open, No Offset is the same data set as was taken two Fridays ago. The damping loops were all off (input disabled -- hence "Loops Open"), so the open loop gain, G = P * K = IN1/EXC was obtained by driving through the DAMP filters. "No Offset" indicates that the P and Y offsets used to align the cavity were removed, for fair of saturation during the excitation.
- 2012-07-07, Loops Closed, No Offset is new data from yesterday that was taken with no offsets again, but this time with damping loops closed. Because the loops are closed, the ratio of IN1/IN2 yields the open loop gain (again, see T1200336 if you don't believe me). The loops were configured as the were for the 2012-06-29 data, in configuration (1) listed in LHO aLOG 3306.
- 2012-07-07, Loops Closed, With Offset Because two things are different between nominal operation and black, the offsets and the loops being closed, we wanted to be sure that the offsets were not causing the difference between black and blue. So, I repeated the measurements with the (what were as of yesterday) nominal offsets ON (P: -2841, Y: 14290). Only L needed 1/2 the drive, the P and Y levels I had used for loops open worked just fine; there were no saturations during any data set.

Note that since IN1/EXC gives you the closed loop gain when loops are closed, the 4 page of each attachment only shows the closed loop gain for the latter two data sets.

The things that are evident from these results:
- There is an obvious difference between the Loops Open and Loops Closed, L and P, open loop gains.
- Because there is little to no difference between the No Offset and With Offset data, we can conclude that the OSEMs (sensors and actuators) are linear over a wide range of offsets (thank god).
- Since there were only two (obvious) differences (Offsets and Loops Open/Closed), and blue to red rules out the offsets, we conclude there is indeed significant cross coupling between L and P that's effecting the performance of the loops.
- We still see a much larger L to P than L to L closed loop gain, where the P to L is much less than P to P in the closed loop gain.
- The shape of the L to P closed loop gain is weird, but a plot of the P to L closed loop gain with loops closed against the open loop gain with loops open show that all the resonances are in the right place (see pg 4 of L plots, in gray)
- As was mentioned many times before, excess motion, is focused around 0.43 Hz. But one can see comparing gray to brown, that open vs. closed loop shows that the reduction is dramatic, and it shows that what is left is not particularly "peaky" in that frequency region.
- The P to L and Y to L closed loop gains are both significantly well below their respective diagonal terms, and in fact show little coherence so even what is shown may be an upper limit.
- There is little to no change in the Y to Y open loop gain between loops closed and loops open. This is what we would expect from an independent degree of freedom.

So. No new answers here, just relevant data that (perhaps) has ruled more things out, and is steering us to a different direction (which Matt seems to have already found some unexpected but good leads with the T loop, as well as a ~0.3% L to Y coupling, most likely do to [mismatched/imperfectly matched] actuators, see his aLOG below).

The next thing to do is calculate the pitch motion at the test mass, given measured ISI input, and using P sensor noise (and do the same thing for yaw), similar to what was done for L and V in G1200712.

------------------
Data can be found here:

/ligo/svncommon/SusSVN/sus/trunk/QUAD/H2/ETMY/SAGM0/Data/
2012-06-29_1425_H2SUSETMY_M0_Mono_L_WhiteNoise_OLGTF.xml
2012-06-29_1425_H2SUSETMY_M0_Mono_P_WhiteNoise_OLGTF.xml
2012-06-29_1425_H2SUSETMY_M0_Mono_Y_WhiteNoise_OLGTF.xml
2012-07-07_1811_H2SUSETMY_M0_Mono_L_WhiteNoise_OLGTF.xml
2012-07-07_1811_H2SUSETMY_M0_Mono_P_WhiteNoise_OLGTF.xml
2012-07-07_1811_H2SUSETMY_M0_Mono_Y_WhiteNoise_OLGTF.xml
2012-07-07_2012_H2SUSETMY_M0_Mono_L_WhiteNoise_OLGTF.xml
2012-07-07_2012_H2SUSETMY_M0_Mono_P_WhiteNoise_OLGTF.xml
2012-07-07_2012_H2SUSETMY_M0_Mono_Y_WhiteNoise_OLGTF.xml