J. Kissel, A. Pele

After closer analysis, the 0.43 [Hz] and 1 [Hz] boost filters recently added to the QUAD L damping loops were on the hairy-edge of stability. However, such levels of damping are *needed* on (at least the) 0.43 [Hz] mode in order to lock the HIFO-Y arm cavity (though admittedly, this has not yet been quantified). 

I've sense re-assessed the "Level 2" L design from 2013-05-01, this time making sure include the same extra boosts and taking the opportunity to tweak the P and R design as well. Further, instead of Matt's BSC-ISI model, I've used Vincent's latest best performance achieved on 2013-05-14 to have a more realistic estimate of the 0.43 and 0.56 [Hz] mode amplitudes.

I have not yet installed these filters, I'll wait on a time when it is convenient for fellow commissioners.

Details:
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Here's a summary of the changes from the 2013-05-01 design:
(Bode plot comparing the two sets of filters on pg 1 of dampingfilters_comparison_2012-05-01vs2013-06-14_MSvs2013-06-14_RS.pdf )

L: 
- Added additional 0p43 [Hz] resonant gain boost as designed (will replace "LOCK" filter)
- (Notably *did not* include 1 [Hz] resonant gain boost -- the 1 [Hz] isn't bothering anyone, and the filter destroys the loop's phase margin)
- Tweaked ellip_L to better isolate and align the notch, and to recover some phase needed after installing the new boost
    - Knee frequency from 5 [Hz] to 4.9 [Hz]
    - Stop band isolation from 30 [dB] to 31 [dB]
    - Q of notch from 15 to 10
R:
- Tweaked ellip_R to better align the notch (because there's plenty of phase with which to play, and with the new L and P filters, R sensor noise started to substantially contribute to the 10 [Hz] L total noise)
    - Knee frequency from 6 [Hz] to 5 [Hz]

P:
- Added additional 0p56 [Hz] resonant gain boost as designed (will replace "LOCK" filter)
- Tweaked ellip_P to better align the notch (because there's plenty of phase with which to play, and with the new L and P filters, R sensor noise started to substantially contribute to the 10 [Hz] L total noise)
    - Knee frequency from 6 [Hz] to 5 [Hz]


I attach the full set of design plots in case this design becomes permanent, but I'll draw your attention to a few plots in particular. Note, for a fair comparison, I attach one set of design figures of merit with Matt's BSC-ISI model used as input motion (dampingfilters_QUAD_2013-06-14_Level2p1.pdf), and one using Vincent's best ETMY data (dampingfilters_QUAD_2013-06-14_Level2p1.pdf), and compare all three in dampingfilters_comparison_2012-05-01vs2013-06-14_MSvs2013-06-14_RS.pdf. "_MS" is "Matt Seismic model" and "_RS" is "Real Seismic data."

Pg 1 of dampingfilters_QUAD_2013-06-14_Level2p1_RealSeismic.pdf:
(1) This new set of filters still meets the 10 [Hz] performance requirements, if not even a little-bitty-bit better because of the tweaks to the P and R loops 

Pg 5 of dampingfilters_QUAD_2013-06-14_Level2p1_RealSeismic.pdf
(2) The 0.43 [Hz] mode in L is now totally squashed, according to the loop design plot.

Pg 6 of dampingfilters_comparison_2012-05-01vs2013-06-14_MSvs2013-06-14_RS.pdf
(3) The pitch spectrum at the 0.43 and 0.56 [Hz] spectra is predicted to be about a factor of ~2 less with the new boost, and a factor of 4 less with real seismic data, at about ~5e-8 [rad/rtHz]. I'd love to install these filters and compare against optical lever signals, to see how my model is doing these days...

For the seismic kids:
(4) Pg 1 and 47:49 of dampingfilters_QUAD_2013-06-14_Level2p1_RealSeismic.pdf
Assuming ETMY BSC-ISI's performance at 10 [Hz] is representative of all BSC-ISIs (which we know is *not* true), what Vincent has achieved thus far is roughly equivalent to the sensor noise performance at 10 [Hz], and only dominates between 8 and 10 [Hz]. Nice! 

Pg 4 and 7 of dampingfilters_comparison_2012-05-01vs2013-06-14_MSvs2013-06-14_RS.pdf
(5) If you're really paying attention, you'll notice that the V and Y seismic noise has *changed* between 2013-05-01 and 2013-06-14_MS, even though I'm using the same M. Evans model. Why? Because of MIT and their silly "X Y RZ Z RX RY" ordering of the cartesian degrees of freedom. Don't ask. The newer representation, 2013-06-14_MS, is correct. And besides, I don't care any more about a model, I've got representative data of an awesomely performing BSC-ISI.

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The new filter design was performed by the script:
${SusSVN}/sus/trunk/QUAD/Common/FilterDesign/design_damping_QUAD_20130614.m

The comparison was done with the script:
${SusSVN}/sus/trunk/QUAD/Common/FilterDesign/compare_quad_dampfilter_design.m

Matlab representations of the new filters live in:
${SusSVN}/sus/trunk/QUAD/Common/FilterDesign/dampingfilters_QUAD_2013-06-14.mat
and the two new models (one with Matt's Seismic Data and one with Vincent's seismic data) are:
${SusSVN}/sus/trunk/QUAD/Common/FilterDesign/
dampingfilters_QUAD_2013-06-14_Level2p1_model.mat
dampingfilters_QUAD_2013-06-14_Level2p1_RealSeismic_model.mat
respectively.

For the input ground motion, I used the "GS13s, ST2, Isolation + Sensor Correction both stages" data, i.e. columns 21, 26, and 31 of
${SeiSVN}/seismic/BSC-ISI/H1/ETMY/Data/Spectra/Isolated/
'H1_ISI_ETMY_Spectra_XYZ_Comparison_Sensor_Correction_20130514_152000.txt'
'H1_ISI_ETMY_Spectra_RX_RY_RZ_Comparison_Sensor_Correction_20130514_152000.txt'
and calibrated by dividing the raw data by
cal = 1e9*squeeze(freqresp(zpk(-2*pi*[0 0 0],-2*pi*[pair(1,45)],1),2*pi*bscData.freq));