J. Kissel

In preparation for the HIFO-Y and DRMI integration phases, I've redesigned the H1SUSBS (a BSFM) damping loops in a similar vein as those for the QUAD (see LLO aLOG 6949 and G1300537). I've tried my best to make the figures of merit identical to that of the QUAD, so if you understand those figures of merit, you'll understand these. Unlike the QUAD, however, one can in-almost-all-cases beat the aLIGO requirements with the same, only-slightly-more-complicated, level/style of filters. Vertical turns out to be the trickiest DOF, if you can believe it; it's the only one that I couldn't get below that DOF's requirements at all frequencies. However, as can be seen on pg 1 of dampingfilters_BSFM_2013-05-15.pdf, the vertical noise projected onto DARM is still a factor of ~10 below even the best aLIGO sensitivity (if all coupling factors are correct). Details below!

Note, I've captured a new safe.snap, copied, and committed both the snap and the newly modified filter file to the userapps repo:
${userapps}/sus/h1/burtfiles/h1susbs_safe.snap
and 
${userapps}/sus/h1/filterfiles/H1SUSBS.txt

Details:
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Since most of the figures of merit are either self-explanatory or the exact same as what's described in detail in the QUAD design (again, see (see LLO aLOG 6949 and G1300537)), I won't go through them in detail, but instead highlight the interesting points where the BSFM differed from the QUAD.

Design Philosophy / Comments:
(These notes are entirely focused on the dampingfilters_BSFM_2013-05-15.pdf attachment)
- Initially, the focus was on reducing the sensor noise for the L degree of freedom. However, because the BSFM is a very long Triple suspension, the L/P modes are relatively low in frequency. This meant that there's plenty of room between the last L/P mode and the goal frequency of 10 [Hz]. 
- Because the BSFM's blades are not diagonally oriented like they are in the QUAD, there is no fundamental cross-coupling between (T/R) motion and (L/P) motion. (L/P), (R/T), V, and Y are entirely independent of each other.
- These two features of the plant (the highest resonances are at lower frequency, and DOFs are much better decoupled) makes rolling of the sensor noise by 10 Hz relatively easy for these degrees of freedom. 
- Even in the fundamentally cross-coupled degrees of freedom, (L/P) and (R/T), the MIMO interaction between them makes it easy to isolate certain modes, and damp them in DOFs where the noise requirement is less stringent. For example, the highest (R/T) modes at 2.1 and 3.2 [Hz], which are the only substantial modes that show up in the R2R plant, can be almost entirely taken care of in R where there is no requirement. This offloads damping authority from the what-would-be-difficult T design. (That being said, the T requirements are so loose, that even the Level 1 controllers beat the requirement by several orders of magnitude).
- The point at which I stopped tuning the L, P, and Y loops was when the sensor noise was reduced to a factor of a few below the M2 actuator noise (as shown on pgs 2/10, 34, and 40). They probably could be made more aggressive, but until the M2 actuator noise is reduced, there's no point. (Remember, there are no actuators on the M3 / optic stage of the BSFM).
- An interesting diversion from the QUAD design for these DOFs was that for R and Y (see pgs 23 and 35), I've moved the boost to reasonably high frequencies, "skipping" the first few modes. They're Qs are reduced enough by the "velocity damping" portion of the controller, and in the case of R, by the T loop as well. Because the boost was so close to the elliptic filter, the phase is evolving a little faster than ideal, but I think I've still managed to squeak out a good looking loop that is fairly insensitive to small changes in gain. 


- Vertical, it turns out was the most difficult to design (see pgs 17-22 of dampingfilters_BSFM_2013-05-15.pdf). The last V mode visible from the top/M1 stage is at 3.8 [Hz], very close to the 10 [Hz] requirements. As such, there's very little phase left for the elliptic filter. 
- On top of this, the last vertical mode at 17.5 [Hz] is invisible at the top stage. This meant that, regardless of whether I could see it in the M1 V2V plant, I needed to get rid of the sensor noise in that region between the two modes, since it shows up in the M1 to M3 V2V transfer function.
- As such, I used a 4th order elliptic instead of the 3rd order I'd used for all of the QUAD DOFs and other BSFM DOFs. In doing so, I tried to get the second notch of the filter as close to 17.5 [Hz] as possible, while still having enough gain to evenly damp the 1st and 2nd V modes, and have enough phase to be stable. 
- In summary, what you see here in this Level 2 V filter is a comprimise between 4 things:
    - The resulting Q of the 1st and 2nd V modes, both in the M1-to-M1 TF (pg 17) and in the GND-to-M3 TF (pg 22)
    - The phase and gain margins (i.e. the stability of the loop)
    - The sensor noise level between 10 Hz and the 3rd V resonance at 17.5 [Hz] as shown on (pg 22) with respect to the specifically-defined, beam splitter vertical requirements (from T010007-v5)
    - The assumed 0.001 V2L cross coupling into DARM as shown on (pg 1) with respect to the BS L requirements (again in T010007) and the current predictions of interferometer sensitivity
- While this compromise does not meet the requirements for the T010007-defined, BSFM vertical, the noise is still a factor of 10-20 away from even the best expected DARM curve, assuming the 
BS2DARM = pi / (sqrt(2) * F)
factor from T080192 is correct (Note, I've used F = 450 for the arm cavity finesse, found in T010075, and T070303).

The configuration:
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For all degrees of freedom,
FMs 1 ("rolloff_*"),2 ("boost_*"),5 ("norm*"), and 10 (ellip_*)
should be engaged. After discussing it with Arnuad, we've decided to fold the overall gains of the loop into the boost_* filter, so that all the EPICs gains are an easy-to-remember -1. Note that this deviates from traditional SUS gains, but it's time for a new era of not-just-velocity-damping-anymore. <gullable, annoying pre-teen voice> Seismic is doing it </gullable, annoying pre-teen voice>. Hence, the new EPICs gains are:
L = T = V = R = P = Y = -1.
In the fullness of time, we intended to go back to QUAD filters and do the same.

As mentioned above, I've already captured a new safe.snap.

The files:
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The 2013-05-15 loops were designed using 
${SusSVN}/sus/trunk/BSFM/Common/FilterDesign/design_damping_BSFM_20130515.m
which saves the .mat file of the filters,
${SusSVN}/sus/trunk/BSFM/Common/FilterDesign/dampingfilters_BSFM_2013-05-15.mat
and produces the dampingfilters_BSFM_2013-05-15 set of plots,  as well as saving the model itself in an additional .mat file,
${SusSVN}/sus/trunk/BSFM/Common/FilterDesign/dampingfilters_BSFM_2013-05-15_model.mat

These were compared with the previous filters, (whose figures of merits were plotted with the similar
${SusSVN}/sus/trunk/BSFM/Common/FilterDesign/design_damping_BSFM_20130130.m
and saved to ${SusSVN}/sus/trunk/BSFM/Common/FilterDesign/dampingfilters_BSFM_20130130.mat)
using the script,
${SusSVN}/sus/trunk/BSFM/Common/FilterDesign/compare_bsfm_dampfilter_design.m

The performance measurement was taken using the DTT template
${SusSVN}/sus/trunk/BSFM/H1/BS/SAGM1/Data/2013-05-15_H1SUSBS_M1_DAMPOUT_Spectra.xml

Note, because of the experience taking the open loop gain transfer functions of the QUAD (low SNR, confusing results at low frequency, but otherwise confirming the MIMO nature of the plant, and the ability for my models to predict it), I did *not* take open loop gain transfer functions.

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As of this edit, all of the above mentioned files are committed to their respective repository, whether it be the userapps, or SUS repos.


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Edit: Replaced the dampingfilters_BSFM_2013*.pdf plot sets because there was a bug in the Title and Legend of the DARM coupling plots -- I'd writting BS2DARM as 2*F instead of sqrt(2)*F. Note, the code that processed the data did/does not have this bug, it was just the plot labels.