J. Kissel

Continuing to compare L1 vs. H1 damping loop designs (see ), I've made a comparison of the QUAD's design, and also with the original low-noise design from which they're derived (see LHO aLOG 6760). Attached are the H1 and L1 designs compared against each other, 
dampingfilters_comparison_2014-11-07_LHOvs2014-11-10_LLO.pdf, as well as both against the original low-noise design dampingfilters_comparison_2014-11-07_LHOvs2013-06-14vs2014-11-10_LLO.pdf. 
As Sheila's quick comparison pointed out (see LHO aLOG 14923), the differences aren't that large (and detailed below).

In summary, both LHO and LLO have modified the low-noise design, but only slightly -- both apparently in order to get a reduction in test-mass impulse response. LLO took the "more sophisticated" in longitudinal by adding a boost instead of just increasing the overall gain, hence their modification preserves some phase margin. 

Because we're giving the LLO ALS DIFF control loops a try, however, we have copied over and installed the LLO design -- assuming that any little bit of difference will matter for these complicated global control transfer functions. Stay tuned...

- T, V, R loops are identical to the original design
The differences are the following modicifations:
- In L
     - LLO "resg1" boost ( resgain(f=1.07 [Hz], Q=4, height=13 [dB]) * gain(6, "dB") )
     - LHO overall gain increased by 2 (from -1 to -2).
- In P
     - LLO "notch60" 60 [Hz] notch ( notch(f=60 [Hz], Q=50, depth=40 [dB]) )
     - LHO overall gain increased by 3 (from -1 to -3).
- In Y
     - LLO "+12db" gain of 3.9811 ( gain(12, "dB") )

Comments:
In L, 
 - The extra "resg1" at LLO, significantly reduces the Q of the *second* (~1 [Hz]) L mode, and therefore significantly modifies the L to L and L to P global control transfer functions -- not only the resonant feature at 1 [Hz], but also the zero at 0.75 [Hz]. Other features are moved around a little, but no such significant change in shape. 
 - As such, the displacement from residual ground motion at 1 [Hz] has been reduced by a factor of 3, though (at least from the modeled input seismic motion) it doesn't contribute much to the over all RMS.  
 - The impulse responses of the two designs are comparable.

In V, and R,
 - As expected from the HSTS design studies, the impulse response of these DOFs reveals that without other local damping (say from optical levers), the highest V and R modes (at 9.7 and 13.8 [Hz]) get excited when the PUM and TST are kicked, and continue undamped at their original extremely large Q. 
 - If needed, both the fundamental V (at 0.55 [Hz]) and R (at 0.86 [Hz]) could use an increase in their resonant gains to decrease the 1/e time for those modes, which seem to dominate the amplitude of the time series for the initial 10-20 seconds. V would be much easier than R, as the LUGF phase margin for R is already pretty small.

In P, 
 - As with the HSTS, the global control transfer functions are barely affected by the differences in design, though -- to be fair -- the differences in design are much less dramatic than in the HSTS. 
 - Test mass impulse times are comparable.
 - The first "pitch" mode at 0.51 [Hz] is more damped (by about a factor of ~2) in the LHO model because of the increase in overall gain. However, since the second mode at ~1 [Hz], is more L motion at the test mass than P, increasing the gain at this frequency by a factor of 5 with the "resg1" in the L design seems to have reduced this "P" mode by the same factor at the test mass. Interesting!
 - The notch at 60 [Hz] has little affect on the loop design -- I suspect this was installed to kill a ground-loop feature in a particularly bad OSEM.

In Y,
 - This is pretty straight forward -- the yaw loop is not particularly limited in phase margin, only in noise re-injection. If we're willing to sacrifice a factor of 4 in noise, cranking up the gain reduces the impulse response by 4, and the Qs of the global transfer functions.