J. Kissel

Since the original study on coherence with pump servos focused on the corner station (see LHO aLOG 16239), I attach some plots (first and second attachment) showing how bad the coherence is between each stations pump servo and the chamber motion. Further, the original study used the HEPI L4Cs -- but these were proven to be sensor noise limited at the boundaries of the coherence. Using the ISI T240s, one can resolve the coherence better, and see that it's worse over a more broad frequency band. Turns out T240s are better sensors than L4Cs. Shocking, I know. Note that I only have shown the Z, RX, RY, and RZ DOFs because (a) X & Y don't show coherence anywhere in either the L4Cs or T240s, and (b) I didn't look at the HP / VPs because there's no combination of the T240s that could reconstruct these DOFs.

Great, but this is sort of old news now. We know the parameters we have installed are bad given all the other flaws in the system (see LHO aLOG 16619). 

So let's design new PID loops with parameters that are better, given the constraints of this sub-par ADC/DAC system, and given our knowledge of the plant (see LHO aLOG 16601).

Assuming we reduce the sampling frequency of the EPICs record that processes the analog input, PID, and output to 1 [Hz] (instead of the claimed 10 [Hz], which was actually some slower frequency due to extra slow processing time), we now know that the integrator coefficient's value will depend on that sampling frequency so we must design accordingly. We also know that SMOO parameter low-pass filters are bad (at least ones that are so close the UGF). We also know that the ADC noise is terrible, and we haven't really resolved when the pressure sensor signal gets above the ADC noise, even though we've measured all the way down to 3 [mHz] (see LHO aLOG 16500). In any event we know that reducing the UGF of the loop does good things -- or at least reduces the bad (see LHO aLOG 16466). As such, I've modeled the right parameters to get a UGF of 10 [mHz]:
         P     I [cycles/min]
Corner   5     0.13   
EX       5     0.04
EY       5     0.04
For plots supporting the model, see the last attachment. 

Why 10 [mHz] you ask? I'm glad you're curious.
- As mentioned above and elsewhere, the sensor signals don't get above the ADC noise floor -- at least down to 3 [mHz] -- but they look like they're on the way up and may surpass the noise by 1 [mHz]. Why not a 1 [mHz] UGF then? Well, one could claim the SR785 measurement of the raw pressure sensor voltage may not have been valid at its lowest frequency points. It'd be a stretch, especially for the return pressure sensor signal, but I'll humor you.
- Do we really have the patience to commission / characterize a 1 [mHz] loop? Not really.
- Do we have to have patience anyway, because the pump servos are causing noise down at these frequencies whether we like it or not? This got me launched on using the T240s. They show the coherence rolls off at a lower frequencies than the L4Cs report BUT the coherence drops BEFORE the T240s hit their noise floor. This drop off happens by 10 [mHz].
- We want to get *some* suppression on these things on the 100 [s] time scale, because when free running, we do see the pressure drift around on the several minute time-scale. Not a lot, but it does. An unagressive UGF of 10 [mHz] gets us a suppression of 10 at 1 [mHz], and continues to increase proportional to 1/f. Should be plenty. 10 [mHz] also plenty far enough away from the sampling frequency that there's no funny phase business going on anymore.

Another side thought -- maybe we should just go back to using the supply pressure alone? It definitely has better SNR than the return pressure signal at these frequencies. We can use the one by the chamber as a compromise.

Hugh and I will post some data tomorrow showing that 
(a) a 1 [s] requested sampling rate reliably produces a 1 [Hz] sampling frequency.
(b) When we request to sample at 0.1 [s], the sampling frequency depends on the number of sensors read in, but the ADC noise floor does not change.
(c) We've permanently set the sampling time to 1 [s], installed the above new PID parameters, and there is no longer any coherence with the chamber's T240s (and hopefully the IFO).

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Data is taken from the template:
/ligo/svncommon/SeiSVN/seismic/HEPI/H1/Common/2015-02-16_H1HPI_EndStation_Coh_wISIT240s.xml

Filters were design with the script:
/ligo/svncommon/SeiSVN/seismic/HEPI/H1/Common/H1HPI_PumpServo_FilterDesign_Ts1Hz_UGF10mHz_20150217.m