Originally, I wanted to track SIB1 just like SNEB, SWEB, SPRB and SDB2 are tracking the superattenuators, but unfortunately SIB1
operates at a setpoint in x of 991 micrometer, and I cannot blend that easily with the LVDTs of EIB.
EIB measures he ground displacement via geophones on the floor below the EIB bench. The phase between the geophone signal and the IB filter0 LVDTs
had a slope and the filtered ground signal for EIB was a bit too small. Therefore, I applied a filter that corrected the phase shift, and another high-pass filter,
to get a better match between the ground noise and the LVDT readings in SIB1.
Figure 1 gives the transfer function between ground-z and Sa_F0_X and also between ground_x and SA_F0_Z.
The reference plot is with the old filter, the blue line with the new filter, which is the old filter times (s(s+1))/(s^2+0.7s+0.08).
Clearly, the phase and the gain are much better. For ground_x, the gain of the subtraction has a slope and we under-subtract ground noise at 1 Hz, but
ground_z is the relevant correction, since that is the distance between EIB and the input mode cleaner (the south direction).
There is some further room for improvement but that requires a new time to try out the filter.
Furthermore, the geophones on the bench seemed completely mis-calibrated. I tried to get a better calibration by injecting Ty noise and changing the filters
a bit. The problem with the geophones on the bench is that at low frequency, the signal is coming from the tilt Tx,Tz of the bench, not from the acceleration.
Therefore it was difficult to do a good calibration. We should do the transfer function between the geophones on the bench and the ground with the bench
blocked, but that requires another 2 shifts (one to measure and implement it with blocked bench and another with floating bench and noise injection, to
see if everything is still OK in the presence of Tx and Tz tilts) so for the moment I think we should leave that.
I did a rough job getting a better calibration with the injected Ty but it is in no way perfect; the bench positions below 1Hz come from the LVDTs and the ground noise and they can be trusted. Above 1Hz, the spring box is used in the controls and the bench geophones are tilt-corrected and used as monitor signal in EIB_x,EIB_ty, EIB_z. Above 1 Hz, these signals are not accurate (but should be better than with the previous geophone filters) but they are not used in
the PID control, so I think that that is OK.
I compared the EIB SAS movement in z (south) direction with the Sa_IB_F0_x (north) direction on April 2, 13:00 UTC with Jan 18, 13:30 UTC;
both days had high wind speed in PISA and extra microseismic activity. In the plots, EIB_ground_z is derived from the geophone on the
ground below the EIB bench. It is this geophone on which a different filter is applied, to match better Sa_IB_F0_x, which id the LVDT
signal from the injection bench superattenuator. So assuming that between 0.1 and 2 Hz the F0_x should be opposite to ground_z, you expect
a transfer function of 1. Before March 27, when the new calibration was applied, we had a large phase difference in the filtered geophone response
and the superattenuator around 0.3 Hz, where the maximum of the microseismic noise appears. After March 27 this phase difference is smaller, albeit
below 100 mHz I now have less reduction of the geophone DC drift (cutting off the part below 100 mHz gave too large phase shifts and too large
reduction in the range 100mHz- 1 Hz).
EIB_LVDT_z is the LVDT reading of the EIB; it should be minus SA_F0_x (since the EIB z-axis points towards the -x direction in IB). Thus optimally,
the transfer function EIB_LVDT_z/Sa_IB_x should be 1 with a phase of -pi. Same for EIB_ground_z/Sa_IB_F0_x. The EIB_LVDT_zb channel is the sum
of EIB_LVDT_z and EIB_ground_z; this is the channel that we try to control to 0 in the closing of the loop. Thus this channel gives an indication of the
residual motion.
As can be seen in plots of Jan 18 and April 2, the LVDTs for EIB_z and Sa_IB_x broadly overlap, but the EIB has extra motion that peaks around 0.8 Hz.
This is about a factor of 5 above the natural resonance of the IP legs of EIB and close to the Ty resonance; this extra motion is due to un-optimal
control in the PID loops, maybe also due to blending the geophones on the springbox with the LVDT. At 0.8 Hz, the EIB motion of the bench is
basically equal to the motion of the ground (EIB_LVDT_z ~ 2*Sa_IB_F0_x and EIB_LVDT_zb, EIB_ground_z ~ 1* SA_IB_F0_x).
You can also see that the ground noise before march 28 was underestimated by about 20% around 0.5 Hz and that the phase difference reaches 90 deg. around 0.2 Hz.
After modifying the filter for EIB_ground_z (which is in the control loop, so it also modifies the bench response in closed loop), on April 2, we see that the
ground motion compared much better with the IB motion; the amplitude of the transfer function is about 1.05 and the phase is much flatter; also the transfer function between EIB_LVDT_z and Sa_IB_F0_z improved. Now the maximal deviation around 0.8 Hz reached about 1.5; giving twice better subtraction of
ground noise. You can also see that EIB_LVDT_zbench is smaller; this is our best measurement of the residual motion of the EIB bench.
In the third figure, I plotted the results for the first 2 figures on top of each other (the reference plot is the April 2 data and the blue line the Jan 18 data)
to compare the change in transfer functions. You can see that the 30 minutes of data of Jan 18 contained a bit more seismic noise than on April 2.
Nevertheless, also the April-2 data contains so much excess microseismic noise that the quality of subtraction can be judged; at april 2 we do better than
at Jan 18. Further improvements could be made, if required, by changing the PID loops, but the EIB is a highly coupled system with tilt stabilization; z and Tx,
x and Tz, and indirectly Tx,Tz and Ty are strongly coupled. It is a priori not clear that we can improve much in the loops and it requires careful study of the
blending of the geophones on the spring box, the loop gains for the vertical and horizontal d.o.f.s etc.
