Today at about 14:30 UTC the wider resonant filter for the computation of 50 Hz feed-forward has been engaged. In fig 1 we can see how the monitoring parameters of the FF have changed. The main improvement regards the stability of the phase adjustment: using the narrow filter, the request was larger, because the jitter of the 50 Hz line was causing a detuning of the filter with respect to the line, which was more visible as a dephasing. The improvement is visible also in the spectrum of the phase error signal (fig 2), and this is probably the reason why the line is better subtracted.

Looking at the normaized spectrogram of hrec (fig 3), it is clearly visible a blue line at 50 Hz starting at about 14:30. This is the proof that the little reduction of the 50 Hz in hrec, observed yesterday, is true and persistent. Other effects, like a subtraction of the small contribution of the bump around the line, is hardly visible in the spectrogram.

In the attached plot, two long periods of stable lock at 57 Mpc with no glitches have been taken in account. The first is one week ago, the second is 2 days ago, with the new 50 HzFF. Both are 2 hours long. There is an evident improvement, not only at the 50 Hz peak. Still I don't know if this is actually due to the FF.

Looking at hoft around 50 Hz, one can see two peaks, separated by 190 mHz from the center (fig 1). The same frequency can be found in the spectrum of the error signal used to adjust the gain of the feed forward (fig 2). This means that the residual 50 Hz is modulated in amplitude at 190 mHz. This frequency is the well known resonance of the long suspensions, which is relevant in the residual motion of each test mass. In fact, the FF gain is coherent at 190 MHz with each test mass longitudinal motion (measured at the levell of F7 - fig 3). Using CARM-DARM base for those motions, one can see that the d.o.f. actually modulating the 50 Hz is CARM (fig 4). There is also coherence with WI transversal motion, but only WI (fig 5).

About WI transversal, probably the coherence is due to the fact that the FF is applied by WI MIR actuators. It could be that the actuation gain is slightly modulated by the transversal motion, changing the efficiency of the subtraction.

About the relationship between CARM and the 50 Hz coupling mechanism, I have no idea, but in principle the lock of CARM should stabilize the situation.

Maria had a look at the coherence before and after the engament of the new 50 Hz FF (that occurred on March 13 at 14:30 UTC, as reported by Paolo). From the attached plots you see that the coherence with the UPS CEB channels reduced by about half in the wide region around 50Hz, also up to 54Hz (Figures 2 and 3) while the UPS spectral noise did not (Figure 1).

The daily BruCo plots confirm this: looking at the summary coherence projection, it is evident that the coherence in the 50Hz bump region reduced across March 13rd, and remained at this lower level since then: we attach here one Bruco summary plot just before, the one just after and the one of yesterday: Figures 4, 5 and 6

So we would conclude that also the reduction of noise in the wider region, well evident up to 54Hz, is related to the engagement of the improved FF (!)

Yesterday after the calibration session a modification to FF50HZ has been implemented: the correction signal is now produced using a flatter filtering (fig 1).

Comparing hoft with respect to previous data (fig 2), no particular improvement is visible. There are differences, which are difficult to attribute to FF change. The 190 mHz sidebands are larger, and this is confirmed by the spectrum of FF GAIN ERR (fig 3). This could be due to an unlucky choice of the gps: in fact, CARM was moving more at that time (fig 4).

According to the coherence between UPS and hoft (fig 5), the subtraction works better, but the statement has to be confirmed, because a lower coherence could be due to an increase of a different noise.

Further refinement will be tested soon, but at the end a dedicated data taking will be needed in order to understand better the performance.

Yesterday after the commissioning break a minor modification of the FF50HZ has been implemented, hoping to have a better behaviour about the 190 mHz modulation.

In the night, very good data have been collected, useful to make a comparison with the previous configuration. The two periods taken in account are 7000 s long.

Fig 1: the conversion from UPS to WI Z CORR now is quite flat. Maybe there is still some margin of improvement.

Fig 2: hoft was better about everywhere this night; it was worse just at the 190 mHz sidebands of the 50 Hz, at 48 Hz (maybe the WE crossbar resonance), and finally two new small lines were visibile at about 36.9 and 38.2 Hz

Fig 3: there was also a clear reduction of the coherence. Now, this fact cannot be explained by an additional noise covering the coherence, because the noise was smaller. So we can conclude that the flatter subtraction works better. It is also worth to remark that the noise reduction cannot be entirely associated to the improved feed-farward: the difference looks too large, and some disappeared bump was out of the region of coherence. The region around 50 Hz seems still affected by some noise which comes and goes, as diffused light use to do.

Fig 4: the feed-forward correction has some structures between 35 and 40 Hz, which in the new configuration could be too high. They are aliasing of the group of calibration lines at 60-65 Hz, and are generated by the loops adapting the gain and the phase of the FF.

Fig 5: the coherence between hoft and WI_CORR is almost the same as the one with UPS (fig 3), where WI_CORR and UPS are linearly connected. No additional  information is present in those region. But there is also some coherence specific of WI_CORR, at the lines which are generated in WI_CORR by a non linear process. This is the worning that the correction has to be reduced. Anyway, the two new lines in hoft mentioned above (36.9, 38.2) cannot be found in the group of WI_CORR. The largest in hoft, coherent with WI_CORR, is at 36.5 Hz, but it was present at about the same level even in the previous FF configuration, when WI_CORR was much smaller. This is true also for the next at 37.5 Hz. Finally, there is also coherence at 34.5 Hz, but the line is very small in WI_CORR, so I don't understand how FF could be the responsible of that line. I tried to do a projection of WI_CORR on hoft (fig 6): even from that, it is difficult to explain the largest lines in hoft. In order to evaluate the possibility on noise injection from FF50HZ, the only clear way I can see is turning FF50HZ off. It has been done for 5 min a few days ago: the result is shown in fig 7, and it is not so clear because the data taking was too short and too far in time.

Fig 8: CARM was higer this night; it is still not clear if the bad behaviour for the 190 mHz sidebands is due to the strategy or to CARM motion.

The lines at 34.5Hz, 36.5Hz and 37.5Hz are calibration lines.

Fig 1. They are subtracted in the calibration, but remain at a few percent of the injected value, which I guess is what is expected as the calibration errors are expected to be a few %.

Fig 2, squinting at the calibration noise budget these are the line from the NE and WE photon calibrator, and a line injected into the NE mirror coils.

The spurious lines in the FF correction, entering from DARM through the parameter adaptation loops, have been removed simply adding a pole to the control filters of those loops (fig 1).

With the last update of FF50HZ strategy, the transfer function from the witness signal to the correction signal is really flat (fig 1). This is the best I can do, and I will not try to improve more the filtering in the next future, unless we find from some measurement the correct target for that transfer function.

From the first data, there is no further reduction of coherence between UPS and hoft (fig 2). The data were not so clean as the previous ones: a certain bump is visible around 50 Hz, and there is also a new line at 51 Hz. It should not be due to the change of the FF, but let's wait for data as good as the better ones, before validating this new configuration.

I think an investigation about the coupling mechanism from UPS to hoft should be carried on, because a reduction of the coupling factor would be appreciable.