The accuracy of the MAR Z actuation balancing can be better measured when the wind is strong (we are waiting for data in that condition), but it is interesting to observe tha data also in quiet condition. The adjustment performed yesterday on WI balancing is visible in the attached plot, but we can see that the improvement is no more visible below 50 mHz because the measurement is too noisy. The same measurement performed on PR is much cleaner, thanks to the cleanliness of the reference signal - tyCorr. The noise on that signal comes from the in-loop angular error signal, which is quite sensible for PR. For the arms, the error signal is a combination of different sensors, one very good (DIFFp), the others not very sensible at low frequency. For this reason, the on-line monitoring of the balancing can be very accurate only on PR. A low threshold used also for the the other DOFs leads the flag to be red too often.

The transfer function from MAR Z CORR to MAR TY CORR for SR is shown in fig 1, before and after the adjustment, in similar condition concerning the wind speed (between 20 and 30 km/h). The adjustment is effective between 10 and 40 mHz, but it goes in the opposite direction at higher frequency. Given that the aim of the action is to reduce the angular fluctuation of the payload, it is useful to look at the error signal, shown in fig 2. One can see an improvement below 40 mHz and a smaller worsening in a bump between 50 and 80 mHz. I would interpret it as a general improvement of the situation, but it remains to explain why the balancing is not effective in the same way at all the frequencies.

The other big difference visible in the error signal, above 0.1 Hz, is not an effect of the different actuation balancing; this is not even a real angular motion, because it is something happening at the level of the sensing. The optical lever that measures the 'horizontal' rotation has a natural coupling with the horizontal translation of the ground. This is normally minimized by the optical setup, putting the PSD perfectly in the focal plane of a lens. The bumps at 0.4 Hz visible in the data are the microseismic peak and are different because the sea activity is different in the two cases. The sensing coupling seems a bit too high, with respect to the performance we normally can obtain. It is not directly a real angular motion, but it produces a lower accuracy of the angular control, because the control reinjects partially the sensing noise as a real rotation (not totally, because the gain of the loop is lower tha 1 at that frequency).

The sensing coupling of the seismic noise on the angular sensor can be a possible explanation of the strange effect discussed above, concernig the effect of the balancing at low frequency. This coupling adds a component in the transfer function from MAR Z CORR to MAR TY CORR, which remains different from zero when the balancing is perfect and produces a bias in the determination of the good balancing. In this case, the balancing can be verified by a direct noise injection in MAR Z CORR, instead of taking data when the locking force is applied.

Coming back to the current performance of SR TY control, I would say that the residual imperfections on the sensing and eventually on the driving are small, with respect to a reasonable requirement. We are talking about a small fraction of urad, while we know that the ITF is tolerant to a few urad of SR misalignment.

The activity regarding the balancing of NI, WI and SR MAR Z actuation is concluded, because there is no margin to reduce more the coupling from Z CORR ot TY CORR by a simple adjusting of driving coefficients.

The impact of the re-balancing on the alignment stability has been evaluated, comparing recent data in moderaterly windy condition with older data in similar condition (fig 1). The spectrum of the alignment error signals correlated to the Z actuation mis-balancing is shown in the following figures. DIFFp_TY, the most important d.o.f. of the arm alignment, is shown in fig 2: there is a clear improvement below 0.1 Hz (the changes above 0.1 Hz are very likely independent on the actuation balancing). In order to understand whether the improvement is big or small in terms if ITF stability, the total rms is the quantity more appropriate to look at. In fig 3, a calibrated version of DIFFp_TY is shown, including the cumulative rms. The data refers to the first time slot, before the optimization of the balancing. We can see that the largest contribution to the alignment fluctuation comes from the frequency band above 0.1 Hz; the margin of rms reduction is about 10 %, in this environmental condition. Following this criterion, the expected improvement of the ITF alignment quality, induced by the actuation re-balancing, is small.

North arm and west arm TY SOFT d.o.f.s are shown in fig 4 and fig 5. Both are more accurate after the balancing; especially north arm. We can guess the total rms to be significantly improved as well, but this analysis is not straightforward, when the in-loop error signals are optical levers. Moreover, we use to consider the ITF quite tolerant respect to SOFT fluctuation and we never had the impression to be close to some limit, concerning the accuracy of those d.o.f.s. In conclusion, it is difficult to assign a grade to the obtained improvement.

Fig 6 shows DIFFp_TY, the last d.o.f. on which NI WI actuation balancing should have an impact. In this case no improvement is visible: the recent data are even worse. This is something to better investigate: a different noise source needs to be identified, which overcome the effect of the actuation mis-balancing.

Fig 7 shows SR_TY: the rebalancing has an effect, likely not relevant, as already discussed in a previous entry.

Finally, let's try to find the effect of the actuation balancing on the usual overall figures of merits: B1p power (fig 8 ) and sidebands power (fig 9). According the choosen data, there is no visible improvement.