KAGRA Logbook

VIS (SR3)

lucia.trozzo - 23:12 Tuesday 25 September 2018 (6282)

SR3 IP: Coil actuator diagonalization

[L.Trozzo, E.Capocasa]

Last week we measured and implemented the sensing and driving matrix for the LVDTs and the actuators of SR3 Inverted pendulum (IP). The details about the geometrical sensing matrix for SR3 are reported in the klog#6235 . We give here some details about the readout driving matrix. How described in the klog #6118, for the driving matrix we injected a line at frequency f0 in the region above the inner resonances of the system. In order to compute the Driving matrix, we followed the procedure adopted for the long suspension (ITMX) by fixing the frequency f0 at 3 Hz:

Driving matrix (f0=3Hz):

L	T	Yaw
-5.3880	-1.7256	-1.2253	H1
-0.0343	5.6013	-0.9601	H2
5.7424	-4.9108	-2.6619	H3

After that we measured the trasfer functions of each diagonalized degree of freedom and we estimated the coupling between each other. Unlike ITMX, for SR3 the coupling measured by using the 3 Hz driving matrix were not low enough, so in order to check if the coupling could be reduced we injected other two lines at 2 Hz and 1 Hz and we computed the related driving matrices

Driving matrix (f0=2Hz):

L	T	Yaw
-2.0954	-1.0938	-0.5038	H1
1.6739	-1.7693	-0.4228	H2
0.2489	3.3462	-1.2048	H3

Driving matrix (f0=1Hz):

L	T	Yaw
-0.4808	-0.2555	-0.1133	H1
0.3882	-0.4185	-0.0946	H2
0.0542	0.7818	-0.2789	H3

Also in these cases we measured the trasfer functions and we estimated the couplings as a function of the frequency. As shown the attached plots (Fig1,Fig2,Fig3,Fig4,Fig5,Fig6) the driving matrix measured injecting the 2 Hz line reduces the couplings while the matrix computed injecting the 1 Hz line make them worse. For this reason we have chosen to implement the 2 Hz driving matrix. Attached to this report there are the transfer functions measured by injecting white noise from diagonalized virtual actuators and looking at diagonalized virtual LVDTs [Fig7,Fig8,Fig9]. We can observe that proper mode IP along the longitudinal direction (L=Y) is at about 0.1 Hz whil along the transvcersal direction (T=X) is at about 0.109 Hz. In Fig9 we can see that the proper mode of Yaw is at about 0.302 Hz.

Images attached to this report

Comments to this report:

yoshinori.fujii - 7:31 Wednesday 26 September 2018 (6286)

Can I ask two questions?:
> Unlike ITMX, for SR3 the coupling measured by using the 3 Hz driving matrix were not low enough
How was it like? Can you compare the values with ITMX's?
Why did we have such large coupling between T and Y? Was it becuase the sensing matrix was not much correct?

lucia.trozzo - 17:42 Wednesday 26 September 2018 (6293)

Hi Fujii, I attach the plots where the residual coupling off ITMX and SR3 are compared: as you can see there are some residual couplings also for ITMX, but they are lower.

Probably this can be due to the fact that at 3 Hz the sensors of SR3 is more noisy. For this reason we have chosen to move to 2 Hz where the noise level of lvdt seems lower.

By the way, I think that the bad behaviour of the driving at 1 Hz is due to the presence of some internal resonce of the system. ( for example if you look at the TF transverse you can see that at about 1 Hz there is a very tight pair of poles and zeros that may have been excited during the noise injection)

I don’t think that the residual coupling is due to a wrong sensing because even for SR3 the sensing matrix has been corrected ( according to the CAD model and visual inspection).

The remaining explanation is that that there is a frequency dependent mechanical coupling that cannot be reduced at all the frequency. Since we have to find a compromise it is probably better to reduce the coupling in the region where unitary gain of the loop for inertial damping is desired (above 2 Hz).

For example with our choice, Y2L, Y2T and T2Y residual coupling (especially in the region between [0.1 0.5] Hz) are not so dramatic, but of course we have to keep them in mind when drawing control loops.

Images attached to this comment