40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
 40m Log Not logged in Message ID: 3912     Entry time: Sat Nov 13 15:53:05 2010     Reply to this: 4718
 Author: yuta Type: Update Category: CDS Subject: diagonalization of MC input matrix

Motivation:
MC is aligned from the A2L measurement, but to do the beam centering more precisely, we need coils to be balanced.
There are several ways to balance the coils, like using oplev or WFS QPD RF channels.
But oplev takes time to setup, especially for MC3. Also, c1ioo WFS channels were newly setup and haven't been checked yet.
So, I decided to use OSEM sensors.
An OSEM sensor itself is sensitive to every DOF of an optic motion, but we can diagonalize them using 4 OSEM sensors and proper input matrix.

Method:

1. Measure transfer functions between
ULSEN and URSEN (H_UR(f))
ULSEN and LRSEN (H_LR(f))
ULSEN and LLSEN (H_LL(f))

2. Make a matrix A.

A =  [[ 1           1           1          ]
[ H_UR(f_pos) H_UR(f_pit) H_UR(f_yaw)]
[ H_LR(f_pos) H_LR(f_pit) H_LR(f_yaw)]
[ H_LL(f_pos) H_LL(f_pit) H_LL(f_yaw)]]

where f_dof are resonant frequencies.

3. A is

where vectors s^T=[ULSEN URSEN LRSEN LLSEN] and d^T=[POS PIT YAW].
So,

d = Bs = (A^TA)^(-1)A^Ts

where A^T is transpose of A.

B is the input matrix that diagonalizes 3 DOFs.

What I did:

1. Measured the TFs using diaggui and exported as ASCII.

2. Made a script that reads that TF file, calculates and sets a new input matrix B.
/cvs/cds/caltech/users/yuta/scripts/inputmatrixoptimizer.py
You need to set resonant frequencies to use the script.

New input matrices for MCs are;
``` C1:SUS-MC1_INMATRIX [[ 1.17649712  0.94315611  0.85065054  1.02969624]  [ 0.55939288  1.28066594 -0.85235358 -1.3075876 ]  [ 1.23467139 -0.74521928 -1.29394051  0.72616882]] C1:SUS-MC2_INMATRIX [[ 1.12630748  1.01451545  0.9013457   0.95783137]  [ 1.03043025  0.67826036 -1.37270598 -0.91860341]  [ 0.83546271 -1.26311029 -0.6456881   1.2557389 ]] C1:SUS-MC3_INMATRIX [[ 1.18212117  1.26419447  0.77744155  0.77624281]  [ 0.79344415  0.84959646 -1.10946339 -1.247496  ]  [ 1.00225331 -0.84807863 -1.21772132  0.93194674]]```

I ignored SIDE this time.

Result:

Spectra of each SUSDOF_IN1_DAQ before diagonalization (INMATRIX elements all 1 or -1) were After diagonalization, spectra are As you can see, each SUSDOF has only single peak (and SIDE peak) after the diagonalization. SUSSIDE still has 4 peaks because SIDE is not included this time.

For MC2, POS to SUSPIT and POS to SUSYAW got worse. I have to look into them.

Effect of resonant frequency drift:

As you can compare and see from the spectra above, resonant frequencies of MC1 are somehow drifted(~0.5%) from Nov 9 to Nov 13.
If resonant frequency you expected was wrong, calculated input matrix will be also wrong.
The effect of 0.5% drift and wrong input matrix can be seen from this spectra. DOFs are not clearly separated. Plan:

- learn how to use diaggui from command line and fully automate this process
- balance the coils using these diagonalized SUSPOS, SUSPIT, SUSYAW

ELOG V3.1.3-