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Entry  Sat Nov 13 15:53:05 2010, yuta, Update, CDS, diagonalization of MC input matrix MCspectraNov09.pngMCspectraNov13.pngMC1spetra_wrongmatrix.png
    Reply  Sun May 15 03:58:19 2011, rana, Update, CDS, diagonalization of MC input matrix mc1.png
       Reply  Thu May 19 00:23:44 2011, rana, Update, CDS, diagonalization of MC input matrix 
       Reply  Sun Jun 26 16:17:22 2011, rana, Update, CDS, diagonalization of MC input matrix inMatDiag.pdf
          Reply  Mon Aug 8 00:12:58 2011, rana, Update, CDS, diagonalization of MC input matrix 
             Reply  Mon Aug 8 00:58:26 2011, rana, Update, CDS, diagonalization of MC input matrix null.png
                Reply  Wed Aug 10 00:21:10 2011, jamie, Update, CDS, updates to peakFit scripts 
                Reply  Sat Aug 27 15:47:59 2011, rana, Update, CDS, OSEM noise / nullstream and what does it mean for satellites Untitled.png
                   Reply  Wed Nov 30 01:35:49 2011, Jenne, Update, CDS, OSEM noise / nullstream and what does it mean for satellites 
             Reply  Mon Aug 8 19:45:27 2011, jamie, Update, CDS, activateDQ script run; SUS channels being acquired again 
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 

  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.


  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

    s = Ad

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

    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.
   You need to set resonant frequencies to use the script.

   New input matrices for MCs are;

[[ 1.17649712  0.94315611  0.85065054  1.02969624]
 [ 0.55939288  1.28066594 -0.85235358 -1.3075876 ]
 [ 1.23467139 -0.74521928 -1.29394051  0.72616882]]

[[ 1.12630748  1.01451545  0.9013457   0.95783137]
 [ 1.03043025  0.67826036 -1.37270598 -0.91860341]
 [ 0.83546271 -1.26311029 -0.6456881   1.2557389 ]]

[[ 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.


  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.


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

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