The sensing and driving matrices measured in the precedent post 69150 were wrong, due to an error on the threshold on the phase that separates the positive from the negative responses between the piezo and the quadrants. The new matrices were computed:
sensing_matrix =
   -0.6230   -0.0278    0.0033    0.0012
    0.0233   -0.3838   -0.0010   -0.0059
   -0.5035   -0.0063   -0.4332   -0.0151
    0.0154    0.3421    0.0166   -0.2886

driving_matrix =
   -1.5909   -0.1001    1.8540   -0.0972
    0.1081   -2.5520    0.0166   -3.0190
   -0.0128    0.0071   -2.2893   -0.1237
   -0.0080    0.0517    0.1270   -3.3971
 
Using the new driving matrix, we managed to lock the BPL loop in drift control (f < 5 Hz). And then in broadband.
When the BPL is locked in broadband, a 122 Hz signal appeard on the QPD signal spectrums.
 
 
In order to measure the open loop transfer function, the BPL loop was open and a colored noise signal with a 0.001 V amplitude was injected on the channels:

• TILT_X_CORR 13:42:00 UTC
• TILT_Y_CORR 13:45:30 UTC
• SHIFT_X_CORR 13:48:40 UTC
• SHIFT_Y_CORR 13:52:00 UTC

To see the transfer function at low frequency, a 0.03 V signal at frequency < 20 Hz was injected on the same channels at the times:

• TILT_X_CORR 14:27:00 UTC
• TILT_Y_CORR 14:30:00 UTC
• SHIFT_X_CORR 14:32:30 UTC
• SHIFT_Y_CORR 14:36:00 UTC

 The shape of the open loop transfer functions from the CORR signal to the corresponding of the quadrant signals are similar. The following plot is a  transfer function from TILT_X_CORR signal to QF_h_norm during a low frequency injection:

 
The 122 Hz noise was due to a saturation of the control loop, so the loop filter was changed. The QPDs signal spectrums in closed loop, with the old and with the new filter are shown in the following plot:
 
The 122 Hz signal disapeared.