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Entry  Fri Jan 14 01:55:26 2011, kiwamu, Update, LSC, X arm locked with C1LSC digital control 
    Reply  Fri Jan 14 11:29:00 2011, kiwamu, Update, LSC, expected open loop TF of X arm locking xarm_oltf.png
    Reply  Fri Jan 14 12:34:08 2011, Koji, Update, LSC, X arm locked with C1LSC digital control 
Message ID: 4154     Entry time: Fri Jan 14 11:29:00 2011     In reply to: 4153
Author: kiwamu 
Type: Update 
Category: LSC 
Subject: expected open loop TF of X arm locking 

Here shows a plot of the expected open loop transfer function (TF) for the X arm locking.


I assume that the delay time of the digital system associated with the ADC/DAC and the digital filtering process is ~100 usec independently from the RFM delay according to Yuta's measurement (#3961).

Also I assume the MC2 pendulum has a pole at 1Hz with Q of ~5, and the X arm has its cavity pole at ~3kHz.

When the lock acquisition takes place, we used the red curve shown above in order to avoid a big DC feedback onto MC2.

Once the X arm became resonant at TEM00, we manually switched FM3 on, which is a boost filter containing a pole at  1Hz and a zero at 50Hz in order to suppress the residual motion below 1Hz.

The expected curve for the boosted state is drawn by the blue curve in the plot. 

With this open loop TF, the UGF can be realized only around 100-300 Hz due to the phase margin condition.

This expectation of the UGF is consistent with our measurement because we obtained the UGF around 200-300Hz.

In fact above 300Hz we observed that the control became unstable and started oscillating.



 (some notes)

 unWhitening filter           pole:15Hz. pole:15Hz, zero:150Hz, zero:150Hz

 C1LSC_MC_FM1   pole:1kHz, zero:10Hz

 Gain in digital control       G ~ -1

measured UGF  ~  200-300 Hz

 measured RFM delay ~ 125 usec 


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