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.
Quote:
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(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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