So, how is the IR error signal stabilized when the IR is brought in to the resonance?
I can see the linear trend of 0.1V/s from 5s to 10s. This corresponds to 100kHz/s and 13nm for the residual beat drift and the arm length motion, respectively. That sounds huge.
I haven't yet taken any data for the IR fluctuation when the Xarm is locked by the green locking.
You are right, the DC drift was due to a lack of the DC gain. But don't worry about that, because this issue has been solved.
(DC gain issue)
The lack of DC gain was because I put an IIR filter called ''DC block" that I made. It has 1/f shape below 30mHz and becomes flat above it.
The purpose of this filter was to avoid a DC kick when it starts feeding back to ETMX.
Usually the output signal from the PLL has an offset, typically ~5V, then this offset is also acquired into the ADC and eventually kicks ETMX through the feedback.
So when I took the time series data I enabled the 'DC block', that's why it drifts slowly.
After taking the time series, I found that without this 'DC block' technique, the lock can be achieved by appropriately subtracting the offsets with epics numerical values.
This subtraction technique, of course, gave me more stable lock at DC.
(open loop transfer function)
Here is the open-loop TF of the arm locking I measured last night:
The IIR filter chain has the following poles and zeros:
pole 0.1Hz, 1000Hz,
zero 1Hz, 30Hz
For the fitting I assume that the ETMX pendulum has a resonance at 1Hz with Q of 5. Also I put the cavity pole at 24 kHz, assuming the finesse is 80 at 532 nm.
I just fitted the gain and the time delay by my eyes.
If I believe the result of the fitting, whole time delay is 330 usec, which sounds pretty large to me.