40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
 40m Log Not logged in
 Mon Jan 19 18:27:16 2015, ericq, Update, ASC, QPD ASC saga continues. Tue Jan 20 02:39:49 2015, ericq, Update, ASC, QPD ASC saga continues. Tue Feb 10 18:37:17 2015, ericq, Update, ASC, QPD ASC ready to go Tue Feb 24 18:54:26 2015, ericq, Update, ASC, Single arm QPD ASC stability
Message ID: 10920     Entry time: Mon Jan 19 18:27:16 2015     Reply to this: 10921   10997
 Author: ericq Type: Update Category: ASC Subject: QPD ASC saga continues.

# Herein, I will try to paint a more thorough picture of this whole QPD ASC mess.

## Motivation for QPD ASC loops:

• We would like to use the QPDs as a DC arm pointing reference during locking attempts, or over multiple days, if possible.
• It would be nice if the QPDs could complement the oplevs to reduce angular motion of the cavity.
• We must not make the single arm longnitudinal noise or RIN worse, because anything observable in the single arm case will be catastrophic at full sensitivity

## Actuation design:

As mentioned in a previous ELOG, in single arm lock, I measured the QPD response with respect to the calibrated oplev signals. They were:

YARM ETMY: QPD PIT / OPLEV PIT =   22.0 count/urad       QPD YAW / OPLEV YAW =   17.1 count/urad ITMY: QPD PIT / OPLEV PIT =   -6.0 count/urad       QPD YAW / OPLEV YAW =    5.9 count/urad
XARM ETMX: QPD PIT / OPLEV PIT = 16.6 count/urad       QPD YAW / OPLEV YAW = -9.3 count/urad ITMX: QPD PIT / OPLEV PIT =  4.0 count/urad       QPD YAW / OPLEV YAW = -6.0 count/urad

For reference, one microradian of either ITM or ETM motion produces about 60um of ETM beam spot displacement, compared to the spot size of ~5mm.

However, given the lenses on the end tables that are used for green mode matching, that the IR transmitted beam also passes through, the QPDs are not directly imaging the ETM spot position; if they were, they would have equal sensitivity to ITM and ETM motion due to our flat/curved arm geometry.

From this data, I calculated the actuation coefficients for each DoF as $A_{ETM} = \frac{d_{ETM}}{\sqrt {d_{ETM}^2 + d_{ITM}^2}}$, and similarly for the ITMs, where the d's come from the table above. However, it occurs to me that maybe this isn't the way to go... I'll mention this later.

## Loop design:

Up until now, at every turn, I had not properly been thinking about how the oplev loop plays into all of this. I went to the foton filters, and grabbed the loop and plant models for the ETMY oplev, and constructed the closed loop gain, 1/1+G, and the modified plant, P/1+G, which is what the ASC loop sees as its plant.

Here, the purple trace explains all of the features I was confused about earlier.

With this in hand, I set up to design a loop to satisfy our motivations.

• Bounce/roll mode notches to avoid exciting them
• 1/f UGF crossing at a few Hz, limited by the gain margin at ~10Hz, which is where the phase will hit 180, due to the notches
• 4th order Elliptic lowpass at 100, to avoid contaminating the longnitudinal signals
• 1/f^2 at low frequencies for DC gain

To do this, I inverted the oplev closed loop plant pole around 4Hz to smooth the whole thing out. Here's a comparison of the measured OLG with what I modelled.

There's a little bit of phase discrepency around 10Hz, but I think it looks about right overall.

## Evaluation:

So, here's the part that counts: How does this actually perform? I took spectra of the QPD error signals, the relevant OpLev signals as out of loop sensors, the PDH error signal and transmitted RIN while single arm locked, with this loop off, and on for all 4 DoFs simultaneously.

Verdict:

• In-loop signals get small, unsurprisingly.
• Cavity signals unchanged.
• ITM oplev signals are unchanged (and not plotted, to not clutter the plots (This isn't surprising since the loops mostly actuate on the ETMs).
• ETM oplev signals get smaller around the 3Hz peak, but are louder in other bands.

This is what makes me think I may need to revisit the actuation matrix. If I did it wrong, I am driving the "invisible" quadrant of the cavity angular DoFs, and this could be what is injecting noise into the oplevs.

## Conclusion:

In the end, I have a better understanding of what is going on, and I don't think we're quite there yet.

 Attachment 1: oplevPlant.pdf  30 kB
 Attachment 2: loopDesignComparison.pdf  25 kB
ELOG V3.1.3-