I have made unbiased open loop gain measurements of all four HARD loops at 430 kW, following a method similar to Craig's, which he describes in this alog. I used his quick_psd program to shape an excitation to match the error signal. I ran the excitation through DTT (different than him), so I could try to catch where the fit was insufficent in real time and update the excitation. I didn't necessarily run with the resolution that he did, but I think I was still able to capture most of the relevant features. I was able to see the results in DTT, but I also extracted the data and plotted it using (IN1/EXC) / (IN2/EXC) and a coherence threshhold based on the number of averages.

One major change in the loops since Craig ran his measurements is that we are no longer running with radiation pressure compensation (RPC). As a part of increasing the IFO power, I moved all ASC loops off RPC and updated the control filters to appropriately compensate for the high power plant. This means the measurement no longer needs to be run from the "A", or blend point, since we do not have parallel control paths for the ASC loops. This change also improved our loop stability and resiliency to various IFO changes (power increase, thermalization, etc). There have also been a slate of changes to these loops improving the low frequency suppression and the high frequency cutoffs.

I have also updated my ASC model for the higher power, lack of RPC and updated controllers. In the interim, while working with Dan Brown, Evan Hall and Kevin Kuns, we determined there was an error in the way I calculated the radiation pressure modified suspension transfer function. This error would affect the frequency response of the plant, such that the model predicted less circulating power than (what we think is) reality. We confirmed the updated model is likely correct by plotting the optomechanical transfer functions using both Optickle and Finesse. The error can be summarized as a missing factor of sqrt(2). The resulting model gives an arm power prediction that is close, if not almost exact, to what we think our current operating arm power is. This prediction holds for both LHO and LLO (see LLO alog 64801).

Other Modeling details:
I use a suspension model based on a fit to the L2/L3 and L3/L3 torque-to-angle (rad/Nm) transfer functions measured at LHO. I calibrate the counts to torque value based on values from dcc document G1100968.
The radiation pressure modified torque-to-angle transfer function (S_R) is modeled like this:
S_R = S_L2 / (1 + R * S_L3)

where S_L2 is the L2/L3 free suspension transfer function and S_L3 is the L3/L3 free suspension transfer function. R is the power-dependent radiation pressure term, calculated from the arm power and the eigenvalue of the angle-to-spot position matrix. See Lisa Barsotti's ASC technical document T0900511 for more information.

I have attached four plots of DHARD P, CHARD P, DHARD Y, and CHARD Y, showing my unbiased OLG measurement and model assuming 430 kW of power. The pitch loops match very well with the model. There is greater deviation in the yaw loops, especially around the upper frequency suspension peak. It appears that there is a double peak feature in DHARD Y. The same could be true for CHARD Y, but that feature is not well resolved (if such a feature exists there). I currently have no explanation for these features.