J. Kissel, E. Goetz, K. Izumi, D. Tuyenbayev

Evan will post the details of the work we've had to do to get the model running, but in the interest of time, I've taken what we needed from the Matlab model to update the CAL-CS front-end filters. Since early results indicate that the only low-frequency (sub-Nyquist) things that have changed from the O1 model are in the sensing function (see LHO aLOG 28171):
   - Lower optical gain = 9.071e5 [ct/m],
   - Lower frequency DARM coupled cavity pole frequency, f_c = 328.7 Hz, and
   - New SRC-detuned optical spring frequency, f_s = 9.831 Hz.
I only needed to update the H1:CAL-CS_DARM_ERR inverse sensing function filter (see further discussion below). 

The new settings have been captured in the SDF system.

Details of the design:
Foton Design String --
       zpk([9.831;-9.831;328.7],[0.1; 0.1;7000],1,"n")gain(9574.81)*gain(1.102e-6)
The gain of 1.102e-6 is 1 / 9.071e5 [ct/m], this lives separately in FM4, called "ER9gain." In FM3, in the filter called "SRC D-2N" for "Signal Recycling Cavity De-Two-Ne" there lies:
- The pair of real poles at 9.831 Hz, one of which is in the right-half-plane, reflect the detuning dynamics. Note that we've rolled of these inversion zeros at low frequency of two real poles 0.1 Hz. 
- The 328.7 Hz is the new f_c, and we retain the same high-frequency roll off of 7000 Hz.  
- The gain of gain(9574.81) which is the correct normalization gain to get the over-all gain to be unity at 100 Hz, which is the frequency at which I matched the no-detuning gain of the (unused) 329:7000 filter in FM3.
The attached PDF shows that the ER9 gains agree between detuning and no detuning, and as expected, the overall optical gain is ~20% lower that O1 because we've not yet digitally compensated for the ~20% lower optical gain (because of 20% lower PRC gain; see LHO aLOG 28133) in the DARM loop.


Further Discussion on why I've only updated the Sensing Function:
All actuation strengths are within ~5% of there O1 values (see LHO aLOG 28130), and we've compensated all electronics better (see LHO aLOGs 27180, 27150, and 28087), so we need not update anything in the actuation chain. Rana and Evan H. have changed the local, top-mass damping loop filters for the QUADs, so nominally the QUAD dynamics have been changed, but that should be a small effect in the GW band. We'll update for O2, but no need for ER9. There have been several changes to effects at high-frequency, but all of those are covered in the GDS FIR filters which absorb the CAL-CS output and acausaly correct for these super-Nyquist frequency effects.