I made some progress in modeling MICH loop.
Putting all the LSC and SUS filters together with the MICH Finesse model I constructed an OLTF model and plot it with the measurement done by Paco and Yuta in this elog (attachment 1).
There are 2 unknown numbers that I had to adjust in order to fit the model with the measurement:
1. The SUS damping loop gain (found to be ~ 2.22), which seems to vary wildly from SUS to SUS.
2. The coil driver gain (found to be 45), which I should measure.
I find coil_driver_gain*SUS_damping_filter_gain by increasing it until the SUS damping loop becomes unstable.
The coil driver gain I find by making the measurement and model overlap.
However, there is one outstanding discrepancy between the measurement and the model: Paco and Yuta measure the MICH calibration to be 1.3e9 cts/m while my model shows it to be 1.3e10 cts/m, an order of magnitude larger.
The model can be summarized with these lines of code (I assume that the product of the ADCs(DACs) and and whitening(dewhitening) filters is unity):
BS2AS55 = TFs["AS_f2"]["BS"]
PD_responsivity = 1e3*0.8 #V/W
ADC_TF = 3276.8 #cts/V
demod_gain = 6.77 #According to https://wiki-40m.ligo.caltech.edu/Electronics/LSC_demoddulators
whitening_gain = 10**(24/20) #24 dB
BS2MICH = BS2AS55*PD_responsivity*demod_gain*whitening_gain*ADC_TF
DAC_TF = 6.285e-4 #V/cts, elog 16161
coil_TF = 0.016 #Newton/Ampere per coil, elog 15846
coil_R = 20e3 #Ohm
actuation_TF = DAC_TF*coil_TF/coil_R
OLTF = (BS2MICH*MICH_ctrl_cmplx*-6*0.5 + OSEM_filters_cmplx*OSEM_TF*2.22)*coil_filters_cmplx*actuation_TF*SUS_cmplx*45
- BS2AS55 is the optical plant, calculated with Finesse
- MICH_ctrl_cmplx is the MICH control filter with gain of -6
- 0.5 factor comes from the LSC output matrix
- OSEM_TF is the product of the OSEMs input filters and damping loop filters.
- coil_filters_cmplx are the coil filters
- SUS_cmplx is the suspension transfer function (w0 = 1Hz, Q=200)