While Louis and I were working on the DARM loop transitions, we revived an old matlab model I had of the DARM loop, in parallel with Louis using pyDARM to produce plots of the loop cross overs.   This imports filters from CALCS for the sensing and actuation functions, and the suspension filters, and makes some plots of the loop.  For some history about this effort to change the DARM loop, see 74790, and for similar plots made using the pyDARM model of the DARM loop, see 74771.

Here are some plots produced by this model for reference.  The first two attachments show the DARM configuration used in O4a and the proposed configuration (New DARM) tested in 74887 (which has different UIM filters than the configuration documented in 747790) Both of these show a DARM OLG measurement with black x's.  In both cases there is a discrepancy between the model and the measurement, especially visible in the phase around 200Hz. Louis exported a model of the sensing function from pyDARM which we tried substituting for the CALCS sensing function model shown in these plots, this actually made the phase discrepancy worse.  I was able to match the measurement better by adding a delay of 250microseconds to the sensing function, but this is not shown in the plots here.  This discrepancy doesn't cause me too much concern: the model seems accurate enough to evaluate the loop stability, and the pyDARM model which is used for calibration does reproduce this OLG accurately.  By flipping between these two plots, you can see that the NEW_DARM configuration has more low frequency gain (which probably isn't needed), more gain in the PUM around a few Hz (which was our goal, to reduce RMS drive on the ESD), and also a better roll off of the UIM so that the UIM gain is not visible on the plot around 150 Hz.  This feature of our current DARM loop has been a complication for calibration, so we are happy about this change.

The third plot shows the model and measurements of the crossovers. To see Louis's write up of how we are evaluting the stability of cross overs see T2300436. In particular, we are refering to the measurement L2_LOCK_L_IN1/L2_LOCK_L_IN1 as G_pum, and the measurement L1_LOCK_L_IN1/L1_LOCK_L_IN2 as G_uim.  To have a stable crossover we need G_pum and G_uim to not be +1.  We made a measurement of G_pum in the new configuration, which matches this model well.  (It didn't match well in 74771)  We had difficulty making this L2 LOCK measurement in the old DARM configuration, as discussed in 74226.  The plot also shows a measurement made at L1 lock in the O4 configuration, we never took this measurement in the new configuration.  While there are some discrepancies with the UIM measurement, these both agree well enough to confirm that the model is fairly correct.

The next two plots show comparisons of the new and old DARM loops, first the OLGs then the distrubution to actuators .  The new loop leaves the PUM/ESD crossover just below 20Hz where it has been, but has a steeper offloading with less phase margin for the PUM. 

We also plotted and looked at the closed loop response to distubances, for the over all loop and for disturbances at the injection points L2 LOCK (1/(1-G_pum)) and at L1 LOCK (1/(1-G_uim)) to look for gain peaking.  This does indicate that the new model has very slightly more gain peaking for the PUM crossover around the frequencies where we are having trouble (2.5-3.5Hz) than the old loop.

This model is in sheila.dwyer/LSC/DARM/DARM_model/DARM_loop_model_Dec2023.m  and attached here.