Rachel and Elenna: 

The goal of this project is to better understand the DARM loop design that was used during O4b and evaluate how well it performed. By identifying where the design worked well and where we observe limitations, we can gain insight into potential improvements for future DARM loop designs.

To do this, I recreated the pydarm.plot.critique() function using valid O4b calibration reports (H1: 20250111T193645Z and L1: 20250102T163026Z). I then broke the DARM loop down into its individual components to understand how each stage contributes to the overall control performance.

The analysis includes comparisons of the open-loop gain (OLG, (G)), the suppression function (1/(1+G)), the digital_out_to_displacement actuation transfer functions, the lock_in_to_displacement actuation transfer functions, annotated crossover frequencies, and the frequency ranges over which each actuation stage dominates. 

Several notable differences emerge between the H1 and L1 DARM loops. H1 has a lower unity gain frequency (72.2 Hz vs. 86.0 Hz), a lower low-frequency OLG magnitude, and substantially less phase margin (22.5º vs. 34.3º). The reduced phase margin is also reflected in the larger gain peaking observed in the suppression function. Regardless of how future DARM loops are offloaded, increasing the available phase margin should be a primary design objective.

The actuator comparisons show that the overall stage hierarchy is similar between the detectors, with the UIM dominating at low frequencies before the TST becomes dominant above approximately 17 Hz. However, the lock_in_to_displacement transfer functions reveal more complicated interactions between the UIM, PUM, and TST at low frequencies than are apparent from the digital_out_to_displacement transfer functions alone.

See: LIGO-G2601606 for slides.