The cavity is locking robustly with the piezo.
After the previous measurement (April 22) I went to test out this process with another piezo, the noliac. Was unsuccessful in locking the cavity only on the fast controller I believe because of the lower resonance on the noliac piezo. Because of this I swapped back to the small Thorlabs piezo. I believe this shifted the location of the piezo on the back of the mirror to a slightly different location, either matching where the beam is hitting on the mirror in the cavity or just now on the center of the mirror. This drastically improves performance of the cavity. This is the difference between this folder and the April 22. Attached are my previous analyses along with a new measurement of very robust piezo lock. By eye this seems to match the quality of lock that the laser provides. Data can be found at \Nextcloud\GQuEST\B102\Output Filter Cavity\FilterCavityScansAndTFs\May1st\test2\.
Note if recreating this: The measurement of G was good at much lower frequencies. Because of this I changed the region where we start approximating K as G. Change the hybridization window to 500-2000 Hz. This can be done in the hybrid() function in the script by changing the line where low_freqs and high_freqs are created to:
low_freqs = np.arange(1,2000,1)
new_freqs = np.arange(500,50001,1)