Ther isn't a consistent set of OSEM coil gains that explains the best actuation vectors we determined yesterday. Here are the explicit matrices:
 POS (tuned to minimize excitation at ~13.5 Hz in the Oplev PIT and YAW error signals):
 PIT (tuned to minimize cross coupled peak in the Oplev YAW error signal at ~10.5 Hz):
 YAW (tuned to minimize cross coupled peak in the Oplev PIT error signal at ~13.5 Hz):
There isn't a solution to the matrix equation , i.e. we cannot simply redistribute the actuation vectors we found as gains to the coils and preserve the naive actuation matrix. What this means is that in the OSEM coil basis, the actuation eigenvectors aren't the naive ones we would think for PIT and YAW and POS. Instead, we can put these custom eigenvectors into the output matrix, but I'm struggling to think of what the physical implication is. I.e. what does it mean for the actuation vectors for PIT, YAW and POS to not only be scaled, but also nonorthogonal (but still linearly independent) at ~10 Hz, which is well above the resonant frequencies of the pendulum? The PIT and YAW eigenvectors are the least orthogonal, with the angle between them ~40 degrees rather than the expected 90 degrees.
Quote: 
So we now have matrices that minimize the cross coupling between these DoFs  the idea is to back out the actuation coefficients for the 4 OSEM coils that gives us the most diagonal actuation, at least at AC.

