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 Thu Apr 18 22:35:23 2019, gautam, Update, SUS, ETMY actuator diagnosis Fri Apr 19 11:36:23 2019, gautam, Update, SUS, No consistent solution for output matrix Fri Apr 19 15:13:38 2019, rana, Update, SUS, No consistent solution for output matrix Fri Apr 19 16:19:42 2019, gautam, Update, SUS, Actuation matrix still not orthogonal Fri Apr 19 19:22:15 2019, rana, Update, SUS, Actuation matrix still not orthogonal Mon Apr 22 22:43:15 2019, gautam, Update, SUS, ETMY sensor diagnosis Thu Apr 25 00:30:45 2019, gautam, Update, SUS, ETMY BR mode
Message ID: 14554     Entry time: Fri Apr 19 11:36:23 2019     In reply to: 14551     Reply to this: 14557
 Author: gautam Type: Update Category: SUS Subject: No consistent solution for output matrix

Ther isn't a consistent set of OSEM coil gains that explains the best actuation vectors we determined yesterday. Here are the explicit matrices:

1. POS (tuned to minimize excitation at ~13.5 Hz in the Oplev PIT and YAW error signals): $\begin{bmatrix} \text{UL} & \text{UR} & \text{LL} & \text{LR} \end{bmatrix}\begin{bmatrix} 0.98 \\ 0.96 \\ 1.04 \\ 1.02 \\ \end{bmatrix}$
2. PIT (tuned to minimize cross coupled peak in the Oplev YAW error signal at ~10.5 Hz): ​$\begin{bmatrix} \text{UL} & \text{UR} & \text{LL} & \text{LR} \end{bmatrix}\begin{bmatrix} 0.64 \\ 1.12 \\ -1.12 \\ -0.64 \\ \end{bmatrix}$
3. YAW (tuned to minimize cross coupled peak in the Oplev PIT error signal at ~13.5 Hz): $\begin{bmatrix} \text{UL} & \text{UR} & \text{LL} & \text{LR} \end{bmatrix}\begin{bmatrix} 1.5 \\ -0.5 \\ 0.5 \\ -1.5 \\ \end{bmatrix}$

There isn't a solution to the matrix equation $\begin{bmatrix} \alpha_1 & \alpha_2 & \alpha_3 & \alpha_4 \end{bmatrix} \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & -1 \\ 1 & -1 & 1 \\ 1 & -1 & -1 \end{bmatrix} =\begin{bmatrix} 0.98 & 0.64 & 1.5 \\ 0.96 & 1.12 & -0.5 \\ 1.04 & -1.12 & 0.5 \\ 1.02 & -0.64 & -1.5 \end{bmatrix}$, 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 non-orthogonal (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.
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