These matrices have been calculated by other people before. However, the description of the their calculations cannot be understood mostly because besides diagrams and formular, there are no explanations. The description of my calculation is definitely not better, but I still worth report it here. It's definitely necessary to write a document with explanations.
- Real sensors: LVDTs H1, H2 and H3.
- Real actuators: actuators H1, H2 and H3.
- Virtual sensors and actuators: L, T and Y.
- H1, H2, H3, L and T are in µm.
- Y is in µrad.
- The positions of the LVDTs and actuators used were taken from JGW-D1605092 page 10.
The name assignment of the LVDT-actuator units can be found in the notebook notes. The actuators have the same names as the LVDTs because they are integrated in the same hardware unit, but they are in a slightly different position.
- An outline of the calculation can be found in this notebook page and in this other one.
- The numerical calculation can be found in the Jupyter notebook attached to this report. If you download the file remove the .txt extension and use .ipynb
- The results reported coincide with a previous calculation done by Mark, although he used slightly different values of the positions of the LVDTs and actuators.
LVDT2EUL = sen_R2V_medm = [[ 0.62217822 -0.51846323 -0.10371499] [ 0.23945501 0.41909464 -0.65854965] [ 0.55434524 0.55434524 0.55434524]]
EUL2COIL = act_V2R_medm = [[ 0.85181837 0.52383724 0.59423 ] [-0.87956555 0.47577773 0.59423 ] [ 0.02774717 -0.99961497 0.59423 ]]