Module gmt_dos_clients_m2_ctrl::preprocessor

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ASM#7 preprocessor

Implementation of the algorithm that ties the obscured actuators of M2 center segment to the neighboring actuators

Lets call p the vector of voice coil positions. The location of the actuators are given by their coordinates (x,y). We define 3 masks

  • m1 for r>0.28m
  • m2 for 0.21m < r < 0.28m
  • m3 for r<0.21m

where r^2 = x^2 + y^2.

The masks define 3 annular regions. Three voice coil position vectors are build from p and the masks:

  • p1 = p[m1]
  • p2 = p[m2]
  • p3 = p[m3]

The stiffness matrix K, that relates p to forces: f = Kp, is split into submatrices Kij=k[mi,mj]. Ordering f and p according to the annular regions lead to

| f1 | = | K11 K12 K13 | | p1 |

| f2 | = | K21 K22 K23 | | p2 |

| f3 | = | K31 K32 K33 | | p3 |

p3 is derived such as the sum of the forces in the annular region #2 and #3 is minimal i.e.p3 minimizes the cost function J = ||f2||^2 + ||f3||^2.

Solving J for p3 gives p3 = Ap1 + Bp2 where A = -K3^{-1}K1 and B=K3^{-1}K2 with

K3 = K23^T K23 + K33^T K33

K1 = K23^T K21 + K33^T K31

K2 = K23^T K22 + K33^T K32

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