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
forr>0.28m
m2
for0.21m < r < 0.28m
m3
forr<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
Structs§
- ASM voicecoil position pre-processor