[Ibex-maneuver-engineering] Pointing error, rev. 4
Mark Tapley
mtapley at swri.edu
Wed Jun 1 11:28:02 EDT 2011
All,
many thanks to Ken for rounding up lots of pointing vectors
for me to play with. The attached spreadsheet (also on the SFTP site)
compares the commanded pointing vectors as captured in the ATS files
to the resulting pointing vector as reported in the Goat Herder for
the same orbit. Generally the vectors should be almost parallel, but
differ slightly because the guidance system halts a pointing maneuver
when it gets within the deadband. This analysis is an attempt to
figure out whether that deadband is a good offset for the commanded
pointing vector.
For the first lap, I normalized both vectors to make sure
they were unit vectors, took the dot-product between the ATS
commanded vector and the Goat-Herder resulting vector, and did an
Arc-Cos to get the angle between them. That's plotted as "Pointing
Error vs. Orbit Number".
Couldn't figure out how to do a histogram neatly, so I
kludged. The Histogram on 0.5 degree bands is shown as "Histogram of
Pointing Errors".
To double-check that the dot-product and arc-Cos on small
angles wasn't causing numerical problems, I then calculated the cross
product, and took the arc-Sin. Differences from the dot-product angle
were tiny (<10^-12) so that was OK. Finally, I plotted the magnitudes
of the components of the cross-product vector, expecting that they
would be mostly in the Z axis. That appears as "Magnitudes of Cross
Product Components", and just below it for reference are the
components of the commanded vector, as "Magnitudes of Commanded
Vector Components".
The cross product vectors were not mostly Z-axis! The
Cross-product clearly leads the commanded vector around by ~90
degrees (ie it points along Earth velocity vector in its orbit around
the Sun, more or less). I *think* that means the error in pointing is
almost always mostly North of the commanded vector, which does not
make much sense to me.
To double-check, I plotted the difference between the ATS
vector and the Goat vector as "Error in pointing by Component"; as
above the difference is dominated by the Z component, which is always
negative, meaning the achieved vector is usually mostly North of the
commanded vector.
Comments welcome; I'll drop this on the SFTP site and mail around.
--
- Mark 210-379-4635
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