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TMT Project Report
MIT Space Systems Lab
Scott A. Uebelhart and Deborah J. Howell
July 6, 2005
Tradespace Analysis of the Thirty Meter Telescope (TMT)
The
goals of this contract were to assist AURA (Association
of Universities for Research in Astronomy) in the selection
of several basic design variables as the first step
in their design of a large, ground-based telescope with
a 30-meter segmented aperture.
The MIT SSL was brought aboard due to our experience
in producing integrated disturbance-to-performance models
of space telescopes (which share many of the flexibility
problems of such a large ground-based telescope), and
our experience in trade study analyses.
This project was supported by AURA under contract
C10413A. The
official title was Development of Methods and Software Tools for Analyzing
Integrated Computer Models of Extremely Large Ground
Based Telescopes with Dr. George Angeli as
the Technical Monitor.
The MIT team consisted of Prof. David Miller,
Prof. Olivier de Weck, Scott Uebelhart, Deborah Howell,
Soon-Jo Chung, and Julien Lamamy.
Four
design variables were identified as important in the
conceptual design phase: primary mirror focal ratio, final focal ratio,
configuration of the secondary mirror (Cassegrain or Gregorian), and position of the elevation axis. In order to examine the effect of changing these
four structural design variables, it was necessary to
build a parameterized model of a TMT-like telescope
so that each variable could be changed and a new realization
of the structure created. Much of the early work involved using a combination
of MATLAB, DOCS (an integrated modeling tool) and the
finite element processor NASTRAN to create automated
finite element representations of the telescope that
could be produced and run for any set of design variable
inputs. The number
of primary segment rafts, the height of the tower holding
the secondary mirror, the truss structure supporting
the primary mirror in addition to the aforementioned
design variables were all made variable. The overall architecture of this parameterized
model was based on the Strawman “point-design” model
provided by AURA. An
optical model, provided by AURA, was appended to this
structural model in order to evaluate the optical performance
of each instantiation of the telescope. Figure 1 shows an example of two different realizations
of the structure.
Figure
1
: Two realizations of the Thirty Meter Telescope automatic
finite element model
Once
the parametric model was assembled, the tradespace,
consisting of the four critical design variables, was
explored. This
provided insights into the system which are not immediately
intuitive such as coupling between variables and areas
of the tradespace warranting further investigation. First, a
static tradespace analysis was performed whereby the
effect of a 650
elevation angle change on mirror distortion under gravity
was investigated. The
elevation angle is a rotation about an axis perpendicular
to the pointing direction. Figure 2 is an example static analysis results
plot comparing the change in image quality (between
00 and 650 elevation angle) vs.
primary mirror (M1) focal ratio for Gregorian configuration
with the elevation axis above the primary mirror. The different colored lines represent different
values of final focal ratio.
Figure 2: TMT static analysis results
Next,
a dynamic analysis was performed whereby sensor and
actuator models, wind models (provided by AURA) and
a simple closed-loop optical control system were appended
to the parametric model in order to evaluate the telescope’s
performance under normal wind-loading conditions. Much
effort was required to model the actuators and sensor,
and to ensure that the final closed loop system was
stable. Figure
3 is an example of the results of the dynamic trade
space analysis relating two output variables, cost and
mass. The dynamic
results were used to select the design variables which
best impacted optical performance, mass and cost.
The final analysis showed the usefulness of parameterized
models to AURA.
Figure
3: TMT dynamic trade space analysis results
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