Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

while the nodal points of the RPT designs are moved in towards the center of the
array. This shift in the mode shape accounts for the greater accumulation of energy
in this mode in the RPT design when compared to the PT design. However, the price
of the increased energy in mode #3 is justifiable since reducing the effect of mode #2
has such a dramatic effect on the worst case performance.
Investigation of the energy distribution among modes and the frequencies and
mode shapes of the PT and RPT designs allows a physical understanding of the
trades that are made to achieve robustness to uncertainty. In the PT design there is
no balance between nominal performance and robustness; instead the resulting system
performs very well nominally, but is highly sensitive to uncertainty. The RPT design
strikes a balance by making a small sacrifice in nominal performance for a dramatic
increase in robustness. The nominal performance of the RPT designs is worse than
that of the PT design since the asymmetric bending mode shapes are no longer
tailored such that the nodal points are at the ends of the truss where the collectors
are located. However, by tailoring the truss such that the mass is concentrated on the
inner truss segments, the frequency of the second mode, and consequently its output
energy, is significantly reduced at the worst-case uncertainty vertices.
3.4 Limitations: Design Regimes
In order to obtain a complete comparison of PT and RPT methods, the tailoring
optimizations and uncertainty propagations are run over a range of uncertainty values
from 0.01% to 25%. Since the RPT AO design is the most robust design in terms
of worst-case performance, it alone is considered in the study. At each uncertainty
level, the optimal design is found and the nominal performance is calculated. Then
the uncertainty vertex resulting in the worst-case performance, σWC,isidentifiedand
applied to the design to produce a worst-case performance prediction.
The results of the simulations are plotted in Fig. 3-11. The PT and RPT AO per-
formance predictions are represented with solid and dash-dotted lines, respectively.
The nominal performance is denoted by circles and the worst case performance by
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