Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

almost exactly with the collector locations. Therefore, when this mode is excited there
is very little OPD accumulated. However, in the robust designs the nodal points are
moved inwards towards the center of the array and away from the collectors. As a
result, the collectors move in opposite directions when this mode is excited leading
to larger OPD.
Y−coordinate [m]
0.2
0.1
0
−0.1
−0.2
PT
RPT:MM
RPT:AO
−15 −10 −5 0 5 10 15
X−coordinate [m]
Figure 3-8: Critical modes shape comparisons of PT (–), MM RPT (- -) and AO RPT
(-.) designs with nominal uncertainty parameters: second bending mode.
In order to understand why the robust designs are so much less sensitive to un-
certainty than the PT design it is necessary to compare the designs at the worst-case
uncertainty parameter values. The output PSDs and cumulative variance plots for
this case are presented in Figure 3-9(a). The PT design is depicted with a solid line,
and the RPT MM and AO design results are plotted in dashed and dash-dotted lines,
respectively. At the worst-case uncertainty vertex a situation directly opposite to
that at the nominal uncertainty values is observed. All of the energy is contained
in the first observable bending mode, while the output energy in both of the RPT
designs is distributed over two critical modes. The exact modal energy numbers for
the critical modes are listed in Figure 3-9(c) along with a bar chart of percent total
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