Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

configuration. The tuned configurations are especially interesting as it is clear that
the tuning parameters are able to drastically reduce the percent energy of this mode
in both the PT and RPTT designs, while the RPT design is not affected as strongly.
To complete the story the relative modal displacement between the collector nodes
for each design is shown in Figure 5-3(b). Again, the results for the nominal, worst-
case and tuned worst-case configurations are shown in black, gray and white, respec-
tively. This metric is important since the y-translation contribution to the OPD is
due to the relative motion of these nodes (Equation 2.9). It is clear from the chart
that the addition of the tuning masses to the PT and RPTT designs reduces the rel-
ative motion between collectors quite drastically. In effect, the asymmetric addition
of tuning mass balances the asymmetry introduced by the uncertainty parameters
at the worst-case vertex. The RPT design also shows a reduction, but it is not as
significant. The tuning parameters are not able to affect the shape of the first mode
as much, because the design is robust to uncertainty but is also robust to tuning.
The RPTT design formulation balances the key elements of the PT and RPT
designs to produce a design that is both robust to uncertainty, yet tunable. In the
SCI development model all effort is directed to the first bending mode as this is the
significant mode in the worst-case uncertainty realization due to asymmetric motion
of the collector nodes. The natural frequency of this mode in the RPTT design is
higher than that of the PT design so that the mode contributes less to the output
energy. However, it is not stiffened as sharply as in the RPT design so that the tuning
parameters have sufficient authority to affect the performance.
5.2.3 Design Regimes
The tuned RPTT design is compared to the PT, RPT, tuned PT and tuned RPT
designs over a range of uncertainty values. The formulation in Equation 5.5 is run
for maximum tuning authority (α =0.0) at various values of uncertainty bound, ∆,
ranging from 0.01% to 25%. The uncertainty values vary ±∆% about nominal and
are the same for both uncertainty parameters. The tuned results are obtained by
running a tuning optimization on the worst-case uncertainty realization. The results
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