Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

it in the worst-case uncertainty realization at 1355µm. Tuning the PT design at this
worst-case vertex improves the performance greatly to 303µm, but does not succeed in
bringing the system performance within the requirement. The RPT design is much
less sensitive to uncertainty, but sacrifices nominal performance, and consequently
tunability, to gain robustness. As a result, it does not meet the requirement in either
the nominal (263.87µm) or tuned worst-case (273.32µm) configurations. The RPTT
design methodology improves on RPT by tailoring for multiple sets of tuning param-
eters instead of just one. RPTT sacrifices some robustness for tunability resulting
in a worst-case performance of 573µm, higher than that of RPT, but this worst-case
hardware realization is tunable to just under 216µm and meets the requirement. In
this context, tunability is considered a form of robustness. Although the design is
somewhat sensitive to uncertainty, the physical hardware is guaranteed to be tunable
to below the requirement resulting in a robust system.
To understand the physical source of the increased tuning authority consider the
energy information provided in Figure 5-2. The output PSDs of the RPTT design
in nominal (solid line), worst-case (dotted line) and tuned worst-case (dash-dot line)
uncertainty configurations are plotted in Figure 5-2(a). The normalized cumulative
variance plot shows that the majority of the energy in the worst-case realization is
concentrated in the first bending mode. This result is consistent with the PT and
RPT designs. The distribution of energy in the nominal and tuned configurations
is similar, but the modal frequencies are much lower in the tuned case due to the
additional tuning mass.
The bar chart, Figure 5-2(b), presents the percent of energy accumulated in the
critical modes. The nominal uncertainty case is shown by the black bars, the worst-
case uncertainty realizations by gray bars and the tuned configurations by white
bars. The first three modes are most critical, and the first bending mode contains
most of the energy in the worst-case uncertainty situation. The accompanying table
(Figure 5-2(c)) lists the modal frequencies, percent energy and absolute RMS of each
mode. Note the large increase in energy in Mode #2 in the worst-case realization and
the drop in frequency of Mode #3 in the tuned case.
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