Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

tuning effort there.
Physical Interpretation: RPT Tuning
The results for the RPT AO design exhibits trends similar, although less dramatic, to
those of the PT design. Recall from Table 4.2 that tuning the worst-case AO design
reduces the performance variance by 11%. The energy results for this design is pre-
sented in Figure 4-5. The cumulative variance and output PSD plots, Figure 4-5(a),
show a decrease in the energy in Mode 2 and the frequency of Mode 3. The bar
chart of percent energy, Figure 4-5(b), supports the PSD plots indicating that energy
distribution has been shifted from the second mode to the third mode and a few
higher modes. It is interesting to compare this bar chart to that of the PT design
(Figure 4-3(b)). Note that the second mode contains a smaller percentage of the
energy in the RPT design, and additional high-frequency modes are critical. Recall
from Chapter 3 that the robust optimization tailors the system to reduce the effect
of the second mode by increasing its frequency. The resulting design is insensitive to
the uncertainty parameters, but is also insensitive to the tuning parameters. How-
ever it is still most advantageous, given the tuning parameters chosen, to place the
mass such that the energy in mode two is reduced further. The table included in
the figure provides additional results that support these observations. Note that the
energy in Mode 2 is reduced from 102.58 to 34.66µm, but there is an increase in the
accumulated RMS in Mode 3.
The second and third mode shapes for the RPT AO design are plotted in Fig-
ure 4-6. The effect of tuning on the second mode (Figure 4-6(a)) is more difficult to
observe in this case. Recall from chapter 3 that the AO design is tailored for robust-
ness and as a result has more effect on the second mode in the worst-case uncertainty
realization. Therefore, since the tuning parameters are limited to masses in only two
locations, there is less tuning authority for this system. The second mode is made
slightly more symmetric through the tuning masses, but not significantly so. The
third mode (Figure 4-6(b)) exhibits characteristics similar to that of the tuned PT
design in that the nodal crossings are shifted slightly inwards resulting in a small
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