Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

The data in Figure 5-2 indicate that the first bending mode at 0.038 Hz is the
focus of the tailoring and tuning mechanisms. Recall from discussions in previous
chapters that this mode is critical for all of the designs. A comparison of the modal
characteristics of this mode among the PT, RPT and RPTT designs in the nominal,
worst-case and tuned configurations is presented in Figure 5-3 to provide insight into
the underlying physics.
The natural frequency of the first bending mode in all three designs is shown in
the upper subplot of Figure 5-3(a). The frequency of the nominal, worst-case and
tuned configurations are marked with circles, squares and diamonds, respectively.
The symbols are difficult to distinguish from one another because, for a given design,
the frequency of the mode does not change appreciably from one configuration to
the next. However, there is quite a difference in the frequency of this mode among
the three designs. The natural frequency in the AO design (0.072Hz) is over twice
that of the PT design (0.022Hz). Recall from the discussion in Chapter 3 that it is
the stiffening of this mode that gives the RPT design its robustness to uncertainty.
However, a side effect is that the RPT design is robust to the tuning parameters,
and little can be done to improve the performance at a given uncertainty realization.
The first bending mode frequency in the RPTT design is between that of the PT and
RPT designs, but is closer to the PT design (0.036Hz) so that tuning authority is
preserved.
The lower subplot in Figure 5-3(a) is a bar chart of the percent energy in the
first bending mode for all three systems in the three configurations. The nominal
configuration is shown in black, worst-case in gray and tuned worst-case in white.
Keep in mind that the total energy of the designs in the different configurations are
different from one another, so that the bars only indicate how the energy is distributed
among the modes, and not the absolute energy in each mode. In the worst-case
configuration the first bending mode is the dominant mode for the PT and RPTT
systems, accounting for over ninety percent of the output energy. In contrast the
RPT design, which is less sensitive to this mode due to its higher natural frequency,
shows only thirty percent of the output energy in first bending in the worst-case
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