Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

anges from 300µ m to 3650µ, while in the RPT performances range from 273µm to
only 665µm. The shorter range suggests that the tuning parameters have less of an
effect on the performance of the RPT design.
It is clear from these reults that tuning the worst-case uncertainty realization
has a significant effect on the performance. In the following sections, a physical
understanding of how the tuning masses improve the performance is obtained by
investigation of the output PSDs and energy distribution among modes.
Physical Interpretation: PT Tuning
To begin, consider the worst-case PT design in both the untuned and tuned config-
urations. As seen from Table 4.2 and Figure 4-1, a 77% reduction in performance
variance is achieved by adding 175 kg of tuning mass to the positive-x arm of the in-
terferometer. The plot of the tuning space (Figure 4-1(b)) shows that this particular
tuning configuration is a global optimum. The RMS increases as mass is added to the
negative-x arm or if more/less mass is added to the positive-x arm. To understand
why this tuning configuration has such an impact on the performance consider the
energy information presented in Figure 4-3.
The first plot (Figure 4-3(a)) is the normalized cumulative variance and output
PSDs for both the untuned (solid line) and tuned (dashed line) worst-case PT sys-
tems. The largest differences in energy distribution between the two systems occur
at low frequencies. The second mode, which accounts for almost all of the RMS in
the untuned case, has only a small effect in the tuned system, and the third mode is
at a lower frequency in the tuned system. The bar chart, (Figure 4-3(b)), shows the
percent of total energy in each of the critical modes. It is clear that the addition of
tuning mass shifts the energy from the second mode to the third mode. The accom-
panying table lists the natural frequencies and energy of each of the critical modes.
The absolute energy values show that not only has the energy been redistributed
among the modes, but the total energy in the modes is greatly reduced. For example
the second mode has 1325µm of RMS in the untuned PT design, but only 14.96µm
in the tuned configuration. The third mode accounts for more energy in the tuned
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