Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

(Figure 3-6(b)). The nominal performance for each design is depicted in the plot with
circles and the worst-case performance, obtained through a vertex analysis, is denoted
with an error-bar to indicate that the true performance could lie anywhere in this
range. The designs are ordered, from highest to lowest, by worst-case performance.
The error bar of the PT design is by far the largest and is many times higher than
those of the RPT designs. The RPT designs all show a significant improvement in
worst-case performance, but the AO design is the clear winner in terms of robustness
as the error-bar is the shortest and the worst-case performance the lowest of all the
designs. The worst-case value for performance of the AO design is only 306.86µ m,
while vertex statistical robustness (VSR) and multiple model (MM) designs have
worst-case value performances of 325.09µm and 362.06µm, respectively. The Monte
Carlo statistical robustness (MCSR) design is the least robust of the RPT designs,
with a worst-case performance of 412.6µm.
The plot andq table show that the nominal performance is inversely related to the
robustness; as the designs become more robust, the nominal performance degrades.
The nominal performance of the PT design is significantly better than that of the
RPT designs, and the AO design has the worst nominal performance of the group.
It is interesting to note, however, that the improvement in worst-case performance
is much more significant that the degradation in nominal performance. The nominal
performance of the PT design is roughly two times better than that of the AO design,
but the worst-case performance of the AO design is nearly 4.5 times better that
that of the PT design. Although there is a trade between nominal performance and
robustness, large improvements in robustness can be achieved with moderate sacrifices
in nominal performance.
The worst-case performance values shown in the plot are obtained through a
vertex uncertainty analysis. These results are listed in Table 3-6(b) along with the
worst-case values resulting from a Monte Carlo uncertainty analysis with 500 samples
chosen from the distribution. Note that the worst-case performance results from the
MC propagation are consistently below those from the vertex method confirming
the assumption of a convex uncertainty space. In addition, the design parameters
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