Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

than the RPT design, 155.45µm to 551.5µm, but is less sensitive to uncertainty than
the PT design. The lower range of the RPTT nominal performance is below the
requirement indicating that some of the nominal hardware simulations are successful
without tuning. More importantly, the entire tuned range, 148.16µm to 211.23µm, is
below the requirement indicating that all of the designs are successful once tuned.
The lower subplot, Figure 5-8(b), is a bar chart showing the percent of simulations
that are successful, i.e. meets requirements, for each design. Successful designs are
broken into two subcategories: those that pass nominally (white bars) and those that
pass after tuning (gray bars). The failed designs are indicated by black bars. The PT
design is largely successful, with 94.5% of the simulations meeting the requirement.
However, the majority of simulations need to be tuned (only 27% pass nominally),
and 5.5% of the simulations fail even with tuning indicating that there is no guarantee
of success with the PT design. The RPT design fares much worse with a 100% failure
rate over the simulations. As discussed in Chapters 3 and 4, the RPT is much less
sensitive to uncertainty, but is also insenstive to the tuning parameters resulting in a
design with a small range on both nominal performance and tuning. Only the RPTT
design is successful for 100% of the simulations. In addition, over half of the RPTT
simulations pass nominally, and tuning is only required in 47.5% of the cases. Even
though the robust weight, α was set to zero, RPTT achieves a blend of tunability and
robustness since the design is tuned at all of the uncertainty vertices. The resulting
design is more robust to uncertainty than the PT design and is more likely to meet
requirements in the nominal hardware configuration.
The results of the simulations at ∆ = 10% are interesting because although RPTT
is the only design that is successfull 100% of the time, it is surprising to see that
the PT design is highly tunable and largely successful despite its high sensitivity
to the uncertainty parameters. To further explore this issue 200 simulations are
run with a higher uncertainty level, ∆ = 21.5%. The design regimes in Figure 5-4
indicate that none of the designs can accomodate such a high uncertainty level and a
requirement of 220µm, so for these simulations the requirement is relaxed to σreq =
330µm. In addition, two RPTT designs are generated, one with α =0.0 and the other
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