Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

and efficiency. The resulting RPTT design is compared to the PT and RPT designs
presented in the previous chapters. The modal energy distributions are explored to
gain physical insight into the tailored and tuned designs. The RPTT methodology is
run over a range of uncertainty bounds, and the design regimes plot presented in the
previous chapters is updated to include the RPTT design. It is shown that RPTT
further extends the uncertainty level that can be tolerated for a given performance
requirement. Finally, random hardware simulations are generated and the entire
tailoring-tuning process is applied using the PT, RPT and RPTT designs. It is
shown that only the RPTT designs can consistently meet aggressive performance
requirements over a large range of uncertainty bounds.
5.1 RPTT Formulation
Robust Performance Tailoring for Tuning extends Robust Performance Tailoring by
designing the system to be tunable across the entire uncertainty space. Recall that the
tailoring process chooses design variables, �x, to optimize the predicted performance
of the final system. In RPT, �x is chosen such that the performance predictions are
insensitive to the uncertainty parameters, �p, given fixed, nominal values for the tun-
ing parameters, �y. The key feature of RPTT is that the prediction accounts for the
fact that the tuning parameters can be adjusted after the hardware is built and the
uncertainty is fixed (and known). The goal of the optimization is to choose �x to
find a design that is tunable across all possible hardware realizations. In the imple-
mentation, the tuning parameters change depending on the uncertainty parameters.
This consideration of future tuning adds extra degrees of freedom to the problem in
the form of additional �y realizations, and, as a result, the optimization is less con-
strained and may have better solutions. Tailoring for tuning idea is similar to an
optimization problem presented by Scokaert and Mayne for application to receding-
horizon model predictive control (MPC)[104]. The MPC formulation accounts for the
fact that future control decisions are made with more information than is currently
available. Scokaert’s min-max problem introduces the notion of feedback into the
152