Robust Optimization: Design in MEMS - University of California ...

45uncertainty. Although the correlated and uncorrelated designs are physically similarand have similar distributions, they are each optimal for the uncertainty model forwhich they were designed.Robust Correlated DesignAverage Design from Φ 1000Worst Design from Φ 1000Target Resonant Frequency140 160 180 200 220 240 260Frequency (kHz)Figure 5.12:uncertainty.Distributions of crab-leg resonant frequencies subject to correlatedIn this chapter we presented the robust design of a six variable crab-leg resonator.We showed how it was possible to determine lower and upper bounds on the resonantfrequency given the design and constraints. We then chose a target frequency of 200kHz, and used our optimization to find a set of 1000 designs that at nominal have aresonant frequency equal to the target. Two uncertainty models, an uncorrelated andcorrelated, were developed and used in solving the robust problem. We then comparedthe cost, F (x, Σ), between our robust designs and the designs in Φ 1000 . Finally, weillustrated frequency distributions, generated from a monte carlo simulation of processvariation, which showed that our robust designs were less sensitive to uncertainty.