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

4List of Figures4.1 Inventory Control Minimization Results. . . . . . . . . . . . . . . . . 245.1 Diagram of Two DOF Resonator. . . . . . . . . . . . . . . . . . . . . 295.2 Feasible design space for 2 DOF resonator and target frequency. . . . 315.3 Sensitivity cost term, s(x, Σ), on the invariant set c 2 (x) = 0 for the 2DOF resonator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.4 3D plot of total cost as a function of design variables. . . . . . . . . . 335.5 Several different paths taken to find the solution from different initialconditions. The starting points are label with numbers on the plot. . 345.6 Diagram of Six Variable Crab-leg Resonator. . . . . . . . . . . . . . . 365.7 Four unique crab-leg resonator designs from Φ 1000 . . . . . . . . . . . . 395.8 Illustration depicting under and overetch of a beam with an end-mass. 415.9 Illustration of the robust designs and two designs from Φ 1000 . . . . . . 425.10 Histogram of the sensitivity cost term, s(x, Σ U ), for the set Φ 1000 . . . 435.11 Distributions of crab-leg resonant frequencies subject to uncorrelateduncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.12 Distributions of crab-leg resonant frequencies subject to correlated uncertainty.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45