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Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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# of occurrences<br />

70<br />

60<br />

50<br />

40<br />

30<br />

20<br />

10<br />

0<br />

0 200 400 600 800 1000 1200 1400<br />

σ(x,p) [µm]<br />

Figure 3-1: Uncertainty propagation results on PT optimized design: histogram - MC<br />

results, (- -) worst-case vertex search, ∆ = 10%.<br />

Table 3.2: Uncertainty propagation results: PT design.<br />

RMS Young’s Modulus [GPa]<br />

[µm] E1 E2<br />

nominal 100.53 72.0 72.0<br />

WC vertex 1355.5 64.8 79.2<br />

WC Monte Carlo 1315.9 64.85 78.73<br />

performance value from the vertex search. The fact that all of the Monte Carlo<br />

performance predictions are below this value is a good indication that the convexity<br />

assumption is valid in this case. The values of nominal and worst case RMS, along<br />

<strong>with</strong> the uncertainty parameter values, are listed in Table 3.2. Note that the worst-<br />

case performance occurs at an asymmetric configuration when E1 and E2 are at the<br />

lower and upper limits, respectively.<br />

The frequency response functions (FRF) from disturbance forces and torques to<br />

the output are presented in Figures 3-2(a) through 3-2(c). The transfer functions for<br />

the PT configuration at nominal uncertainty values are depicted <strong>with</strong> a solid line,<br />

while those for the worst-case uncertainty configuration obtained through the vertex<br />

78

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