Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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Performance [µm] 1400 1200 1000 800 600 400 200 0 PT MCSR MM VSR AO (a) σ0 σWC [µm] X-S diameters [m] mass [kg] [µm] Vertex MC d1 d2 m1 m2 mtruss PT 100.53 1355.5 1240.9 0.03 0.03 0.0 0.1934 72.15 MCSR 178.74 412.75 403.92 0.0360 0.0485 0.0 0.0 144.61 MM 214.75 362.06 352.63 0.0432 0.0529 0.0 22.61 184.89 VSR 223.45 325.09 312.40 0.0423 0.0540 0.0 0.0 185.97 AO 263.87 306.86 300.54 0.0486 0.0581 0.0 0.0 227.04 (b) Figure 3-6: Nominal and worst case performance for PT and RPT optimizations. 94
(Figure 3-6(b)). The nominal performance for each design is depicted in the plot with circles and the worst-case performance, obtained through a vertex analysis, is denoted with an error-bar to indicate that the true performance could lie anywhere in this range. The designs are ordered, from highest to lowest, by worst-case performance. The error bar of the PT design is by far the largest and is many times higher than those of the RPT designs. The RPT designs all show a significant improvement in worst-case performance, but the AO design is the clear winner in terms of robustness as the error-bar is the shortest and the worst-case performance the lowest of all the designs. The worst-case value for performance of the AO design is only 306.86µ m, while vertex statistical robustness (VSR) and multiple model (MM) designs have worst-case value performances of 325.09µm and 362.06µm, respectively. The Monte Carlo statistical robustness (MCSR) design is the least robust of the RPT designs, with a worst-case performance of 412.6µm. The plot andq table show that the nominal performance is inversely related to the robustness; as the designs become more robust, the nominal performance degrades. The nominal performance of the PT design is significantly better than that of the RPT designs, and the AO design has the worst nominal performance of the group. It is interesting to note, however, that the improvement in worst-case performance is much more significant that the degradation in nominal performance. The nominal performance of the PT design is roughly two times better than that of the AO design, but the worst-case performance of the AO design is nearly 4.5 times better that that of the PT design. Although there is a trade between nominal performance and robustness, large improvements in robustness can be achieved with moderate sacrifices in nominal performance. The worst-case performance values shown in the plot are obtained through a vertex uncertainty analysis. These results are listed in Table 3-6(b) along with the worst-case values resulting from a Monte Carlo uncertainty analysis with 500 samples chosen from the distribution. Note that the worst-case performance results from the MC propagation are consistently below those from the vertex method confirming the assumption of a convex uncertainty space. In addition, the design parameters 95
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Dynamic Tailoring and Tuning for Sp
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Acknowledgments This work was suppo
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3.2 RPT Formulation . . . . . . . .
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List of Figures 1-1 Timeline of Ori
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List of Tables 1.1 Effect of simula
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Nomenclature Abbreviations ACS atti
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dk optimization search direction f
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1.1 Space-Based Interferometry NASA
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unfettered by the Earth’s atmosph
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the SCI, both the size and flexibil
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maybethatitbecomescertain that the
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Table 1.1: Effect of simulation res
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Table 1.2: Effect of simulation res
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has been found that structural desi
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precision telescope structure for m
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attractive, and more conservative a
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to solve the performance tailoring
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Chapter 2 Performance Tailoring A c
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ometer (SCI). In the following sect
Page 43 and 44: The equations of motion of the unda
Page 45 and 46: The frequency response functions fr
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Page 51 and 52: 2.3.3 Design Variables The choice o
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Page 59 and 60: initial design variable state, x =
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Page 73 and 74: through careful and experienced mod
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Page 77 and 78: ic, σz(�x, �p), that is depend
Page 79 and 80: Magnitude, OPD/F x [µm/N] Magnitud
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Page 83 and 84: metric to the cost function. Note,
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Page 89 and 90: Table 3.3: Algorithm performance: a
Page 91 and 92: Statistical Robustness The statisti
Page 93: Performance [µm] 1400 1200 1000 80
Page 97 and 98: Norm. Cum. Var. [µm 2 ] PSD [µm 2
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Page 101 and 102: Y−coordinate [m] Y−coordinate [
Page 103 and 104: RMS performance, [µm] 400 350 300
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Page 107 and 108: Chapter 4 Dynamic Tuning Robust Per
Page 109 and 110: on a physical truss. Since tailorin
Page 111 and 112: Table 4.1: Tuning parameters for SC
Page 113 and 114: m 2 [kg] J ∗ # # time y ∗ [kg]
Page 115 and 116: m 2 [kg] 800 700 600 500 400 300 20
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Page 119 and 120: Norm. Cum. Var. [µm 2 ] PSD [µm 2
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Page 135 and 136: # Func. Evals Performance RMS (µm)
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Page 139 and 140: Data: initial iterate, p0, performa
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Uncertainty Bounds Test �y [kg] S
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Table 4.6: Tuning results on fifty
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eters are discussed. The optimizati
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Chapter 5 Robust Performance Tailor
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MPC optimization by allowing a diff
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where the notation yij indicates th
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(Table 4.1), and the uncertainty pa
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Table 5.2: Performance and design p
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it in the worst-case uncertainty re
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The data in Figure 5-2 indicate tha
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configuration. The tuned configurat
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same requirement. The effect become
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indicating that this requirement is
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E 2 [Pa] 7.8 7.6 7.4 7.2 7 6.8 6.6
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than the RPT design, 155.45µm to 5
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have a very small nominal performan
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of these simulations fail to meet r
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and that it is the only design meth
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Chapter 6 Focus Application: Struct
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optical path differences between th
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Table 6.1: RWA disturbance model pa
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FRF Magnitude 10 1 10 0 10 −1 10
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Y Z Z X Y (a) w (c) w Y h Z Figure
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Table 6.6: Primary mirror propertie
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OP1 STAR Z OP2 OP3 Coll 1 Coll 2 Bu
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PSD OPD14 [m 2 /Hz] CumulativeOPD14
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6.2 Design Parameters In order to a
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6.2.2 Tuning The tuning parameters
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complex and the normal modes analys
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does not change with the design par
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(a) (b) (c) Figure 6-11: SCI TPF PT
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Table 6.14: Performance predictions
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performance trends similar to those
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Chapter 7 Conclusions and Recommend
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a statistical robustness measure su
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and the worst-case performance is a
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- Consider uncertainty analysis too
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Appendix A Gradient-Based Optimizat
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such that the gradient direction is
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the descent direction. In some case
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Bibliography [1] Jpl planet quest w
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[24] Nightsky Systems Carl Blaurock
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[48] S. C. O. Grocott, J. P. How, a
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[74] M. Lieber. Development of ball
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AIAA/ASME/ASCE/AHS/ASC Structures,
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