Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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Norm. Cum. Var. [µm 2 ] PSD [µm 2 /Hz] 1 0.5 0 10 10 10 0 10 −2 PT RPT:MM RPT:AO 10 0 Frequency [Hz] (a) 10 2 % Energy 100 90 80 70 60 50 40 30 20 10 0 1 2 3 Mode # 5 7 RPT: Multiple Model RPT: Anti-optimization Mode fn energy σ 2 z σz fn energy σ 2 z σz # (Hz) % (µm 2 ) (µm) (Hz) % (µm 2 ) (µm) 1 0.036 8.34 10933 30.20 0.043 13.70 12902 42.04 2 0.061 61.21 80242 221.63 0.073 33.43 31479 102.58 3 0.399 26.86 35207 97.24 0.488 46.63 43906 143.08 5 1.655 1.87 2449 6.76 1.808 3.85 3625 11.81 7 3.819 1.02 1341 3.70 4.30 1.40 1315 4.29 Total: 99.30 130172 359.53 99.01 93227 303.80 (c) (b) PT RPT:MM RPT:AO Figure 3-9: Modal energy breakdown for PT and RPT designs <strong>with</strong> worst-case uncertainty: (a) output PSDs (b) % energy comparison: PT (dark), RPT MM (light) RPT AO (white) (c) results table. 100
Y−coordinate [m] Y−coordinate [m] 0.05 0.04 0.03 0.02 0.01 0 −0.01 −0.02 −0.03 −0.04 −0.05 0.15 0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 −0.25 PT RPT:MM RPT:AO −15 −10 −5 0 5 10 15 X−coordinate [m] (a) PT RPT:MM RPT:AO −15 −10 −5 0 5 10 15 X−coordinate [m] (b) Figure 3-10: Critical modes shape comparisons of PT (–), MM RPT (- -) and AO RPT (-.) designs <strong>with</strong> worst-case uncertainty parameters: (a) first bending mode (b) second bending mode. 101
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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
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The equations of motion of the unda
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The frequency response functions fr
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the output covariance matrix, Σz,
Page 49 and 50: where the subscript indicates the i
Page 51 and 52: 2.3.3 Design Variables The choice o
Page 53 and 54: and then, by inspection, the inerti
Page 55 and 56: algorithms begin at an initial gues
Page 57 and 58: at least locally optimal, and the s
Page 59 and 60: initial design variable state, x =
Page 61 and 62: and the RMS OPD is computed using E
Page 63 and 64: # Designs 25 20 15 10 5 Accepted, b
Page 65 and 66: does not provide information on why
Page 67 and 68: energy is distributed almost evenly
Page 69 and 70: also symmetric as seen in the figur
Page 71 and 72: Chapter 3 Robust Performance Tailor
Page 73 and 74: through careful and experienced mod
Page 75 and 76: described above. However, one can r
Page 77 and 78: ic, σz(�x, �p), that is depend
Page 79 and 80: Magnitude, OPD/F x [µm/N] Magnitud
Page 81 and 82: % Energy 100 90 80 70 60 50 40 30 2
Page 83 and 84: metric to the cost function. Note,
Page 85 and 86: tion: ∂hi (z,�x, �pi) ∂�x
Page 87 and 88: values are chosen from their statis
Page 89 and 90: Table 3.3: Algorithm performance: a
Page 91 and 92: Statistical Robustness The statisti
Page 93 and 94: Performance [µm] 1400 1200 1000 80
Page 95 and 96: (Figure 3-6(b)). The nominal perfor
Page 97 and 98: Norm. Cum. Var. [µm 2 ] PSD [µm 2
Page 99: energy by mode for easy comparison.
Page 103 and 104: RMS performance, [µm] 400 350 300
Page 105 and 106: The requirement chosen here is some
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
Page 117 and 118: configuration than the untuned, but
Page 119 and 120: Norm. Cum. Var. [µm 2 ] PSD [µm 2
Page 121 and 122: Performance Requirement [µm] 400 3
Page 123 and 124: is considered. 4.2.1 Hardware-only
Page 125 and 126: and added to the objective function
Page 127 and 128: using either a decreasing step-size
Page 129 and 130: for tailoring, but tuning parameter
Page 131 and 132: tained by randomly choosing paramet
Page 133 and 134: p [GPa] y ∗ [kg] Performance [µm
Page 135 and 136: # Func. Evals Performance RMS (µm)
Page 137 and 138: tion changes in the updated solutio
Page 139 and 140: Data: initial iterate, p0, performa
Page 141 and 142: the new tuning configuration is ver
Page 143 and 144: Performing an AO tuning optimizatio
Page 145 and 146: Uncertainty Bounds Test �y [kg] S
Page 147 and 148: Table 4.6: Tuning results on fifty
Page 149 and 150: 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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