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 10 0 Frequency [Hz] (a) not tuned tuned 10 2 % Energy 100 90 80 70 60 50 40 30 20 10 0 not tuned tuned 1 2 3 11 Mode # Not tuned Tuned Mode fn energy σ 2 z σz fn energy σ 2 z σz # (Hz) % (µm 2 ) (µm) (Hz) % (µm 2 ) (µm) 1 0.013 0.61 11144 8.22 0.013 27.68 25446 83.93 2 0.023 99.09 1820600 1343.10 0.021 4.93 4537 14.96 3 0.281 0.14 2641 1.95 0.097 64.03 58852 194.12 11 31.77 0.14 2554 1.88 30.95 2.05 1884 6.21 Total: 99.98 1836939 1355.15 98.69 90719 298.22 (c) Figure 4-3: Modal energy breakdown for worst-case PT design (a) output PSDs (b) % energy comparison: not tuned (blue), tuned (green) (c) results table. 116 (b)
configuration than the untuned, but the increase is only from 1.33µm to 194.13µm so that the total energy is much lower when the design is tuned. Y−coordinate [m] 0.05 0.04 0.03 0.02 0.01 0 −0.01 −0.02 −0.03 −0.04 −0.05 not tuned tuned −15 −10 −5 0 5 10 15 X−coordinate [m] (a) Y−coordinate [m] 0.25 0.2 0.15 0.1 0.05 0 −0.05 −0.1 −0.15 −0.2 −0.25 −15 −10 −5 0 5 10 15 X−coordinate [m] Figure 4-4: Mode shape comparisons, worst-case PT untuned (blue solid) and tuned (green dashed): (a) Mode #2, first bending (b) Mode #3, second bending. The second and third modes of the untuned and tuned PT designs are plotted in Figure 4-4. Recall from the last chapter that the worst-case PT design has a high RMS due to an asymmetric uncertainty distribution that results in an asymmetric first bending mode shown <strong>with</strong> the solid line in Figure 4-4(a). When the design is tuned, mass is added asymmetrically (only to the positive-x arm) to counter the asymmetric uncertainty distribution. As a result, the second mode in the tuned system (dashed line) is nearly symmetric, and little OPD is accumulated by this motion. The price that is paid for this improvement is observable in the third mode, Figure 4-4(b). Note that the outer nodal points of the untuned mode (solid line) are located very close to the ends of the structure where the collectors are located resulting in little OPD accumulation. However, when the design is tuned (dashed line), these nodal points move towards the center of the array, and the collector nodes experience greater relative displacement. The increase in OPD in the third mode energy (192.8µm) is more than offset by the decrease in that of the second mode (1310.84µm). The tuning algorithm properly identifies the second mode as the critical one and focuses all the 117 (b)
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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,
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where the subscript indicates the i
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2.3.3 Design Variables The choice o
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and then, by inspection, the inerti
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algorithms begin at an initial gues
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at least locally optimal, and the s
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initial design variable state, x =
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and the RMS OPD is computed using E
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# Designs 25 20 15 10 5 Accepted, b
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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,
Page 85 and 86: tion: ∂hi (z,�x, �pi) ∂�x
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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
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Page 101 and 102: Y−coordinate [m] Y−coordinate [
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]
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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
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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)
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Page 139 and 140: Data: initial iterate, p0, performa
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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
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Page 153 and 154: MPC optimization by allowing a diff
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Page 159 and 160: Table 5.2: Performance and design p
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Page 163 and 164: The data in Figure 5-2 indicate tha
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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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Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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