Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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tuning effort there. Physical Interpretation: RPT <strong>Tuning</strong> The results for the RPT AO design exhibits trends similar, although less dramatic, to those of the PT design. Recall from Table 4.2 that tuning the worst-case AO design reduces the performance variance by 11%. The energy results for this design is pre- sented in Figure 4-5. The cumulative variance and output PSD plots, Figure 4-5(a), show a decrease in the energy in Mode 2 and the frequency of Mode 3. The bar chart of percent energy, Figure 4-5(b), supports the PSD plots indicating that energy distribution has been shifted from the second mode to the third mode and a few higher modes. It is interesting to compare this bar chart to that of the PT design (Figure 4-3(b)). Note that the second mode contains a smaller percentage of the energy in the RPT design, and additional high-frequency modes are critical. Recall from <strong>Chapter</strong> 3 that the robust optimization tailors the system to reduce the effect of the second mode by increasing its frequency. The resulting design is insensitive to the uncertainty parameters, but is also insensitive to the tuning parameters. How- ever it is still most advantageous, given the tuning parameters chosen, to place the mass such that the energy in mode two is reduced further. The table included in the figure provides additional results that support these observations. Note that the energy in Mode 2 is reduced from 102.58 to 34.66µm, but there is an increase in the accumulated RMS in Mode 3. The second and third mode shapes for the RPT AO design are plotted in Fig- ure 4-6. The effect of tuning on the second mode (Figure 4-6(a)) is more difficult to observe in this case. Recall from chapter 3 that the AO design is tailored for robustness and as a result has more effect on the second mode in the worst-case uncertainty realization. Therefore, since the tuning parameters are limited to masses in only two locations, there is less tuning authority for this system. The second mode is made slightly more symmetric through the tuning masses, but not significantly so. The third mode (Figure 4-6(b)) exhibits characteristics similar to that of the tuned PT design in that the nodal crossings are shifted slightly inwards resulting in a small 118
Norm. Cum. Var. [µm 2 ] PSD [µm 2 /Hz] 1 0.5 10 5 10 0 0 10 −5 10 −2 10 0 Frequency [Hz] (a) 10 2 not tuned tuned % Energy 60 50 40 30 20 10 0 not tuned tuned 1 2 3 4 5 7 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 0.043 13.70 12902 42.04 0.043 17.64 13179 48.22 2 0.073 33.43 31478 102.58 0.072 12.68 9474 34.66 3 0.487 46.63 43906 143.08 0.336 57.43 42907 156.98 4 0.599 0.19 175 0.57 0.578 5.64 4217 15.43 5 1.808 3.85 3625 11.81 1.754 3.57 2670 9.77 7 4.300 1.34 1315 4.29 3.864 1.69 1265 4.62 Total: 99.14 93401 304.37 98.65 73712 269.68 (c) Figure 4-5: Modal energy breakdown for worst-case RPT AO design (a) output PSDs (b) % energy comparison: not tuned (blue), tuned (green) (c) results table. 119 (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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does not provide information on why
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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]
Page 115 and 116: m 2 [kg] 800 700 600 500 400 300 20
Page 117: configuration than the untuned, but
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 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
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
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Page 153 and 154: MPC optimization by allowing a diff
Page 155 and 156: where the notation yij indicates th
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Page 159 and 160: Table 5.2: Performance and design p
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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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