Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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Table 6.8: TPF SCI instrument elements. Element ID Element Type Description 5000 GRID 5010 CONM2 Combiner 5101 RBAR 3000 PSHELL, MAT1 Collector glass properties 10001-10085 GRID 13001 - 13060 CQUAD8 Collector 1 (X=-18m) Mirror 14001 - 14024 CTRIA6 12203 - 12206 12200 CBAR PBAR, MAT1 Collector 1 Mounts 20001-20085 GRID 23001 - 23060 CQUAD8 Collector 2 (X=-6m) Mirror 24001 - 24024 CTRIA6 22203 - 22206 22200 CBAR PBAR, MAT1 Collector 2 Mounts 30001-30085 GRID 33001 - 33060 CQUAD8 Collector 3 (X=+6m) Mirror 34001 - 34024 CTRIA6 32203 - 32206 32200 CBAR PBAR, MAT1 Collector 3 Mounts 40001-40085 GRID 43001 - 43060 CQUAD8 Collector 4 (X=+18m) Mirror 44001 - 44024 CTRIA6 42203 - 42206 42200 CBAR PBAR, MAT1 Collector 4 Mounts 192
OP1 STAR Z OP2 OP3 Coll 1 Coll 2 Bus Coll 3 Coll 4 RWA Combiner OP4 Figure 6-6: Structural model schematic showing optical paths. the combiner through each collector are all equal to B 2 X + R, where R is the distance from the star to the collector. These paths are shown in in Figure 6-6. However, if the collectors and/or combiner are perturbed from their nominal positions, the path lengths are affected as follows: OP1 = R − Z1 + Xc − X1 + B 2 OP2 = R − Z2 − Xc − X2 +2x3 + B 2 OP3 = R − Z3 + Xc − 2X2 + x3 + B 2 OP4 = R − Z4 − Xc + X4 + B 2 (6.4) (6.5) (6.6) (6.7) where Zi and Xi are the Z and X coordinates of the i th collector, and Zc and Xc are the Z and X coordinates of the combiner. The OPDs are then found by simply subtracting the relevant path lengths: OPD12 = Z2 − Z1 +2Xc − X1 + X2 − 2X3 (6.8) OPD13 = Z3 − Z1 − X1 +2X2 − X3 (6.9) OPD14 = Z4 − Z1 +2Xc − X1 − X4 (6.10) where OPDij is the optical path difference between the i th and j th collectors. Equa- tions 6.8 through 6.10 form the optical sensitivity matrix from the instrument position states to the performance metrics. 193
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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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energy is distributed almost evenly
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also symmetric as seen in the figur
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Chapter 3 Robust Performance Tailor
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through careful and experienced mod
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described above. However, one can r
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ic, σz(�x, �p), that is depend
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Magnitude, OPD/F x [µm/N] Magnitud
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% Energy 100 90 80 70 60 50 40 30 2
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metric to the cost function. Note,
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tion: ∂hi (z,�x, �pi) ∂�x
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values are chosen from their statis
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Table 3.3: Algorithm performance: a
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Statistical Robustness The statisti
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Performance [µm] 1400 1200 1000 80
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(Figure 3-6(b)). The nominal perfor
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Norm. Cum. Var. [µm 2 ] PSD [µm 2
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energy by mode for easy comparison.
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Y−coordinate [m] Y−coordinate [
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RMS performance, [µm] 400 350 300
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The requirement chosen here is some
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Chapter 4 Dynamic Tuning Robust Per
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on a physical truss. Since tailorin
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Table 4.1: Tuning parameters for SC
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m 2 [kg] J ∗ # # time y ∗ [kg]
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m 2 [kg] 800 700 600 500 400 300 20
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configuration than the untuned, but
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Norm. Cum. Var. [µm 2 ] PSD [µm 2
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Performance Requirement [µm] 400 3
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is considered. 4.2.1 Hardware-only
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and added to the objective function
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using either a decreasing step-size
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for tailoring, but tuning parameter
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tained by randomly choosing paramet
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p [GPa] y ∗ [kg] Performance [µm
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# Func. Evals Performance RMS (µm)
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tion changes in the updated solutio
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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
Page 149 and 150: eters are discussed. The optimizati
Page 151 and 152: Chapter 5 Robust Performance Tailor
Page 153 and 154: MPC optimization by allowing a diff
Page 155 and 156: where the notation yij indicates th
Page 157 and 158: (Table 4.1), and the uncertainty pa
Page 159 and 160: Table 5.2: Performance and design p
Page 161 and 162: it in the worst-case uncertainty re
Page 163 and 164: The data in Figure 5-2 indicate tha
Page 165 and 166: configuration. The tuned configurat
Page 167 and 168: same requirement. The effect become
Page 169 and 170: indicating that this requirement is
Page 171 and 172: E 2 [Pa] 7.8 7.6 7.4 7.2 7 6.8 6.6
Page 173 and 174: than the RPT design, 155.45µm to 5
Page 175 and 176: have a very small nominal performan
Page 177 and 178: of these simulations fail to meet r
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Page 181 and 182: Chapter 6 Focus Application: Struct
Page 183 and 184: optical path differences between th
Page 185 and 186: Table 6.1: RWA disturbance model pa
Page 187 and 188: FRF Magnitude 10 1 10 0 10 −1 10
Page 189 and 190: Y Z Z X Y (a) w (c) w Y h Z Figure
Page 191: Table 6.6: Primary mirror propertie
Page 195 and 196: PSD OPD14 [m 2 /Hz] CumulativeOPD14
Page 197 and 198: 6.2 Design Parameters In order to a
Page 199 and 200: 6.2.2 Tuning The tuning parameters
Page 201 and 202: complex and the normal modes analys
Page 203 and 204: does not change with the design par
Page 205 and 206: (a) (b) (c) Figure 6-11: SCI TPF PT
Page 207 and 208: Table 6.14: Performance predictions
Page 209 and 210: performance trends similar to those
Page 211 and 212: Chapter 7 Conclusions and Recommend
Page 213 and 214: a statistical robustness measure su
Page 215 and 216: and the worst-case performance is a
Page 217 and 218: - Consider uncertainty analysis too
Page 219 and 220: Appendix A Gradient-Based Optimizat
Page 221 and 222: such that the gradient direction is
Page 223 and 224: the descent direction. In some case
Page 225 and 226: Bibliography [1] Jpl planet quest w
Page 227 and 228: [24] Nightsky Systems Carl Blaurock
Page 229 and 230: [48] S. C. O. Grocott, J. P. How, a
Page 231 and 232: [74] M. Lieber. Development of ball
Page 233 and 234: AIAA/ASME/ASCE/AHS/ASC Structures,
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