Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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4-11 Isoperformance tuning algorithm. . . . . . . . . . . . . . . . . . . . . 139 4-12 Isoperformance tuning results on SCI model: p1 = E1, p2 = E2. . . . . 142 4-13 Isoperformance tuning results on SCI model: p1 = E1, p2 = ρ1. . . . . 145 5-1 Nominal, worst-case and tuned performance for all designs. . . . . . . 160 5-2 Modal energy: RPTT design. . . . . . . . . . . . . . . . . . . . . . . 162 5-3 Modal characteristics of first bending mode in all designs. . . . . . . . 164 5-4 Performance requirement vs uncertainty: all designs. . . . . . . . . . 166 5-5 RPTT design performance vs. weighting. . . . . . . . . . . . . . . . . 168 5-6 Hardware simulation algorithm. . . . . . . . . . . . . . . . . . . . . . 170 5-7 Monte Carlo uncertainty space, ∆ = 10%. . . . . . . . . . . . . . . . 171 5-8 PT, RPT and RPTT Simulation results, ∆ = 10%, σzreq = 220µm . . 172 5-9 Monte Carlo uncertainty space, ∆ = 21.5%. . . . . . . . . . . . . . . 174 5-10 PT, RPT and RPTT Simulation results, ∆ = 21.5%, σzreq = 330µm. . 176 5-11 RPTT design performance vs. weighting. . . . . . . . . . . . . . . . . 178 6-1 Schematic of TPF SCI Model. . . . . . . . . . . . . . . . . . . . . . . 182 6-2 SCI TPF plant finite element model. . . . . . . . . . . . . . . . . . . 183 6-3 RWA disturbance model. . . . . . . . . . . . . . . . . . . . . . . . . . 186 6-4 Transfer functions of Isolator models. . . . . . . . . . . . . . . . . . . 187 6-5 TPF SCI truss bay geometry. . . . . . . . . . . . . . . . . . . . . . . 189 6-6 Structural model schematic showing optical paths. . . . . . . . . . . . 193 6-7 Output PSD and cumulative variance from nominal TPF SCI design. 195 6-8 Mode Shapes of nominal SCI TPF design. . . . . . . . . . . . . . . . 196 6-9 Schematic of TPF SCI tailoring parameters. . . . . . . . . . . . . . . 198 6-10 Implementation flow for generating integrated TPF model. . . . . . . 202 6-11 SCI TPF PT design . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 6-12 SCI TPF RPT Design . . . . . . . . . . . . . . . . . . . . . . . . . . 205 6-13 SCI TPF RPTT Design . . . . . . . . . . . . . . . . . . . . . . . . . 206 6-14 Nominal, worst-case and tuned performances for all TPF SCI designs. 206 10
List of Tables 1.1 Effect of simulation results on mission. . . . . . . . . . . . . . . . . . 26 1.2 Effect of simulation results on mission with tuning. . . . . . . . . . . 28 2.1 Mass breakdown of SCI development model. . . . . . . . . . . . . . . 42 2.2 Natural frequencies and mode shapes of nominal SCI model . . . . . 43 2.3 Tailoring parameters for SCI sample problem. . . . . . . . . . . . . . 51 2.4 PT optimization results, J0 = 471 µm. . . . . . . . . . . . . . . . . . 61 2.5 SA algorithm parameters. . . . . . . . . . . . . . . . . . . . . . . . . 62 2.6 PT optimization: MC SQP optimizations. . . . . . . . . . . . . . . . 64 3.1 Uncertainty parameters for SCI development model. . . . . . . . . . . 76 3.2 Uncertainty propagation results: PT design. . . . . . . . . . . . . . . 78 3.3 Algorithm performance: anti-optimization. . . . . . . . . . . . . . . . 89 3.4 Algorithm performance: multiple model, βi =1/npv. . . . . . . . . . . 90 3.5 Algorithm performance: statistical robustness, α =0.5. . . . . . . . . 91 4.1 Tuning parameters for SCI development model. . . . . . . . . . . . . 111 4.2 Tuning performance summary for PT and RPT designs. . . . . . . . 111 4.3 Hardware Model Data. . . . . . . . . . . . . . . . . . . . . . . . . . . 131 4.4 Uncertainty parameters for SCI development model. . . . . . . . . . . 143 4.5 Hardware Model Data: Example 2. . . . . . . . . . . . . . . . . . . . 144 4.6 Tuning results on fifty hardware simulations. . . . . . . . . . . . . . . 147 5.1 Algorithm performance: RPTT, α =0.0, ∆ = 0.1. . . . . . . . . . . . 158 5.2 Performance and design parameters for optimal designs. . . . . . . . . 159 5.3 Performance and parameters for tuned worst-case realizations. . . . . 159 6.1 RWA disturbance model parameters. . . . . . . . . . . . . . . . . . . 185 6.2 TPF SCI model mass breakdown. . . . . . . . . . . . . . . . . . . . . 188 6.3 Truss properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 6.4 Truss element and grid numbering. . . . . . . . . . . . . . . . . . . . 189 6.5 Bus model elements and properties. . . . . . . . . . . . . . . . . . . . 190 6.6 Primary mirror properties. . . . . . . . . . . . . . . . . . . . . . . . . 191 6.7 Primary mirror mount properties. . . . . . . . . . . . . . . . . . . . . 191 6.8 TPF SCI instrument elements. . . . . . . . . . . . . . . . . . . . . . . 192 6.9 Critical modes of nominal TPF SCI design. . . . . . . . . . . . . . . . 195 6.10 TPF SCI model tailoring parameters. . . . . . . . . . . . . . . . . . . 197 11
Page 1: Dynamic Tailoring and Tuning for Sp
Page 4 and 5: Acknowledgments This work was suppo
Page 6 and 7: 3.2 RPT Formulation . . . . . . . .
Page 9: List of Figures 1-1 Timeline of Ori
Page 13 and 14: Nomenclature Abbreviations ACS atti
Page 15: dk optimization search direction f
Page 18 and 19: 1.1 Space-Based Interferometry NASA
Page 20 and 21: unfettered by the Earth’s atmosph
Page 22 and 23: the SCI, both the size and flexibil
Page 24 and 25: maybethatitbecomescertain that the
Page 26 and 27: Table 1.1: Effect of simulation res
Page 28 and 29: Table 1.2: Effect of simulation res
Page 30 and 31: has been found that structural desi
Page 32 and 33: precision telescope structure for m
Page 34 and 35: attractive, and more conservative a
Page 36 and 37: to solve the performance tailoring
Page 39 and 40: Chapter 2 Performance Tailoring A c
Page 41 and 42: 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
Page 47 and 48: 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 =
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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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the new tuning configuration is ver
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Performing an AO tuning optimizatio
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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
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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