Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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at α =0.1 to further explore the trade between robustness and tuning authority. The uncertainty parameters used in this set of simulations are plotted in Figure 5-9. Note that the bounds on the uncertainty parameters are increased compared to those in the corresponding figure from the previous set of simulations, Figure 5-7. The 200 samples do not cover the entire space evenly, but do provide decent coverage across the grid. E 2 [Pa] 8.5 8 7.5 7 6.5 6 x 10 10 6 6.5 7 7.5 8 8.5 x 10 10 E [Pa] 1 Figure 5-9: Uncertainty points considered in Monte Carlo hardware simulation study, ∆=21.5%. The nominal and tuned perfromances from the hardware simulations are plotted in Figure 5-10 along with a bar chart indicating the success rate of each design. The performance plot (Figure 5-10(a)) is similar in trend to that from the previous set of simulations (Figure 5-8(a)), but there are some key differences. First, the range of the PT nominal performance values is much higher due to the increase in uncertainty bounds. The PT hardware simulations range from 101.87µm allthe way to 2591.10µm, over twice the value of the maximum at ∆ = 10%. A similar increase occurs in the tuned range as well (112.98µm to 740.47µm), and the maximum tuned value is over twice that of the requirement. The RPT design simulations 174
have a very small nominal performance range (341.43µm to 369.1µm) indicating that the design is quite robust to uncertainty. Unfortunately, the robustness comes at the price of nominal performance and none of the hardware simulations meet the requirement. Upon tuning these hardware simulations the performance range shrinks further (331µm to 349.63µm) due to a lack of tuning authority in the robust design, and all of the tuned designs also fail to meet the requirement. The two RPTT designs are differentiated in the plot by the value of α placed parenthetically in the label. As seen in the previous simulation, both RPTT designs show a blend of the PT and RPT design characteristics. At α = 0, the nominal performance range (232.52µm to 565.5µm) is greater than that of the RPT design but much smaller than that of the PT design. This result indicates that even with no weight on the robustness cost the RPTT formulation produces a design that is dra- matically less sensitive to uncertainty than the PT optimization. The RPTT design also has greater tuning authority than the RPT design, and the tuned performances range from 237.67µm to 312.45µm. The maximum value of this range is well below the requriement of 330µm, so that all of the tuned RPTT designs are successful. The second RPTT design, acheived through an RPTT optimization with α =0.1, shows increased robustness to uncertainty with a nominal performance ranging from 261.10µm to 448.9µm. The range of tuned performances is also smaller than that in the first RPTT design starting at 274.30µm and continuing to just under the requirement at 320.15µm. All of the design simulations are again tunable to below the requirement, but the RPTT design with α =0.1 issuperiortothatforα =0in that it is just tunable enough and therefore more robust to uncertainty. The tuning authority and robustness is balanced such that the design is perfectly tailored to meet the requirement. The accompanying bar chart, Figure 5-10(b), presents the percent of successful simulations for each design. As seen in the previous hardware simulation (Fig- ure 5-8(b)) only the RPTT designs are successful for all of the simulations, and the RPT design never meets requirements. At the higher uncertainty level just over 70% of the PT simulations succeed, with 51% requiring hardware tuning. Over a quarter 175
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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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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
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Page 147 and 148: Table 4.6: Tuning results on fifty
Page 149 and 150: eters are discussed. The optimizati
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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
Page 165 and 166: configuration. The tuned configurat
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Page 171 and 172: E 2 [Pa] 7.8 7.6 7.4 7.2 7 6.8 6.6
Page 173: than the RPT design, 155.45µm to 5
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Page 181 and 182: Chapter 6 Focus Application: Struct
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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 and 192: Table 6.6: Primary mirror propertie
Page 193 and 194: OP1 STAR Z OP2 OP3 Coll 1 Coll 2 Bu
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
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Page 205 and 206: (a) (b) (c) Figure 6-11: SCI TPF PT
Page 207 and 208: Table 6.14: Performance predictions
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Page 211 and 212: Chapter 7 Conclusions and Recommend
Page 213 and 214: a statistical robustness measure su
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Page 217 and 218: - Consider uncertainty analysis too
Page 219 and 220: Appendix A Gradient-Based Optimizat
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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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