Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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h1. h 1 w1 w 2 h 2 (a) Y (b) Figure 6-9: Schematic of TPF SCI tailoring parameters (a) XZ-plane (b) XY-plane. Geometric tailoring is also allowed in the XY-plane through the parameters w1 and w2. These parameters are the width of the batten frame at the end and in the center of the array as shown in Figure 6-9(b). The width tailoring is similar to the height tailoring in that the batten widths vary linearly in x and are symmetric about the center of the array. However, in this plane the tailoring is also symmetric about the x-axis, since the positions of the optics are not affected by the batten frame widths. There are constraints on the tailoring parameters in order to keep the design within practical limits. Both the height and width parameters are subject to a lower bound of 10 cm. In addition, the total mass of the system is constrained to be less than 4000 kg. This number is based on launch vehicle mass limits and ensures that the resulting design is realistic. 198 Z X X
6.2.2 Tuning The tuning parameters are chosen from a small subset of design variables that could practically be adjusted on hardware during component testing or on-orbit operation. Only two tuning parameters are used in order to keep the number of design variables required for the RPTT problem small. The parameters are the cross-sectional radius of the primary mirror supports, rPM and the corner frequency of the RWA isolator, fiso. The nominal tuning parameter values are listed in Table 6.11. Adjusting the parameter rPM is equivalent to changing the stiffness of the optical mount. Although the radii of the support bars are not easily adjusted on the hardware, this parameter is used to model a tunable optical mount stiffness. The isolator corner frequency parameter models a type of active isolator in which the corner frequency can be adjusted through some unspecified mechanism. Table 6.11: TPF SCI model tuning parameters. y Description y0 Units rPM XS radius of primary mirror support 0.05 m fiso RWAisolatorcornerfrequency 8 Hz The tuning parameters are subject to constraints that keep them within realistic limits. The radius of the primary mirror support structure is constrained by a lower bound of 1 cm to ensure that the primary mirrors stay connected to the truss. Although the radius of the optical mount supports does in fact affect the mass of the system, this parameter is not included in the mass constraint calculation. The reason for this omission is that in reality only the stiffness of the mount will change and not the physical properties of the support. The corner frequency of the RWA isolator is constrained to be between 2 and 10 Hz based on engineering judgment and experience. 6.2.3 Uncertainty The uncertainty parameters considered for the TPF SCI model are very similar to those in the development model and are listed in Table 6.12. The Young’s Modulus of 199
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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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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
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
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
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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
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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 and 174: than the RPT design, 155.45µm to 5
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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 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
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Page 201 and 202: complex and the normal modes analys
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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
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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Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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