Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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6.11 TPF SCI model tuning parameters. . . . . . . . . . . . . . . . . . . . 199 6.12 TPF SCI model uncertainty parameters. . . . . . . . . . . . . . . . . 200 6.13 Design parameters for nominal and optimal TPF SCI designs. . . . . 204 6.14 Performance predictions for all TPF SCI designs. . . . . . . . . . . . 207 6.15 Tuning parameters for tuned worst-case TPF SCI realizations. . . . . 207 12
Nomenclature Abbreviations ACS attitude control system AO anti-optimization BSD barrier steepest descent DOCS Disturbance Optics Controls Structures CSI control-structures interaction CTE coefficient of thermal expansion ESO European Southern Observatory FEM finite element model FRF frequency response function GSE governing sensitivity equation HST Hubble Space Telescope JPL Jet Propulsion Laboratory JWST James Webb Space Telescope LOS line of sight LQR lineaer quadratic regulator IR infrared MC Monte Carlo MM multiple model MPC Model Predictive Control MUF model uncertainty factor NGST Next Generation Space Telescope OPD optical pathlength difference PM primary mirror PSD power spectral density PT Performance Tailoring QP quadratic programming RMS root mean square RPT Roubst Performance Tailoring RPTT Robust Performance Tailoring for Tuning RWA reaction wheel assembly 13
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 and 10: List of Figures 1-1 Timeline of Ori
Page 11: List of Tables 1.1 Effect of simula
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 =
Page 61 and 62: 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
Page 155 and 156:
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
Page 179 and 180:
and that it is the only design meth
Page 181 and 182:
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
Page 213 and 214:
a statistical robustness measure su
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and the worst-case performance is a
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- Consider uncertainty analysis too
Page 219 and 220:
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
Page 225 and 226:
Bibliography [1] Jpl planet quest w
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[24] Nightsky Systems Carl Blaurock
Page 229 and 230:
[48] S. C. O. Grocott, J. P. How, a
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[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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