Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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Acknowledgments This work was supported by a Michelson Fellowship from the Jet Propulsion Labo- ratory with SharonLeah Brown as MIT Fiscal Officer. 4
Contents 1 Introduction 17 1.1 Space-Based Interferometry . . . . . . . . . . . . . . . . . . . . . . . 18 1.1.1 Astrometry and Imaging . . . . . . . . . . . . . . . . . . . . . 18 1.1.2 Planet Detection . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.1.3 Technical Challenges . . . . . . . . . . . . . . . . . . . . . . . 21 1.1.4 Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 1.2.2 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.2.3 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . 28 1.3 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.4 Thesis Roadmap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2 Performance Tailoring 39 2.1 PT Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.2 SCI Development Model . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.3 PT Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.3.1 Performance Metric . . . . . . . . . . . . . . . . . . . . . . . . 46 2.3.2 Performance Gradients . . . . . . . . . . . . . . . . . . . . . . 48 2.3.3 Design Variables . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.3.4 Finite Element Gradients . . . . . . . . . . . . . . . . . . . . . 52 2.3.5 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.4 Optimization Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.4.1 Sequential Quadratic Programming . . . . . . . . . . . . . . . 55 2.4.2 Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . 57 2.5 Performance Tailoring Results . . . . . . . . . . . . . . . . . . . . . . 60 2.5.1 Comparison of Optimization Algorithms . . . . . . . . . . . . 61 2.5.2 Performance Tailored Design . . . . . . . . . . . . . . . . . . . 64 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3 Robust Performance Tailoring 71 3.1 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.1.1 Uncertainty Models . . . . . . . . . . . . . . . . . . . . . . . . 73 3.1.2 Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . . . 73 3.1.3 Example: SCI Development Model . . . . . . . . . . . . . . . 76 5
Page 1: Dynamic Tailoring and Tuning for Sp
Page 6 and 7: 3.2 RPT Formulation . . . . . . . .
Page 9 and 10: List of Figures 1-1 Timeline of Ori
Page 11 and 12: List of Tables 1.1 Effect of simula
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 =
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
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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
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AIAA/ASME/ASCE/AHS/ASC Structures,
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