Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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3.2 RPT Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.2.1 Anti-optimization . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.2.2 Multiple Model . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.2.3 Statistical Robustness Metric . . . . . . . . . . . . . . . . . . 86 3.3 RPT Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.3.1 Algorithm comparisons . . . . . . . . . . . . . . . . . . . . . . 88 3.3.2 Objective function comparisons . . . . . . . . . . . . . . . . . 93 3.3.3 Comparison to PT design . . . . . . . . . . . . . . . . . . . . 96 3.4 Limitations: Design Regimes . . . . . . . . . . . . . . . . . . . . . . . 102 3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 4 Dynamic Tuning 107 4.1 Tuning Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 4.1.1 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 4.1.2 Design Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.2 Tuning in Practical Application . . . . . . . . . . . . . . . . . . . . . 122 4.2.1 Hardware-only Tuning . . . . . . . . . . . . . . . . . . . . . . 123 4.2.2 Model-only Tuning . . . . . . . . . . . . . . . . . . . . . . . . 127 4.2.3 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 4.3 Isoperformance Updating for Tuning . . . . . . . . . . . . . . . . . . 134 4.3.1 Model Updating . . . . . . . . . . . . . . . . . . . . . . . . . . 136 4.3.2 Isoperformance . . . . . . . . . . . . . . . . . . . . . . . . . . 137 4.3.3 Tuning Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 138 4.3.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 4.3.5 Comparison of Tuning Methods . . . . . . . . . . . . . . . . . 146 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 5 Robust Performance Tailoring with Tuning 151 5.1 RPTT Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 5.2 SCI Development Model . . . . . . . . . . . . . . . . . . . . . . . . . 156 5.2.1 Optimization Algorithms . . . . . . . . . . . . . . . . . . . . . 157 5.2.2 Comparison to PT and RPT Designs . . . . . . . . . . . . . . 158 5.2.3 Design Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . 165 5.3 RPTT Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 5.3.1 Tuning Authority . . . . . . . . . . . . . . . . . . . . . . . . . 167 5.3.2 Hardware Simulations . . . . . . . . . . . . . . . . . . . . . . 169 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 6 Focus Application: Structurally Connected TPF 181 6.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 6.1.1 Reaction Wheel Assembly Disturbances . . . . . . . . . . . . . 183 6.1.2 Vibration Isolation . . . . . . . . . . . . . . . . . . . . . . . . 185 6.1.3 Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 6.1.4 Attitude Control System . . . . . . . . . . . . . . . . . . . . . 194 6.1.5 Integrated Model Nominal Performance . . . . . . . . . . . . . 194 6
6.2 Design Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 6.2.1 Tailoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 6.2.2 Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 6.2.3 Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 6.3 Optimization Implementation . . . . . . . . . . . . . . . . . . . . . . 200 6.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 7 Conclusions and Recommendations 211 7.1 Thesis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 7.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 7.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 A Gradient-Based Optimization 219 A.1 Steepest Descent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 A.1.1 Stepsize Selection . . . . . . . . . . . . . . . . . . . . . . . . . 221 A.2 Newton’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 A.3 Conjugate Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 7
Page 1: Dynamic Tailoring and Tuning for Sp
Page 4 and 5: Acknowledgments This work was suppo
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
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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
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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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Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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