Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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parameters obtained by tuning the model and the performance variance of the nominal and tuned models as well as that of the tuned hardware. These results are plotted graphically in Figure 4-9(b) with open circles, filled circles and black x’s representing the nominal model, tuned model and tuned hardware performance RMS, respectively. The tuned hardware preformance is obtained by applying the tuning parameters resulting from a given tuning algorithm to the hardware simulation. The requirement is indicated by the solid line, and the untuned hardware performance by the dashed line. It is clear from both the table and the figure that none of the model-only tuning schemes result in a tuning configuration that successfully tunes this hardware simulation since none of the x’s lie below the requirement line. This result is not surprising for the nominal, AO and worst-case model methods since there no hardware data are used at all in those techniques. Both the nominal and worst-case model tuning provide tuning configurations that improve the model performance, but make the hardware performance worse. The AO tuning fails to find a tuning configuration that improves all of the uncertainty vertices. The untuned configuration is actually the most robust since the uncertainty space is so large. Therefore the nominal and tuned model performance (open and filled circles) are directly on top of each other and the hardware performance (black x) stays at its nominal value. It is a bit more surprising that optimal model tuning also fails to improve hardware performance. The optimal model has uncertainty parameters chosen specifically to result in a model prediction equal to the hardware performance. This goal is met as indicated in Figure 4-9(b) by the fact that the open circle is directly on the dashed line for the optimized model case. However, despite the fact that the performances are the same, the tuned configuration obtained from the optimized model does not also tune the hardware. In fact, in the figure, the x associated with this method is well above the HW performance line indicating that tuning has made the performance worse. This result suggests that the uncertainty parameters found by the optimization are a non-unique solution and there are multiple uncertainty configurations that result in the same performance. This problem of uniqueness is well-known in the field of 132
p [GPa] y ∗ [kg] Performance [µm] E1 E2 m1 m2 Model Tuned Model Tuned HW NomMod 72 72 28.61 0.0 263.87 259.07 317.19 AOMod 72 72 0.0 0.0 263.87 263.87 290.83 WCMod 64.8 79.2 81.04 0.0 306.86 273.32 346.46 OptMod 65.5 76.7 59.92 0.0 290.83 262.81 332.79 Performance RMS [µm] 350 340 330 320 310 300 290 280 270 260 250 Model Tuned Model Tuned HW HW performance Requirement (a) NomMod AOMod WCMod OptMod (b) Figure 4-9: Results of model-only tuning algorithms (a) table of results (b) nominal model (open circle), tuned model (filled circle) and tuned hardware (black x) performance, σHW0 = 290.83µm (dashed line) and σreq = 280µm (solid line). 133
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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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Page 91 and 92: Statistical Robustness The statisti
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Page 95 and 96: (Figure 3-6(b)). The nominal perfor
Page 97 and 98: Norm. Cum. Var. [µm 2 ] PSD [µm 2
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Page 119 and 120: Norm. Cum. Var. [µm 2 ] PSD [µm 2
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Page 139 and 140: Data: initial iterate, p0, performa
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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
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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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