Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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∆E 2 0.1 0.05 0 −0.05 −0.1 iso seg 1 z = 290.83µm iso seg 2 −0.1 −0.05 0 ∆E 1 0.05 0.1 (a) Uncertainty Bounds Test �y [kg] Source p1 p2 σHW # m1 m2 ∆L ∆U ∆L ∆U [µm] 1 0.0 0.0 nominal HW -0.1 0.1 -0.1 0.1 290.83 2 81.04 0.0 AO tune: iso-seg 1 -0.1 0.05 -0.62 0.1 346.47 3 0.0 81.05 AO tune: iso-seg 2 0.05 0.1 -0.1 0.62 264.07 (b) Figure 4-12: Isoperformance tuning, �p = � � E1 E2 : (a) uncertainty space and isoperformance contours, actual hardware parameters are denoted <strong>with</strong> black circle (b) table of hardware tests, uncertainty bounds and results. 142
Performing an AO tuning optimization about the uncertainty space of the first iso- segment results in the tuning configuration listed in the table under Test 2. These parameters are set on the hardware and a new performance measure of 346.47µm is obtained. This tuned configuration does not meet requirements, and in fact, is worse than the nominal hardware performance indicating that the hardware parameters are most likely on the second iso-segment. Performing an AO tuning optimization on the other iso-segment results in a tuning configuration that is symmetric to that found in Test 2. This tuning configuration successfully tunes the hardware performance to below the requirement ending the process after only three hardware tests. Comparing these results to the baseline tuning results in Table 4.3 it is interesting to note that the isoperformance tuning methodology results in a similar tuning configuration and leads to a hardware performance that is very close to the baseline tuned performance. Table 4.4: Uncertainty parameters for SCI development model. Name Description p0 E1 Young’s Modulus of truss 1 & 2 72 [GPa] ρ1 material density of truss 1 & 2 2900 [kg\m 3 ] m1 00 11 000 111 00 11 d1 d2 000 111 d2 00 11 000 111 00 11 000 111 00 11 000 111 m 2 E1 ρ1 E1 ρ1 E2 ρ2 E2 ρ2 Y d1 000 111 000 111 000 111 000 111 000 111 The development model tunes easily <strong>with</strong> isoperformance tuning due to the sym- metry in the model. The iso-contours are distinct mirror images of each other allowing a dramatic reduction of the uncertainty space from only one hardware measurement. In order to demonstrate the latter half of the algorithm, the search for intersecting subsets of the isoperformance space, a slight variation of the development model is considered. In this example the uncertainty parameters are Young’s Modulus, E1, and density, ρ1, of the beams in truss segments 1 and 2, as listed in Table 4.4 and shown in the accompanying figure. In addition, the uncertainty range is increased to ±50% about the nominal parameter values. Since the uncertainty model has changed 143 X
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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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Page 171 and 172: E 2 [Pa] 7.8 7.6 7.4 7.2 7 6.8 6.6
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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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Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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