Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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anges from 300µ m to 3650µ, while in the RPT performances range from 273µm to only 665µm. The shorter range suggests that the tuning parameters have less of an effect on the performance of the RPT design. It is clear from these reults that tuning the worst-case uncertainty realization has a significant effect on the performance. In the following sections, a physical understanding of how the tuning masses improve the performance is obtained by investigation of the output PSDs and energy distribution among modes. Physical Interpretation: PT <strong>Tuning</strong> To begin, consider the worst-case PT design in both the untuned and tuned config- urations. As seen from Table 4.2 and Figure 4-1, a 77% reduction in performance variance is achieved by adding 175 kg of tuning mass to the positive-x arm of the in- terferometer. The plot of the tuning space (Figure 4-1(b)) shows that this particular tuning configuration is a global optimum. The RMS increases as mass is added to the negative-x arm or if more/less mass is added to the positive-x arm. To understand why this tuning configuration has such an impact on the performance consider the energy information presented in Figure 4-3. The first plot (Figure 4-3(a)) is the normalized cumulative variance and output PSDs for both the untuned (solid line) and tuned (dashed line) worst-case PT systems. The largest differences in energy distribution between the two systems occur at low frequencies. The second mode, which accounts for almost all of the RMS in the untuned case, has only a small effect in the tuned system, and the third mode is at a lower frequency in the tuned system. The bar chart, (Figure 4-3(b)), shows the percent of total energy in each of the critical modes. It is clear that the addition of tuning mass shifts the energy from the second mode to the third mode. The accom- panying table lists the natural frequencies and energy of each of the critical modes. The absolute energy values show that not only has the energy been redistributed among the modes, but the total energy in the modes is greatly reduced. For example the second mode has 1325µm of RMS in the untuned PT design, but only 14.96µm in the tuned configuration. The third mode accounts for more energy in the tuned 114
m 2 [kg] 800 700 600 500 400 300 200 100 J ∗ # # time y ∗ [kg] Algorithm [µm] iter fvals [sec] m1 m2 SA 298.28 68 1980 18.97 6.77 0.02 SQP 273.32 6 18 18.36 81.05 0.0 MC SQP 273.32 84 259 264.3 80.99 0.0 ES 273.32 N/A 1271 12.42 80.05 0.0 (a) 0 0 200 400 600 800 m [kg] 1 (b) Figure 4-2: RPT AO worst-case tuning results: (a) table of algorithm performance results (b) solution space, 2D surface view. 115 650 600 550 500 450 400 350 300
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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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Page 91 and 92: Statistical Robustness The statisti
Page 93 and 94: Performance [µm] 1400 1200 1000 80
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 101 and 102: Y−coordinate [m] Y−coordinate [
Page 103 and 104: RMS performance, [µm] 400 350 300
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Page 111 and 112: Table 4.1: Tuning parameters for SC
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Page 119 and 120: Norm. Cum. Var. [µm 2 ] PSD [µm 2
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Page 133 and 134: p [GPa] y ∗ [kg] Performance [µm
Page 135 and 136: # Func. Evals Performance RMS (µm)
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Page 139 and 140: Data: initial iterate, p0, performa
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Page 153 and 154: MPC optimization by allowing a diff
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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
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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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