Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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1.1 Space-Based Interferometry NASA’s Origins program is an on-going effort aimed at exploring both the nature of the universe and its inhabitants. The specific goals of the program are to answer questions about the origin of our universe and to search for other Earth-like plan- ets in nearby solar systems. The program consists of a family of missions that span over twenty years (Figure 1-1). The earliest telescopes, including the Hubble Space Telescope (HST), are in operation and provide valuable information to scientists and astronomers at the time of this writing. Upcoming missions include SIM, JWST, and TPF (interferometer and coronograph). All three of these missions have ambi- tious science goals that push the boundaries of engineering across many disciplines, including optics, structures and control. Figure 1-1: Timeline of Origins missions [3]. 1.1.1 Astrometry and Imaging In order to achieve the first of Origins’ goals, mapping the universe and exploring its origins, a telescope with very high angular resolution is necessary. Angular resolution 18
is an optical metric that describes the accuracy of an optical system. It is defined as the minimum resolvable angular separation between two objects [54]. Consider two objects located far from a telescope, but very close to each other. A low-angular resolution telescope is unable to resolve the two objects, and they appear to an observer as a single blurred object. A telescope with high angular resolution, however, presents an image of two distinct light sources. One challenge faced in the design of these telescopes is the limitations imposed by a trade-off between system mass and optical performance. In the case of a monolithic telescope, such as HST, the angular resolution of the system scales proportionally with the diameter of the primary mirror. However, as the primary mirror becomes larger it also becomes more massive and more expensive to manufacture and launch. Therefore mass and cost budgets limit the angular resolution that can be achieved with a monolithic system. One alternative to the monolithic telescope design that has generated much inter- est over the past few decades is astronomical interferometers [105, 8]. These instru- ments provide high resolution imaging and astrometry at a significant savings of mass and volume compared to a monolithic design. Interferometers function by combining the light gathered by two or more smaller apertures separated by a large baseline. The angular resolution of an interferometer increases proportionally to the length of this baseline. Therefore, it is not necessary to manufacture and launch very large mirrors. Instead, it is only necessary to place collecting mirrors sufficiently far away from each other to achieve the desired performance. A number of ground-based stellar interferometers are currently in operation. These include the Keck Observatory [29] on Mauna Kea in Hawaii, the Sydney University Stellar Interferometer [33, 34] (SUSI) in Australia, and the Navy Prototype Optical Interferometer [9] (NPOI) in Flagstaff, Arizona. These systems have already provided valuable astronomical data [58, 59, 30, 38, 77, 32] such as stellar images, astromet- ric measurements of stellar positions and stellar angular diameters. However, the optical performance of these ground interferometers is limited by atmospheric distor- tions. The next logical step is to place these systems in space where they can operate 19
Page 1: Dynamic Tailoring and Tuning for Sp
Page 4 and 5: Acknowledgments This work was suppo
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 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
Page 63 and 64: # Designs 25 20 15 10 5 Accepted, b
Page 65 and 66: does not provide information on why
Page 67 and 68: 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
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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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