Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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Bibliography [1] Jpl planet quest website: Space interferometry mission [online, cited February 13, 2004]. Available from: http://planetquest.jpl.nasa.gov/SIM/sim index.html. [2] Jpl planet quest website: Terrestrial planet finder [online, cited February 13, 2004]. Available from: http://planetquest.jpl.nasa.gov/TPF/tpf index.html. [3] Nasa origins website [online, cited February 13, 2004]. Available from: http://origins.jpl.nasa.gov/missions/index.html. [4] Northern lights optics [online, cited September 20, 2004]. Available from: http://www.minerals.sk.ca/atm design/materials/ule.html. [5] E. Anderson. <strong>Robust</strong> Placement of Actuators and Dampers for Structural Control. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, October 1993. [6] J.R.P. Angel and N. J. Woolf. An imaging nulling interferometer to study extrasolar planets. The Astrophysics Journal, 475(1):373–379, January 1997. [7] D. K. Anthony and S. J. Elliott. On reducing vibration transmission in a two-dimensional cantilever truss structure using geometric optimization and active vibration control techniques. Journal of Accoustical Society of America, 110(2):1191–1194, 2001. [8] J. T. Armstrong, D. J. Hutter, K. J. Johnston, and D. Mozurkewich. Stellar optical interferometry in the 1990s. Physics Today, 48:42–49, May 1995. [9] J.T. Armstrong, D. Mozurkewich, L. J. Rickard, D. J. Hunter, J. A. Benson, P. F. Bowers, N. M. Elias II, C. A. Hummel, K. J. Johnston, D. F. Buscher, J. H. Clark III, L. Ha, L.-C. Ling, N. M. White, and R. S. Simon. The navy prototype optical interferometer. The Astrophysical Journal, 496:550–571, March 1998. [10] A. Ashkenazi and A. E. Bryson. Control logic for parameter insensitivity and disturbance attenuation. Journal of Guidance, Control and Dynamics, 5(4):383–388, July-August 1982. 225
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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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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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Page 181 and 182: Chapter 6 Focus Application: Struct
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Page 185 and 186: Table 6.1: RWA disturbance model pa
Page 187 and 188: FRF Magnitude 10 1 10 0 10 −1 10
Page 189 and 190: Y Z Z X Y (a) w (c) w Y h Z Figure
Page 191 and 192: Table 6.6: Primary mirror propertie
Page 193 and 194: OP1 STAR Z OP2 OP3 Coll 1 Coll 2 Bu
Page 195 and 196: PSD OPD14 [m 2 /Hz] CumulativeOPD14
Page 197 and 198: 6.2 Design Parameters In order to a
Page 199 and 200: 6.2.2 Tuning The tuning parameters
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Page 205 and 206: (a) (b) (c) Figure 6-11: SCI TPF PT
Page 207 and 208: Table 6.14: Performance predictions
Page 209 and 210: performance trends similar to those
Page 211 and 212: Chapter 7 Conclusions and Recommend
Page 213 and 214: a statistical robustness measure su
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Page 217 and 218: - Consider uncertainty analysis too
Page 219 and 220: Appendix A Gradient-Based Optimizat
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Page 223: the descent direction. In some case
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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