Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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unfettered by the Earth’s atmosphere [8]. 1.1.2 Planet Detection The second main goal of the Origins program is to search for life in other solar systems. This aim requires the detection and study of extra-solar, Earth-like planets. Currently, planet detection is done by ground-based telescopes that measure the motion of a star due to an orbiting planet. This technique has been successful in locating a number of Jupiter-sized planets, but is not sensitive enough to find smaller planets with mass comparable to that of the Earth. Therefore, the concept of a single instrument that detects Earth-like planets through their radiated heat and then performs a spectroscopic analysis to find signatures of carbon dioxide, water and ozone has been proposed [6]. There are two main challenges associated with this type of detection scheme. First, it is necessary to distinguish the radiated heat from that of the star. If the observing instrument is located on Earth, the heat from the planet is entirely swamped by the radiation from the Earth’s atmosphere and the ambient temperature of the optical elements. However, even if the instrument is placed in space, removing these sources of noise, the contrast ratio of the star to the planet is on the order of 10 7 . It is necessary, then, to find a way to separate the star radiation from that of the planet. A second challenge arises due to the small angular separation between the planet and the star. As discussed above, a high-angular resolution instrument is necessary to resolve the two sources. A nulling interferometer operating in the infrared (IR) has been proposed as the solution to the planet detection problem. The concept was first introduced by Bracewell [20]. He and his colleagues suggested using an interferometer to destruc- tively interfere star radiation captured by two apertures separated by a baseline [21]. The destructive interference results in the cancellation of the stellar flux over a broad waveband. If the instrument is designed correctly, the planet emission, which is slightly off-axis from the star, constructively interferes and is reinforced allowing the detection of the planet despite the stronger stellar radiation. Designs for nulling IR 20
interferometers have been proposed by Leger et al. [71], Mennesson and Mariotti [86] and Angel and Woolf [6]. 1.1.3 Technical Challenges While interferometers do provide solutions to the astrometry and planet detection problems, they also pose a significant set of engineering challenges. In order to pro- duce astrometric measurements, images or to achieve nulling, the interferometers must be able to acquire fringes. Interferometric fringes are the dark and light zones that result from the interference of two light sources (see [54] for a full discussion on interferometry). The acquisition of fringes is possible given that the distances the light travels through the two sides of the interferometer are equal to within a fraction of a wavelength. This optical metric is known as the optical path difference (OPD). Recall that the angular resolution of the system scales with the baseline. Large baseline can be achieved by placing the collecting and combining optics on a deploy- able or articulating truss structure or by flying them on individual spacecraft. The first configuration is known as a structurally-connected interferometer (SCI), while the latter is called a formation flown interferometer or a separated spacecraft interferometer [72]. A high-resolution interferometer operating in the visible regime requires that the light paths be equal to within a few nanometers over a baseline of ten or one hundred meters. In the case of the SCI architecture, flexibility in the support- ing structure and the presence of on-board disturbances place a large demand on the structural dynamics and control systems to achieve the required stability. The formation flown problem is also difficult, but its challenge lies in the knowledge of position and the control of the spacecraft formation. The work included in this thesis is focused on the SCI architecture. A second area of difficulty associated with space-based interferometers is system integration and test. A full system integration test (SIT) previous to launch is not practical due to the large contrast between the ground testing and operations environ- ments. The system is designed for operation in a vacuous, zero-gravity environment, but a ground test is influenced by gravity and atmospheric distortions. In the case of 21
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 18 and 19: 1.1 Space-Based Interferometry NASA
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
Page 69 and 70: 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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