Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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Table 1.2: Effect of simulation results on mission with tuning. # Simulation Action On-Orbit Action Result Prediction Performance 1 meet req launch good none success 2 meet req launch bad tune success 3 within bound launch good none success 4 within bound launch bad tune success eration of model uncertainty. Robust Performance Tailoring (RPT) refers to robust structural optimization in which robustness to a specified uncertainty model is in- cluded in the design objective. Robust Performance Tailoring for Tuning (RPTT) is an extension to RPT in which a design is optimized for performance, robustness and tunability. In this approach the tuning or adjustment on hardware is anticipated and explicitly planned for during the design optimization. 1.2.3 Research Objectives The main objective of this thesis is to develop a design methodology that is appropriate for high-performance and high-risk systems such as space-based interferometers. Available robust design tools are applied to this problem and evaluated for effective- ness. An extension to robust design that includes a formal tuning methodology is developed. The specific research goals, and thesis chapters in which they are ad- dressed, are as follows: • Apply structural optimization and the robust design framework and tools to space-based interferometer design. Identify control and noise parameters relevant to the design of precision structures for optical space systems [Chapters 2 and 3]. • Evaluate the performance of robust design techniques on high-performance and high-uncertainty systems [Chapter 3]. • Formalize an efficient tuning methodology that can be applied to flight hardware either during component testing or on-orbit operation to bring the system 28
performance within requirements [Chapter 4]. • Extend robust design techniques to include tailoring for tuning. Define the concept of tunability and incorporate the idea into robust optimization resulting in a formal relationship between structural tailoring and tuning [Chapter 5]. • Demonstrate through simulation that RPTT guarantees that the desired performance can be achieved given an accurate model of parametric uncertainty [Chapter 5]. • Apply the RPTT design methodology to an integrated model of a precision optical space structure. Choose appropriate tailoring and tuning parameters for the focus application [Chapter 6]. 1.3 Previous Work The research presented in this thesis draws from previous work in systems engineering, structural dynamics, integrated modeling, optimization and robust design. In this section a review of the relevant work in these fields is presented. Structural optimization is a well-developed field with a rich history. The advent of the digital computer made optimizing structural elements in the design process practical. Numerous examples can be found in the literature of sizing, shape and topology optimization [64]. Sizing optimization is typically applied to a truss structure and uses parameters such as member cross-sectional area and plate thickness as design variables. In shape optimization the topology is fixed, but the structural boundaries are allowed to change [56]. In topology optimization much less is known about the structure and the search is for optimal material distributions to yield a preliminary structural configuration [114, 73]. A large body of work exists on the application of sizing optimization to truss prob- lems to minimize mass subject to static constraints such as maximum stress. Many different optimization techniques have been applied to variations of this problem. The reader is referred to Kirsch [66] for an overview of gradient methods and examples. It 29
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 20 and 21: unfettered by the Earth’s atmosph
Page 22 and 23: the SCI, both the size and flexibil
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Page 26 and 27: Table 1.1: 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
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Page 71 and 72: Chapter 3 Robust Performance Tailor
Page 73 and 74: through careful and experienced mod
Page 75 and 76: described above. However, one can r
Page 77 and 78: 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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