Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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updating for tuning is developed and demonstrated on the SCI development model. The tuning methods are compared to one another for performance and testing cost over a large sample of hardware simulations, and it is shown that only isoperformance tuning consistently requires a small number of hardware tests and is successful across the sample space. 4.1 Tuning Formulation In this thesis, dynamic tuning is defined as adjustments made to the hardware once it is built to affect the performance and bring it within requirements. Consider a situation in which models predict that the system meets performance requirements across most of the uncertainty space, but not at the extremes. If only one such system is built, there is a possibility that the physical system may lie outside the area in which the RPT design meets requirements. However, if there are tuning adjustments that can be made to the hardware at this stage to affect the performance, it may be possible to improve the system performance to within the desired range. Due to model inaccuracies and manufacturing discrepancies, situations such as this arise frequently in practice. Engineers often make ad hoc adjustments to hardware to improve performance or bring a component or entire system within specifications. However, this type of tuning is not formalized, and it is difficult to find references on these practices. Dynamic tuning is a hardware-based procedure, and therefore, the tuning parameters must be chosen carefully. As in the case of performance tailoring, the parameters must have some effect on the performance metric. The range of this effect, or the difference between the tuned and untuned performance, is referred to as the tuning authority. In addition, the parameters must be easy to adjust on the hardware, signif- icantly limiting the possible design variables compared to those available for tailoring. For example, although it has been shown previously that the cross-sectional diameters of the truss members are good tailoring parameters for the SCI development model, they are not well-suited for tuning as there is not an easy way to change these values 108
on a physical truss. Since tailoring takes place on models it is easy to try a range of truss diameters and optimize the design in this manner. However, tuning with these parameters requires physically cutting into the existing truss and replacing members. This procedure is expensive and may have undesired global effects on the performance resulting in mission delays. One example of dynamic tuning on hardware is found in a recent paper by Glaese and Bales [46]. The authors study the effects of a range of structural adjustments to a gossamer structure. In the paper, they call the process dynamic tailoring because the goal is to affect the dynamic performance of the membrane. However, in the context of this thesis, their efforts are classified as dynamic tuning since the authors make adjustments to the hardware itself. A 80-inch major diameter, 8-inch minor diameter, pre-formed Kapton torus is the structure used to demonstrate the dynamic tuning. The authors choose four possible tuning parameters: inert masses added at random locations on the structure to minimize the disturbance forces by increasing the effective impedance, tuned mass dampers to reduce narrow-band disturbance effects, piezo-electro actuators and sensors that enhance broadband structural damping, and shunts added to the piezo-electric elements to actively control the flow of energy in the structure. All of these techniques are good examples of tuning parameters since they can be added to the structure and adjusted with minimal disruption to the hardware itself. The formulation of the tuning optimization problem is similar to performance tailoring with the major distinction being that the system performance is now a function of the tailoring, �x, uncertainty, �p, and tuning parameters, �y, but the tuning parameters are the only design variables: min f (˜x, �y, ˜p) �y (4.1) s.t. �g (˜x, �y) ≤ 0 where ˜x and ˜p are the actual values of the tailoring and uncertainty parameters realized in the hardware and g (˜x, �y) are constraints on the design variables. The 109
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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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Page 59 and 60: initial design variable state, x =
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Page 63 and 64: # Designs 25 20 15 10 5 Accepted, b
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Page 73 and 74: through careful and experienced mod
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Page 77 and 78: ic, σz(�x, �p), that is depend
Page 79 and 80: Magnitude, OPD/F x [µm/N] Magnitud
Page 81 and 82: % Energy 100 90 80 70 60 50 40 30 2
Page 83 and 84: metric to the cost function. Note,
Page 85 and 86: tion: ∂hi (z,�x, �pi) ∂�x
Page 87 and 88: values are chosen from their statis
Page 89 and 90: Table 3.3: Algorithm performance: a
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
Page 105 and 106: The requirement chosen here is some
Page 107: Chapter 4 Dynamic Tuning Robust Per
Page 111 and 112: Table 4.1: Tuning parameters for SC
Page 113 and 114: m 2 [kg] J ∗ # # time y ∗ [kg]
Page 115 and 116: m 2 [kg] 800 700 600 500 400 300 20
Page 117 and 118: configuration than the untuned, but
Page 119 and 120: Norm. Cum. Var. [µm 2 ] PSD [µm 2
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Page 123 and 124: is considered. 4.2.1 Hardware-only
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Page 129 and 130: for tailoring, but tuning parameter
Page 131 and 132: tained by randomly choosing paramet
Page 133 and 134: p [GPa] y ∗ [kg] Performance [µm
Page 135 and 136: # Func. Evals Performance RMS (µm)
Page 137 and 138: tion changes in the updated solutio
Page 139 and 140: Data: initial iterate, p0, performa
Page 141 and 142: the new tuning configuration is ver
Page 143 and 144: Performing an AO tuning optimizatio
Page 145 and 146: Uncertainty Bounds Test �y [kg] S
Page 147 and 148: Table 4.6: Tuning results on fifty
Page 149 and 150: eters are discussed. The optimizati
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Page 153 and 154: MPC optimization by allowing a diff
Page 155 and 156: where the notation yij indicates th
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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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