Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

More documents

Recommendations

Info

4-11 Isoperformance tuning algorithm. . . . . . . . . . . . . . . . . . . . . 139 4-12 Isoperformance tuning results on SCI model: p1 = E1, p2 = E2. . . . . 142 4-13 Isoperformance tuning results on SCI model: p1 = E1, p2 = ρ1. . . . . 145 5-1 Nominal, worst-case and tuned performance for all designs. . . . . . . 160 5-2 Modal energy: RPTT design. . . . . . . . . . . . . . . . . . . . . . . 162 5-3 Modal characteristics of first bending mode in all designs. . . . . . . . 164 5-4 Performance requirement vs uncertainty: all designs. . . . . . . . . . 166 5-5 RPTT design performance vs. weighting. . . . . . . . . . . . . . . . . 168 5-6 Hardware simulation algorithm. . . . . . . . . . . . . . . . . . . . . . 170 5-7 Monte Carlo uncertainty space, ∆ = 10%. . . . . . . . . . . . . . . . 171 5-8 PT, RPT and RPTT Simulation results, ∆ = 10%, σzreq = 220µm . . 172 5-9 Monte Carlo uncertainty space, ∆ = 21.5%. . . . . . . . . . . . . . . 174 5-10 PT, RPT and RPTT Simulation results, ∆ = 21.5%, σzreq = 330µm. . 176 5-11 RPTT design performance vs. weighting. . . . . . . . . . . . . . . . . 178 6-1 Schematic of TPF SCI Model. . . . . . . . . . . . . . . . . . . . . . . 182 6-2 SCI TPF plant finite element model. . . . . . . . . . . . . . . . . . . 183 6-3 RWA disturbance model. . . . . . . . . . . . . . . . . . . . . . . . . . 186 6-4 Transfer functions of Isolator models. . . . . . . . . . . . . . . . . . . 187 6-5 TPF SCI truss bay geometry. . . . . . . . . . . . . . . . . . . . . . . 189 6-6 Structural model schematic showing optical paths. . . . . . . . . . . . 193 6-7 Output PSD and cumulative variance from nominal TPF SCI design. 195 6-8 Mode Shapes of nominal SCI TPF design. . . . . . . . . . . . . . . . 196 6-9 Schematic of TPF SCI tailoring parameters. . . . . . . . . . . . . . . 198 6-10 Implementation flow for generating integrated TPF model. . . . . . . 202 6-11 SCI TPF PT design . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 6-12 SCI TPF RPT Design . . . . . . . . . . . . . . . . . . . . . . . . . . 205 6-13 SCI TPF RPTT Design . . . . . . . . . . . . . . . . . . . . . . . . . 206 6-14 Nominal, worst-case and tuned performances for all TPF SCI designs. 206 10
List of Tables 1.1 Effect of simulation results on mission. . . . . . . . . . . . . . . . . . 26 1.2 Effect of simulation results on mission with tuning. . . . . . . . . . . 28 2.1 Mass breakdown of SCI development model. . . . . . . . . . . . . . . 42 2.2 Natural frequencies and mode shapes of nominal SCI model . . . . . 43 2.3 Tailoring parameters for SCI sample problem. . . . . . . . . . . . . . 51 2.4 PT optimization results, J0 = 471 µm. . . . . . . . . . . . . . . . . . 61 2.5 SA algorithm parameters. . . . . . . . . . . . . . . . . . . . . . . . . 62 2.6 PT optimization: MC SQP optimizations. . . . . . . . . . . . . . . . 64 3.1 Uncertainty parameters for SCI development model. . . . . . . . . . . 76 3.2 Uncertainty propagation results: PT design. . . . . . . . . . . . . . . 78 3.3 Algorithm performance: anti-optimization. . . . . . . . . . . . . . . . 89 3.4 Algorithm performance: multiple model, βi =1/npv. . . . . . . . . . . 90 3.5 Algorithm performance: statistical robustness, α =0.5. . . . . . . . . 91 4.1 Tuning parameters for SCI development model. . . . . . . . . . . . . 111 4.2 Tuning performance summary for PT and RPT designs. . . . . . . . 111 4.3 Hardware Model Data. . . . . . . . . . . . . . . . . . . . . . . . . . . 131 4.4 Uncertainty parameters for SCI development model. . . . . . . . . . . 143 4.5 Hardware Model Data: Example 2. . . . . . . . . . . . . . . . . . . . 144 4.6 Tuning results on fifty hardware simulations. . . . . . . . . . . . . . . 147 5.1 Algorithm performance: RPTT, α =0.0, ∆ = 0.1. . . . . . . . . . . . 158 5.2 Performance and design parameters for optimal designs. . . . . . . . . 159 5.3 Performance and parameters for tuned worst-case realizations. . . . . 159 6.1 RWA disturbance model parameters. . . . . . . . . . . . . . . . . . . 185 6.2 TPF SCI model mass breakdown. . . . . . . . . . . . . . . . . . . . . 188 6.3 Truss properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188 6.4 Truss element and grid numbering. . . . . . . . . . . . . . . . . . . . 189 6.5 Bus model elements and properties. . . . . . . . . . . . . . . . . . . . 190 6.6 Primary mirror properties. . . . . . . . . . . . . . . . . . . . . . . . . 191 6.7 Primary mirror mount properties. . . . . . . . . . . . . . . . . . . . . 191 6.8 TPF SCI instrument elements. . . . . . . . . . . . . . . . . . . . . . . 192 6.9 Critical modes of nominal TPF SCI design. . . . . . . . . . . . . . . . 195 6.10 TPF SCI model tailoring parameters. . . . . . . . . . . . . . . . . . . 197 11
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: List of Figures 1-1 Timeline of Ori
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
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
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
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
Page 99 and 100:
energy by mode for easy comparison.
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 and 108:
Chapter 4 Dynamic Tuning Robust Per
Page 109 and 110:
on a physical truss. Since tailorin
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
Page 121 and 122:
Performance Requirement [µm] 400 3
Page 123 and 124:
is considered. 4.2.1 Hardware-only
Page 125 and 126:
and added to the objective function
Page 127 and 128:
using either a decreasing step-size
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
Page 151 and 152:
Chapter 5 Robust Performance Tailor
Page 153 and 154:
MPC optimization by allowing a diff
Page 155 and 156:
where the notation yij indicates th
Page 157 and 158:
(Table 4.1), and the uncertainty pa
Page 159 and 160:
Table 5.2: Performance and design p
Page 161 and 162:
it in the worst-case uncertainty re
Page 163 and 164:
The data in Figure 5-2 indicate tha
Page 165 and 166:
configuration. The tuned configurat
Page 167 and 168:
same requirement. The effect become
Page 169 and 170:
indicating that this requirement is
Page 171 and 172:
E 2 [Pa] 7.8 7.6 7.4 7.2 7 6.8 6.6
Page 173 and 174:
than the RPT design, 155.45µm to 5
Page 175 and 176:
have a very small nominal performan
Page 177 and 178:
of these simulations fail to meet r
Page 179 and 180:
and that it is the only design meth
Page 181 and 182:
Chapter 6 Focus Application: Struct
Page 183 and 184:
optical path differences between th
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
Page 201 and 202:
complex and the normal modes analys
Page 203 and 204:
does not change with the design par
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
Page 215 and 216:
and the worst-case performance is a
Page 217 and 218:
- Consider uncertainty analysis too
Page 219 and 220:
Appendix A Gradient-Based Optimizat
Page 221 and 222:
such that the gradient direction is
Page 223 and 224:
the descent direction. In some case
Page 225 and 226:
Bibliography [1] Jpl planet quest w
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,
show all

Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

Create successful ePaper yourself

Delete template?

Save as template?