Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

More documents

Recommendations

Info

Frequency [Hz] Relative Modal Displacement 0.08 0.07 0.06 0.05 0.04 0.03 100 90 80 70 60 50 40 30 20 10 0 Modal Energy [%] 0.02 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Nominal Worst−Case Tuned Nominal Worst−Case Tuned PT RPT RPTT (a) Modal frequency (upper) and percent energy (lower) Nominal Worst−Case Tuned PT RPT RPTT (b) Relative modal displacement Figure 5-3: Modal characteristics of first bending mode for PT, RPT and RPTT designs in the nominal (blue, circle), worst-case (green, square) and tuned (white, diamond) configurations. 164
configuration. The tuned configurations are especially interesting as it is clear that the tuning parameters are able to drastically reduce the percent energy of this mode in both the PT and RPTT designs, while the RPT design is not affected as strongly. To complete the story the relative modal displacement between the collector nodes for each design is shown in Figure 5-3(b). Again, the results for the nominal, worst- case and tuned worst-case configurations are shown in black, gray and white, respec- tively. This metric is important since the y-translation contribution to the OPD is due to the relative motion of these nodes (Equation 2.9). It is clear from the chart that the addition of the tuning masses to the PT and RPTT designs reduces the relative motion between collectors quite drastically. In effect, the asymmetric addition of tuning mass balances the asymmetry introduced by the uncertainty parameters at the worst-case vertex. The RPT design also shows a reduction, but it is not as significant. The tuning parameters are not able to affect the shape of the first mode as much, because the design is robust to uncertainty but is also robust to tuning. The RPTT design formulation balances the key elements of the PT and RPT designs to produce a design that is both robust to uncertainty, yet tunable. In the SCI development model all effort is directed to the first bending mode as this is the significant mode in the worst-case uncertainty realization due to asymmetric motion of the collector nodes. The natural frequency of this mode in the RPTT design is higher than that of the PT design so that the mode contributes less to the output energy. However, it is not stiffened as sharply as in the RPT design so that the tuning parameters have sufficient authority to affect the performance. 5.2.3 Design Regimes The tuned RPTT design is compared to the PT, RPT, tuned PT and tuned RPT designs over a range of uncertainty values. The formulation in Equation 5.5 is run for maximum tuning authority (α =0.0) at various values of uncertainty bound, ∆, ranging from 0.01% to 25%. The uncertainty values vary ±∆% about nominal and are the same for both uncertainty parameters. The tuned results are obtained by running a tuning optimization on the worst-case uncertainty realization. The results 165
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
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: The data in Figure 5-2 indicate tha
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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?