Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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25 cm Y Z 120 (a) Configuration 45 X X Variance [N 2 ] PSD [N 2 /Hz] 0.04 0.02 10 −2 10 −4 10 −6 10 −8 0 10 −10 10 0 RWA DIST Fx[N] RWA DIST FY[N] RWA DIST Fz[N] RWA DIST Tx[Nm] RWA DIST Ty[Nm] RWA DIST Tz[Nm] 10 1 Frequency [Hz] (b) Power Spectral Densities Figure 6-3: RWA disturbance model. series between the RWA disturbances and the plant as shown in Figure 6-1. The isolator transfer functions are: Giso = (2πfiso) 2 s 2 +2ζiso(2πfiso)s +(2πfiso) 2 10 2 (6.3) where Giso is the transfer function from the input to the isolated disturbance, fiso is the corner frequency of the isolator (Hz), and ζiso is the isolator damping ratio. The damping ratio for both isolators is assumed to be 0.1 and the frequencies of the first and second stages are set to 3 Hz and 8 Hz, respectively. The transfer functions for both stages are shown in Figure 6-4. 6.1.3 Plant The plant is a finite element model of a baseline design of the TPF structurally- connected interferometer concept consisting of four collecting apertures, a supporting 186
FRF Magnitude 10 1 10 0 10 −1 10 −2 10 −3 RWA Isolator Bus Isolator 10 −2 10 0 Frequency [Hz] Figure 6-4: Transfer functions of Isolator models: RWA isolator, ζiso = 0.4 and fiso = 8 Hz (solid line), bus isolator, ζiso =0.1 andfiso = 3 Hz (dashed line). truss and a combiner. The interferometric baseline, measured as the distance between the centers of the two outermost collectors, is 36 meters. The collectors are evenly spaced along the baseline such that there are 12 meters between any two neighboring collectors. The plant model is built mainly in NASTRAN and is shown in its nominal configuration in Figure 6-2. It is comprised of NASTRAN beam elements (CBAR), concentrated masses (CONM2), plate elements (CQUAD8, CTRIA6) and rigid elements (RBAR, RBE2). The reader is referred to the NASTRAN documentation for more information on these finite elements [94]. The inputs to the plant are the six isolated RWA disturbances, three forces and three torques. The plant outputs are three OPD metrics from the interferometer pairs and three angular rotations from the ACS sensor. The structural mass breakdown of the plant model is given in Table 6.2. The masses listed are based on current best estimates from JPL, and the total structural mass is 2679 kg. Truss The main structural component of the TPF model is the supporting truss. The origin of the spacecraft frame is at the center of the truss so that the truss is broken into 187 10 2
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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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at least locally optimal, and the s
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initial design variable state, x =
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and the RMS OPD is computed using E
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# Designs 25 20 15 10 5 Accepted, b
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does not provide information on why
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energy is distributed almost evenly
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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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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
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Page 181 and 182: Chapter 6 Focus Application: Struct
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Page 185: Table 6.1: RWA disturbance model pa
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
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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,
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Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

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