Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT
Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT
SA simulated annealing SCI structurally-connected interferometer SIM Space Interferometry Mission SIT system intergration test SQP sequential quadratic programming SR statistical robustness TPF Terrestrial Planet Finder TT Tailoring for Tuning ULE ultra-low expansion WC worst-case Symbols Ai cross-sectional area A, B, C state-space matrices ˆB(·) barrier function Bˆxw disturbance input mapping matrix BI interferometric baseline Ci amplitude coefficient Czˆx output mapping matrix Ei Young’s Moudulus Fx, Fy, Tz force and torque disturbances G(·) transfer function H Hessian I identity matrix, area moment of inertia K finite element stiffness matrix J optimzation cost L Langrangian L length M finite element mass matrix Mcolli collector mass Mcomb combiner mass ¯M total mass limit P uncertainty parameter space Piso isoperformance set T temperature R distance to star Szz output PSD Sww disturbance PSD X, Y, Z coordinate system axes Y tuning parameter space cross-sectional diameter di 14
dk optimization search direction f frequency f(·) performance function �g(·), �h(·) constraints h height hi harmonic number kc, ka, kr, kT simulated annealing paramters mi design mass �p uncertainty parameters q modal degrees of freedom s Laplace variable w white noise, width ˆx physical degrees of freedom �x tailoring parameters �y tuning paramters z output metric, dummy optimization cost ∆ uncertainty level Ω, ωj natural frequeny Φ, φj mode shapes Σz output covariance matrix Σq state covariance matrix Z, ξ, ζ damping ratio αk optimization step size α, β optimization weights λ Lagrange multiplier µk barrier sequence ν Poisson’s ratio ρ material density σ2 variance (mean square if zero mean) σ standard deviation (RMS if zero mean) Subscripts and Superscripts (·) ∗ optimal solution (·) H Hermitian (complex-conjugate tanspose) (·)HW hardware value (·) T transpose (·)WC worst-case value (·)0 nominal value (·)req requirement (·)t tuned value 15
- 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: Nomenclature Abbreviations ACS atti
- 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
SA simulated annealing<br />
SCI structurally-connected interferometer<br />
SIM Space Interferometry Mission<br />
SIT system intergration test<br />
SQP sequential quadratic programming<br />
SR statistical robustness<br />
TPF Terrestrial Planet Finder<br />
TT <strong>Tailoring</strong> for <strong>Tuning</strong><br />
ULE ultra-low expansion<br />
WC worst-case<br />
Symbols<br />
Ai cross-sectional area<br />
A, B, C state-space matrices<br />
ˆB(·) barrier function<br />
Bˆxw disturbance input mapping matrix<br />
BI interferometric baseline<br />
Ci amplitude coefficient<br />
Czˆx output mapping matrix<br />
Ei Young’s Moudulus<br />
Fx, Fy, Tz force and torque disturbances<br />
G(·) transfer function<br />
H Hessian<br />
I identity matrix, area moment of inertia<br />
K finite element stiffness matrix<br />
J optimzation cost<br />
L Langrangian<br />
L length<br />
M finite element mass matrix<br />
Mcolli collector mass<br />
Mcomb combiner mass<br />
¯M total mass limit<br />
P uncertainty parameter space<br />
Piso isoperformance set<br />
T temperature<br />
R distance to star<br />
Szz output PSD<br />
Sww disturbance PSD<br />
X, Y, Z coordinate system axes<br />
Y tuning parameter space<br />
cross-sectional diameter<br />
di<br />
14
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