Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

the truss material is a source of uncertainty and is allowed to vary asymmetrically in
the two interferometer arms as in the development model. The resulting asymmetry
in the two interferometer arms greatly affects the performance and models the effects
of many uncertainty parameters while keeping the computational effort low. A third
uncertainty parameter, the modal damping, is added to the parameter set. Damping
is a mechanism that is not well-understood and most models of it are conservative
approximations to the physical reality. Therefore it is a prime candidate for uncer-
tainty. In this example, a singl modal damping ratio is applied globally to all modes.
Table 6.12: TPF SCI model uncertainty parameters.
p Description p0 Units ∆ [%]
E1 Young’s Modulus of -X truss 111.7 GPa 25
E2 Young’s Modulus of +X truss 111.7 GPa 25
ξn modal damping ratio 0.001 none 40
A bounded uncertainty model of the form in Equation 3.1 is used. The percent
bounds on the uncertainty parameters are given by ∆ and are listed in Table 6.12.
The truss Young’s Modulus is allowed to vary ±25% about its nominal value and the
modal damping ranges in value ±40% about nominal. The range on the damping
parameter is larger than that of the Young’s Moduli to capture the high uncertainty
inherent in the modal damping model.
6.3 Optimization Implementation
It is shown in the previous chapters that a combination of SA and SQP finds the
best design consistently and efficiently in the case of the development model. Unfor-
tunately, running the SQP optimization on the TPF model is not straightforward.
Recall from Chapter 2 that the SQP algorithm requires performance gradients, and
that the calculation of the gradients requires the gradients of the eigenvalues and
eigenvectors. The development model is relatively simple and as a result, these quan-
tities can be derived directly. The TPF model, on the other hand, is much more
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