Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

optical metric. Disturbance analysis methods for evaluating performance RMS and
sensitivity analyses that provide performance gradients are discussed. Both gradient
based and stochastic search techniques are applied to the sample problem to obtain
a performance tailored design.
2.1 PT Formulation
The objective of performance tailoring is to design a system using a set of design vari-
ables, �x, such that a desired performance metric, f(�x), is below some required value,
freq. One approach to this problem is to formulate an optimization that minimizes
the performance metric:
min f (�x)
�x
(2.1)
s.t. �g (�x) ≤ �0
where f (�x) is the performance, or cost, function, �x is a vector of design variables that
affect the performance, and �g (�x) are constraints on the design variables. Examples
of performance metrics include first mode natural frequency and the variance of the
displacement of a particular structural element. For example, consider the design
of a truss that must achieve a specified level of stability at a given point, such as
the tip, when subjected to a dynamic disturbance environment. A PT optimization
would minimize the variance of the tip motion within a given frequency range by
varying the cross-sectional areas of the truss bars. Due to practical considerations,
the cross-sectional areas may be constrained by a lower bound set by manufacturing
and local buckling considerations and an upper bound on the mass of the structure.
2.2 SCI Development Model
The PT formulation is applied to the problem of high-performance systems through
a simple sample structure that is representative of a structurally-connected interfer-
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