Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

The transfer function from torque to OPD is nonzero at zero frequency because
the model is unconstrained and there is a rigid body rotation about the center of
the array. This motion results in equal, but opposite displacement at the ends of the
structure, where the collecting optics are located. It is clear from Equation 2.9 that
such a motion results in infinite OPD contribution. The transfer function from Fx to
OPD does not show any contribution from axial rigid body motion. The translational
rigid body modes are unobservable in the output since OPD is only affected by relative
changes in the positions of the collectors and combiners.
2.3 PT Implementation
In the next section the PT optimization formulation is applied to the development
model. First, the performance metric is defined, then design variables for tailoring
the structure are selected.
2.3.1 Performance Metric
The output of interest, z, is the OPD between the two arms of the interferometer
which changes as a function of time with the disturbance. The output variance, σ 2 z ,is
a common measure of system performance that reduces the output time history to a
scalar quantity. If the output signal is zero mean, then the variance is also the mean
square and its square root is called the root mean square [112] (RMS). Output RMS is
often used in disturbance, or jitter, analysis to predict the broadband performance of a
system in the presence of a dynamic disturbance environment. Performance variance
is calculated in the frequency domain from the power spectral density (PSD), of the
output signal, Szz:
Szz = GzwSwwG H zw
(2.11)
where Gzw is the system transfer function from disturbance to output, Sww is the PSD
of the input signal and () H is the matrix Hermitian. Given that z(t) is zero-mean,
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