TPF-C Technology Plan - Exoplanet Exploration Program - NASA

Chapter 4
Figure 4-8. Comparison of passive isolation performance versus DFP performance for line-ofsight
stability requirement.
outputs. In this analysis, two reaction wheels were assumed to spin at the same speed with
random phasing, the structural damping ratio was assumed to be 0.1%, and model uncertainty
factors were also added to increase conservatism.
Figure 4-8 illustrates the LOS performance for the passive isolation design (red line) and DFP
(blue line), as well as the requirement (green line). The passive isolation design cannot alter the
system response for frequencies below the isolator break frequency, typically ~2 Hz, but can
achieve 40–60 dB attenuation per stage at frequencies sufficiently above the break frequency.
Although the passive isolation design does not meet the LOS requirement at low wheel speeds, it
is simple to limit wheel speeds to above 2 Hz where passive isolation can meet the requirement
with a large margin. The DFP, on the other hand, does not have a theoretical limit in rejecting
vibrations at low frequencies. As a result, the active DFP design can meet the LOS requirement
for all wheel speeds and demonstrate vibration reduction about two orders of magnitude better
than the passive isolation design.
The wavefront error (WFE) due to telescope deformation, expressed in terms of the first 15
Zernike amplitudes, is plotted in Figure 4-9. The top graph shows the margin in dB for each
Zernike amplitude:
⎛ max Z
i
( ω)
⎞
− 20 log
⎜
⎟,
i = 4...15
⎝ Ri
⎠
where Z i is the amplitude of Zernike mode i versus wheelspeed, and R i is the requirement for
mode i. The bottom graph shows the peak Zernike amplitude from the passive isolation and DFP
designs as blue and green lines, respectively, along with the requirement for each mode in
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