  Directly imaging Earth-like exoplanets (``exoEarths'') with a coronagraph
instrument on a space telescope requires a stable wavefront with optical path
differences limited to tens of picometers RMS during exposure times of a few
hours. While the structural dynamics of a segmented mirror can be directly
stabilized with telescope metrology, another possibility is to use a
closed-loop wavefront sensing and control system in the coronagraph instrument
that operates during the science exposures to actively correct the wavefront
and relax the constraints on the stability of the telescope. In this paper, we
present simulations of the temporal filtering provided using the example of
LUVOIR-A, a 15~m segmented telescope concept. Assuming steady-state aberrations
based on a finite element model of the telescope structure, we (1)~optimize the
system to minimize the wavefront residuals, (2)~ use an end-to-end numerical
propagation model to estimate the residual starlight intensity at the science
detector, and (3)~predict the number of exoEarth candidates detected during the
mission. We show that telescope dynamic errors of 100~pm~RMS can be reduced
down to 30~pm~RMS with a magnitude 0 star, improving the contrast performance
by a factor of 15. In scenarios where vibration frequencies are too fast for a
system that uses natural guide stars, laser sources can increase the flux at
the wavefront sensor to increase the servo-loop frequency and mitigate the high
temporal frequency wavefront errors. For example, an external laser with an
effective magnitude of -4 allows the wavefront from a telescope with 100~pm~RMS
dynamic errors and strong vibrations as fast as 16~Hz to be stabilized with
residual errors of 10~pm~RMS thereby increasing the number of detected planets
by at least a factor of 4.
