  The Laser Interferometer Space Antenna (LISA), space-based gravitational wave
observatory involves a complex multidimensional closed-loop dynamical system.
Its instrument performance is expected to be less efficiently isolated from
platform motion than was its simpler technological demonstrator, LISA
Pathfinder. It is of crucial importance to understand and model LISA dynamical
behavior accurately to understand the propagation of dynamical excitations
through the response of the instrument down to the interferometer data streams.
More generally, simulation of the system allows for the preparation of the
processing and interpretation of in-flight metrology data. In this work, we
present a comprehensive mathematical modeling of the closed-loop system
dynamics and its numerical implementation within the LISA Consortium simulation
suite. We provide, for the first time, a full time-domain numerical
demonstration of post-processing Time Delay Interferometer techniques combining
multiple position measurements with realistic control loops to create a
synthetic Michelson interferometer. We show that in the absence of physical
coupling to spacecraft and telescope motion (through tilt-to-length, stiffness
and actuation cross-talk) the effect of noisy spacecraft motion is efficiently
suppressed to a level below the noise originating in the rest of the
instrument.
