Nematic Liquid Crystal Adaptive Phase Screens (NLC-APS) may be used as wavefront correctors for adaptive optics in astronomical uses, provided special techniques are applied to improve their time performance. The advantage of LC-based wavefront correctors are mechanical stability (no moving parts involved), avoidance of mechanical resonances, potential low-cost, and optically transmissive corrections for multiconjugate AO after the telescope focal plane. We do not deal in this paper with other types of LCs which could be used for such purpose, because we find them less favorable, and applicable only to very special observing modes, if any. We have described previously the theoretical and experimental results that have led us to this conclusion. Our goal here is to study the feasibility and the performance of such a wavefront corrector when it is inserted in an adaptive servo-loop, and driven by a 16 X 16 Shack-Hartmann sensor and the reconstructor electronics. The study is carried out via a complete simulation of the system, at the 3.58-m Telescopio Nazionale Galileo (TNG), to be built on La Palma (Canary Islands).