  In this paper, we present a new discrete-time Fast Terminal Sliding Mode
(FTSM) controller for mirror-based pointing systems. We first derive the
decoupled model of those systems and then estimate the parameters using a
nonlinear least-square identification method. Based on the derived model, we
design a FTSM sliding manifold in the continuous domain. We then exploit the
Euler discretization on the designed FTSM sliding surfaces to synthesize a
discrete-time controller. Furthermore, we improve the transient dynamics of the
sliding surface by adding a linear term. Finally, we prove the stability of the
proposed controller based on the Sarpturk reaching condition. Extensive
simulations, followed by comparisons with the Terminal Sliding Mode (TSM) and
Model Predictive Control (MPC) have been carried out to evaluate the
effectiveness of the proposed approach. A comparative study with data obtained
from a real-time experiment was also conducted. The results indicate the
advantage of the proposed method over the other techniques.
