  This paper presents a novel adaptive fast smooth second-order sliding mode
control for the attitude tracking of the three degree-of-freedom (3-DOF)
helicopter system with lumped disturbances. Combining with a non-singular
integral sliding mode surface, we propose a novel adaptive fast smooth
second-order sliding mode control method to enable elevation and pitch angles
to track given desired trajectories respectively with the features of
non-singularity, adaptation to disturbances, chattering suppression and fast
finite-time convergence. In addition, a novel adaptive-gain smooth second-order
sliding mode observer is proposed to compensate time-varying lumped
disturbances with the smoother output compared with the adaptive-gain
second-order sliding mode observer. The fast finite-time convergence of the
closed-loop system with constant disturbances and the fast finite-time
uniformly ultimately boundedness of the closed-loop system with the
time-varying lumped disturbances are proved with the finite-time Lyapunov
stability theory. Finally, the effectiveness and superiority of the proposed
control methods are verified by comparative simulation experiments.
