Robust control of nonlinear uncertain systems via sliding mode with backstepping design

This paper presents a new combination of sliding mode and backstepping for output tracking of coupled two tank system. The proposed controller can greatly reduce chattering of sliding modes of the system, and it has certain robustness with respect to the external disturbances and good adaptability with respect to the parametric uncertainty. It is proved that the proposed systematic backstepping design method is able to guarantee global uniformly ultimately boundedness of all the signals in the closed-loop system. The tracking error is proven to converge to a small neighborhood of the origin. Finally, some experimental results are demonstrated to validate the proposed controllers.