Terminal Sliding Mode Control for Nonlinear Systems with both Matched and Unmatched Uncertainties

In this paper, we extend the sliding mode idea to a class of unmatched uncertain variable structure systems. This method is achieved with introducing a new terminal sliding variable and the finite time stability of proposed method is proved using a new particular finite time condition in both reaching and sliding phases. In reaching phase new sliding mode controller is derived to guarantee the finite time stability of sliding surface with considering matched uncertainty. Also in sliding phase, because of introducing a new terminal sliding variable, the finite time stability of state variables with considering unmatched uncertainty has been guarantee. Therefore in proposed algorithm we are able to adjust reaching and sliding times in the presences of both matched and unmatched uncertainty. This algorithm is applied to designing control law for a moving cart system with bounded matched and unmatched uncertainties. Simulation results show the effectiveness and robustness of the proposed algorithm.