Novel sliding-mode control for a class of second-order systems with mismatched disturbances

This article investigates a novel sliding-mode control (SMC) approach for a class of second-order nonlinear systems subject to mismatched disturbances. To solve this problem, a novel sliding surface is designed based on the disturbance estimation of the nonlinear disturbance observer (DOB). By designing a novel time-varying switching gain, a DOB-based improved SMC law is constructed to compensate the influence of mismatched disturbances on the system output and make the system output converge asymptotically to zero. The novel SMC scheme owns two advantages. One is that the switching gain is an exponential decay function varying synchronously with the disturbance estimation error, which substantially alleviates the chattering problem. The other one is that a new function is defined as the switching gain coefficient based on the disturbance estimation, which helps the proposed approach to maintain the nominal control performance of the system, that is, the novel SMC law degrades to the baseline SMC law in the absence of disturbances. A numerical simulation example verifies the effectiveness and superiority of the developed approach by comparisons.