A novel sliding mode control for a class of second-order mechanical systems

This paper considers the tracking control problem of a class of second-order mechanical systems involving parametric uncertainty and external disturbance by a sliding mode control (SMC) without reaching phase. Specifically, an SMC strategy with modified variable-gain proportional–integral–derivative (PID)-type sliding function is proposed, by which the existence of a sliding mode throughout an entire response of the system starting from the initial time instance is ensured. Meanwhile, the introduction of a variable gain in the sliding function design effectively solves the dilemma between quicker response and smaller overshoot. The effectiveness of the proposed strategy is verified by both theoretical analysis and simulation results.