Improving continuous approximation of Sliding Mode Control

This paper proposes a continuous approximation of Sliding Mode Control (SMC) designed to fully reject constant disturbances. The main advantage of standard continuous approximation is knew to be chattering reduction while maintaining the state in a well defined boundary of the sliding surface. However, in classical implementations, the effect of even a simple constant disturbance causes the state to leave the sliding surface and move unpredictably in the boundary layer. The proposed solution is a first order SMC approximation, presented with a theoretical proof for the rejection of constant disturbances. The efficacy of the control law is demonstrated in a real-life implementation and comparisons with higher order SMC are carried on. Despite the simplicity of the proposed law, experiments in a robotic application show performances comparable with state of the art second order SMC.