An Improved Discrete‐Time Super‐Twisting Control Algorithm With Double‐Power Reaching Law

ABSTRACT Compared with traditional sliding mode control, the super‐twisting control algorithm not only exhibits disturbance rejection performance but also has the ability to suppress system chattering. However, for the sampling control system, while the discrete‐time super‐twisting control algorithm still exhibits favorable control effects, it inevitably results in larger system chattering. To address these limitations, this paper proposes an improved discrete‐time double‐power super‐twisting control algorithm (DDSTA). By introducing the double‐power term, the convergence performance of the system is improved, and the chattering of the system is reduced using the boundary layer approach. Starting with an undisturbed first‐order continuous system, we establish that the trajectory under DDSTA converges within a bounded region around the origin. We further examine the stability of the perturbed continuous system using a geometric method. Finally, experimental studies on the gantry manipulator system are presented to demonstrate the effectiveness of the proposed methods.