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

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.