Implicit discrete-time fast terminal sliding mode control with disturbance compensation

In this paper, an implicit discrete-time fast terminal sliding mode (DFTSM) control with disturbance compensation is designed and analyzed for uncertain high-order systems. First, a recursive discrete sliding surface is constructed based on implicit Euler technique, which can completely eliminate discretization chattering so as to significantly reduce the boundary layer of sliding mode motion. With the help of a high-order disturbance compensator, the accuracy limitation of implicit DFTSM control systems is overcome by increasing the order of sliding mode. Then the finite-time convergence of implicit DFTSM is proved for the first time, and the influence relationship of control parameters on the convergence speed and control accuracy of the algorithm is established. Finally, two numerical examples are provided to demonstrate the effectiveness and superiority of the proposed design approach.