Implicit Discrete-Time Terminal Sliding Mode Control for Second-Order Systems

One of the main problems of terminal sliding mode control (TSMC) is the severe numerical chattering caused by its discretization during the discrete-time realization, which significantly deteriorates the control performances. This brief proposes two novel realization schemes for the second-order TSMC based on implicit Euler methods. The first one treats the TSMC as the first-order SMC by solving the nonlinear equation of sliding surface. The latter one treats the second-order TSMC as nested signum functions without solving the nonlinear equation. Both schemes reduce the magnitude of numerical chattering while the second one totally remove the numerical chattering after attaining on the discrete-time sliding surface. The proposed two novel realizations have higher control performances in term of smaller control errors of steady state. These advantages of the proposed schemes are demonstrated through a buck converter circuit system in the presence of model uncertainties by comparing to the conventional implementations of TSMC.