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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. [ABSTRACT FROM AUTHOR]

This brief proposes a new discrete-time realization of the super-twisting algorithm based observer. While keeping the property of chattering suppression, the estimation precision of the proposed realization scheme is consistent with the continuous-time super-twisting algorithm (STA), that is, in the absence of noises, the estimation errors satisfy the standard asymptotical accuracy level, i.e., |e1| ~ μ1h2 and |e2|~ μ2h with sampling time h and two positive constants μ1 and μ2. Comparing to the conventional explicit Euler method, the proposed scheme is more exact in the term of smaller constants μ1 and μ2. The superiority of the proposed scheme is demonstrated through an example of typical buck converter circuit system. [ABSTRACT FROM AUTHOR]

This brief proposes new discrete-time algorithms of the super-twisting observer and the twisting controller to be applied to second-order systems. The algorithms are based on the full implicit-Euler discretization, which contributes to the elimination of chattering. Proofs of some stability properties of the discretized twisting controller are also provided. Simulations show that, as compared to traditional explicit-Euler schemes, the proposed scheme avoids the chattering both in trajectory tracking output and control input in the presence of external disturbances. [ABSTRACT FROM AUTHOR]