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The quasi-static operations of MEMS mirror are very sensitive to undesired oscillations due to its very low damping. It has been shown that closed-loop control can be superior to reduce those oscillations than open-loop control in the literature. For the closed-loop control, the conventional way of implementing sliding mode control (SMC) algorithm is forward Euler method, which results in numerical chattering in the control input and output. This paper proposes an implicit Euler implementation scheme of super twisting observer and twisting control for a commercial MEMS mirror actuated by an electrostatic staggered vertical comb (SVC) drive structure. The famous super-twisting algorithm is used as an observer and twisting SMC is used as a controller. Both are discretized by an implicit Euler integration method, and their implementation algorithms are provided. Simulations verify that, as compared to traditional sliding mode control implementation, the proposed scheme reduces the chattering both in trajectory tracking output and control input in presence of model uncertainties and external disturbances. The comparison demonstrates the potential applications of the proposed scheme in industrial applications in terms of feasibility and performance.