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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.

This paper analyses a frequency domain performance of an adaptive windowing parabolic sliding mode filter (AW-PSMF) by using Describing Function method. The analysis results show that AW-PSMF has similar gain characteristics to that of the second-order Butterworth low-pass filter (2-LPF), but AW-PSMF produces flatter gain behaviour than 2-LPF does at cutoff frequency. In addition, AW-PSMF produces smaller phase lag than 2-LPF does.

This paper studies the super‐twisting algorithm (STA) for adaptive sliding mode design. The proposed method tunes the two gains of STA on line simultaneously such that a second order sliding mode can take place with small rectifying gains. The perturbation magnitude is obtained exactly by employing a third‐order sliding mode observer in opposition to the conventional approximations by using a first order low pass filter. While driving the sliding variable to the sliding mode surface, one gain of the STA automatically converges to an adjacent area of the perturbation magnitude in finite time. The other gain is adjusted by the above gain to guarantee the robustness of the STA. This method requires only one parameter to be adjusted. The adjustment is straightforward because it just keeps increasing until it fulfills the convergence constraints. For large values of the parameter, chattering in the update law of the two gains is avoided by employing a geometry based backward Euler integration method. The usefulness is illustrated by an example of designing an equivalent control based sliding mode control (ECBC‐SMC) with the proposed adaptive STA for a perturbed LTI system. [ABSTRACT FROM AUTHOR]