Second-order sliding mode control of a 2D torsional MEMS micromirror with sidewall electrodes

Abstract

A second-order sliding mode control (2-SMC) scheme with a proportional integral derivative (PID) sliding surface, to achieve enhanced transient response, accurate positioning and precise tracking performance of a 2-degree-of-freedom (2D) torsional MEMS micromirror with sidewall electrodes, is developed in this paper. The PID sliding surface is chosen to achieve a zero steady-state error of the closed-loop system. The 2-SMC is able to reduce the chattering phenomena, which comprises of an equivalent control and switching control to dominate model uncertainty and external disturbances leading to an enhanced performance of the controlled system. Finite-time convergence of the closed-loop system in the presence of bounded parameter uncertainties and external disturbances is guaranteed through Lyapunov stability analysis. The proposed 2-SMC is programmed in a LABVIEW environment and implemented based on National Instrument (NI) field-programmable gate array hardware to verify the effectiveness and robustness. The experimental results of set-point regulation and sinusoidal trajectory tacking demonstrate that the closed-loop system with the proposed control scheme significantly improves the transient performance, accurate positioning and trajectory tracking with robustness against external disturbance. The 95% settling time is shortened from 70 to 3 ms for the X-axis and from 60 to 3 ms for the Y-axis respectively, the overshoots and steady-state errors are eliminated in both axes, and less than 5% maximum positioning error is achieved in the presence of external disturbance.