Predictive Gradient Based Control Using Hammerstein Model for MEMS Micromirrors

For high-definition (HD) display, the scanning micromirror needs to perform high-speed scanning at high frequencies, and the bandwidth of the fabricated micromirror should be greater than the maximum scanning frequency. On the other hand, the impact of time delay in both sensor and actuation mechanism on the performance of micromirror cannot be ignored at high scanning rates. Therefore, delay compensation has become one of the important issues in achieving satisfactory angle control for high-speed scanning. In this article, a predictive gradient-based control (PGBC) method is proposed for angle control of electromagnetic scanning micromirror (ESM). In this method, the characteristics of ESM are described by a Hammerstein model with hysteresis and time delay. To deal with the time delay compensation of ESM, a d-step-ahead nonlinear predictor is developed. Then, a predictive gradient optimization (PGO) algorithm is proposed to predict the gradient changes in the future to accelerate the convergence. Also, the corresponding convergence analysis of the PGO method is presented. Afterward, the stability of the PGBC system is studied. Moreover, an estimator for unknown disturbances is introduced to suppress the effects of model mismatch and disturbance. Finally, the proposed control scheme is evaluated by simulation, and validated in the angle control of a MEMS micromirror.