In this paper, 10 resonant modes were divided based on the structure of a specific two-dimensional electromagnetic micromirror from Professor Shen’s team and Finite Element Method (FEM), and using as many as 10 resonant modes to do such analysis was the first time according to the best of our knowledge. The results showed that the slow axis can participate in several resonant motions under the signals of resonant frequencies. In particular, participating in Mode 1 for slow-scan axis was the key reason to the instability of Vertical Refreshing Scanning (VRS) in raster scanning. In addition, a piecewise PID control based on filters design for this electromagnetic micromirror was proposed to suppress the unexpected resonant oscillation and to improve the angular positioning accuracy in slow-scan axis control. Finally, the proposed method was applied to electromagnetic micromirror stages, and the experimental results showed that the proposed approach was reliable.

In this paper, a simplified dynamic model is constructed to describe the main characteristic of electromagnetic micro-mirror. Then, based on the information provided by the derived simplified model, a model-guided extremum seeking control (MGESC) scheme with backtracking line search is developed, which can automatically estimate the best value of step-size at each search iteration to improve the performance of the control system for target tracking. Then, the convergence of the proposed MGES algorithm is proved. Finally, the experimental results and the simulations are presented to verify the proposed method.

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Now two problems result in bad control in the development of the electromagnetic micromirror system. One is that theoretical model in electromagnetic micromirror system is difficult to be determined; Another is that parameters in common control need to be tuned according to the experience. In this paper, cost function concept is proposed to determine the model order in slow-scan axis control of the electromagnetic micromirror. Then recursive least square scheme is built to off-line identify this model. Furthermore, an advanced extremum seeking scheme along with backtracking line search is exploited, which can automatically identify the best parameter value before each extremum search to improve the controllability based on this model for the target trajectory in slow-scan axis control. And the convergence of it is proved. Finally, the experiments and the simulations verify this method proposed valid.