Modeling and experimental validation of hysteretic scan behavior of quasi-static piezoelectric micromirror

MEMS mirrors are at the core of miniaturized projection systems based on Laser Beam Scanning (LBS) which are involved in a wide range of applications in the field of Augmented/Mixed Reality and LiDAR. Most of these applications require at least one axis to be scanned with constant velocity by a quasi-static micromirror, which needs a good driving voltage to angle linearity. In practical implementations, electro-mechanical response of quasi-static micromirrors is strongly affected by MEMS nonlinearities which can be pure mechanical, like geometric nonlinearity, or can arise from the actuation principle, like electrostatic softening in comb-finger actuators or the hysteresis in piezoelectric actuators. As a result, the open loop response of the opening angle can significantly deviate from the ideal linear one affecting the final system performance. Piezoelectric micromirrors are becoming even more common in the current LBS-based product scenario. A proper and accurate modeling technique for handling the mirror scanning trajectory affected by piezoelectric hysteresis is needed for setting up the most appropriate control strategy. In this work, a modeling approach based on Bouc-Wen model describing the hysteretic behavior of piezoelectric MEMS mirrors is presented. Furthermore, a mono-axial quasi-static PZT actuated MEMS mirror has been investigated through a characterization phase focusing on the relation between the input driving voltage and the output scanning angle. A final validation stage with a comparison between collected data and model results is reported.