Modeling of biaxial gimbal-less MEMS scanning mirrors

One- and two-dimensional MEMS scanning mirrors for resonant or quasi-stationary beam deflection are primarily known as tiny micromirror devices with aperture sizes up to a few Millimeters and usually address low power applications in high volume markets, e.g. laser beam scanning pico-projectors or gesture recognition systems. In contrast, recently reported vacuum packaged MEMS scanners feature mirror diameters up to 20 mm and integrated high-reflectivity dielectric coatings. These mirrors enable MEMS based scanning for applications that require large apertures due to optical constraints like 3D sensing or microscopy as well as for high power laser applications like laser phosphor displays, automotive lighting and displays, 3D printing and general laser material processing. This work presents modelling, control design and experimental characterization of gimbal-less MEMS mirrors with large aperture size. As an example a resonant biaxial Quadpod scanner with 7 mm mirror diameter and four integrated PZT (lead zirconate titanate) actuators is analyzed. The finite element method (FEM) model developed and computed in COMSOL Multiphysics is used for calculating the eigenmodes of the mirror as well as for extracting a high order (n < 10000) state space representation of the mirror dynamics with actuation voltages as system inputs and scanner displacement as system output. By applying model order reduction techniques using MATLABR a compact state space system approximation of order n = 6 is computed. Based on this reduced order model feedforward control inputs for different, properly chosen scanner displacement trajectories are derived and tested using the original FEM model as well as the micromirror.