Modeling of electro-statically actuated two-axis (tip-tilt) MEMS torsion micro-mirrors for laser beamsteering

Abstract

The availability of recently developed MEMS micro-mirror technology provides an opportunity to replace macro-scale actuators for free-space laser beamsteering in lidar and communication systems. Such an approach is under investigation at the Johns Hopkins University Applied Physics Laboratory for use on space-based platforms. Precision modeling of mirror pointing and its dynamics are critical to optimal design and control of MEMS beamsteerers. Beginning with Hornbeck's torque approach, this paper presents a first-principle, analytically closed-form torque model for an electro-statically actuated two-axis (tip-tilt) MEMS structure. An Euler dynamic equation formulation describes the gimbaled motion as a coupled pair of damped harmonic oscillators with a common forcing function. Static physical parameters such as MEMS mirror dimensions, facet mass, and height are inputs to the model as well as dynamic harmonic oscillator parameters such as damping and restoring constants fitted from measurements. A Taylor series expansion of the torque function provides valuable insights into basic one dimensional as well as two dimensional MEMS behavior, including operational sensitivities near "pull-in." The model also permits the natural inclusion and analysis of pointing noise sources such as electrical drive noise, platform vibration, and molecular Brownian motion. MATLAB and SIMULINK simulations illustrate performance sensitivities, controllability, and physical limitations, important considerations in the design of optimal pointing systems.