Dynamic modeling and decoupling control of a clear-aperture tip-tilt-piston piezoelectric platform with high bandwidth and large stroke

Stable optical link establishment requires three-degree-of-freedom (3-DOF) compensation for both beam pointing errors (tip/tilt) and defocus drift (piston), demanding both high natural frequency (> 1 kHz) and high positioning accuracy (μrad/nm-level). However, small or nonexistent clear apertures in existing platforms restrict their integration into the primary optical path. This work proposes a 3-DOF piezoelectric platform featuring a large clear aperture and a decoupling control strategy, enabling unobstructed high-precision beam transmission. The mechanism utilizes three sandwich-type piezoelectric actuators (SPAs) coupled to a central mirror seat via flexible hinges to generate decoupled rotation about the x/y-axes and translation along the z-axis. Integrated strain sensing beams monitor SPA deformation in real-time, facilitating precise calculation of angle and displacement. Through kinematic analysis and static modeling, the functional relationship between driving signals and motion outputs is established, achieving 3-DOF decoupling. A dynamic model based on the pseudo-rigid-body method further characterizes its vibrational behavior. In terms of bandwidth and decoupling ability, compared with existing tip-tilt-piston platform that exhibit first-order natural frequencies below 1 kHz and cross-axis coupling above 1.8%, this work achieves a first-order natural frequency of 5075 Hz and cross-axis coupling below 1.64%. Experimental validation using the strain sensing system demonstrates strokes of 1.64 mrad (x-axis), 1.89 mrad (y-axis), and 13.62 μm (z-axis), with resolutions of 2.66 μrad, 3.08 μrad, and 21.9 nm, respectively. Closed-loop control suppresses hysteresis within 1.57%, eliminates creep, and maintains steady-state errors within ± 8 μrad. High-frequency beam steering validates its effectiveness for angle error compensation, while defocus drift compensation in microscopy improves image sharpness by at least 12.6%.