Hierarchical dual-loop control for piezo-hydraulic fast steering mirrors in high-precision optical tracking

High-precision optical tracking using piezo-hydraulic fast steering mirrors (FSMs) is challenged by piezoelectric hysteresis, coupled electro-hydro-mechanical dynamics, fluid-structure interactions, and parasitic cross-axis coupling. This study presents a hierarchical dual-loop control framework for a piezo-hydraulic FSM together with an integrated strain-gauge-based angular sensor optimized through stress analysis. In the inner loop, a pressure-sensorless generalized extended state observer and a super-twisting sliding mode controller with active feedforward compensation are developed to reconstruct unmeasured states and estimate lumped disturbances using only angular feedback. In the outer loop, a proportional-integral controller combined with a linear tracking differentiator filters noisy position-sensitive-detector measurements and generates smooth kinematic references without direct numerical differentiation. Experiments on a large-aperture prototype show a rise time below 5.7 ms and inter-axis coupling below 10 μrad. For Lissajous tracking at 47 Hz and 45 Hz along the x- and y-axes, respectively, the proposed method achieves a root-mean-square error of 4.0 μrad, improving tracking accuracy by up to 66.6% relative to the baseline controllers. In dual-loop tracking of a maneuvering aircraft with a trajectory unknown to the controller, the overall RMSE is 5.5 μrad. These results validate the effectiveness of the proposed framework for high-precision optical tracking and line-of-sight stabilization.