Modeling-free Learning Control of Cross-coupled Fast Steering Mirror for 2-D Trajectory

Abstract

This paper proposes modeling-free inversion-based iterative control (MF-IIC) for a fast steering mirror, which is a dual-input dual-output system to generate 2-D optical scanning trajectories. To explicitly compensate for the cross-coupling motions, the MF-IIC iteratively updates the control inputs by learning from the previous trials based on a 2 × 2 Jacobian matrix. To operate the MF-IIC without system identification in advance, it estimates the Jacobian matrix including the non-diagonal elements for the cross-coupling dynamics simultaneously during learning. For experiments, 19 Hz and 20 Hz sine waves with an amplitude of 0.65° are used for a Lissajous pattern as a reference trajectory. Experimental results show that a tracking error of 320 × 10−3 degrees when feedback control is used for stability. By additionally combing the proposed MF-IIC, the error is decreased by a factor of 68 to 4.64 × 10−3 degrees. It is smaller than MF-IIC without considering the cross coupling explicitly, which achieves a tracking error of 12.1 × 10-3 deg. These two MF-IIC algorithms are also compared by the resulting sampled trajectories in the spatial domain. For that purpose, maximum dead zone diameter is defined as a diameter of the largest circle without sampled points in a scanning area in this paper. While the MF-IIC without considering the cross coupling explicitly for comparison creates a Lissajous pattern with a maximum dead zone diameter of 74.8 × 10−3 degrees, the proposed MF-IIC achieves a Lissajous pattern with a smaller maximum dead zone diameter of 72.9 × 10−3 degrees, demonstrating its effectiveness for high-quality scanning trajectories.