Composite control of a piezoelectric fast steering mirror using a mamba-based dual-axis inverse model

Abstract

Accurate tracking of piezoelectric fast steering mirrors (FSMs) is limited by rate-dependent hysteresis and cross-axis mechanical coupling. We developed a composite controller in which a Mamba-based joint dual-axis inverse model generates feedforward commands from coupled reference histories, while proportional–integral–derivative (PID) feedback corrects residual errors. The contribution lies in the system-level integration of joint inverse modeling, implicit inter-axis compensation, and residual feedback for the evaluated fixed-load FSM, based on a Mamba inverse model. Across four trajectories, the Mamba inverse model achieved lower mean spatial tracking error than the evaluated rate-dependent Prandtl–Ishlinskii (RDPI) and multi-nonlinear autoregressive moving average L2 (Multi-NARMA-L2) baselines. For the asynchronous Lissajous trajectory, its mean Euclidean root-mean-square tracking error was 8.63 μrad, compared with 10.65 μrad for Multi-NARMA-L2 and 36.49 μrad for RDPI. Computational tests characterized complementary execution modes. For length-1024 whole-sequence inference on an RTX 2060 GPU, Mamba required 0.63 ms, whereas long short-term memory (LSTM) required 4.21 ms. In a single-thread host-CPU recurrent-kernel benchmark, Mamba and LSTM required 45.84 μs and 30.74 μs per step, respectively. Together, these results show that Mamba-based inverse modeling improves feedforward tracking, while its integration with residual PID feedback supports closed-loop disturbance rejection for the evaluated fixed-load FSM.