LSTM-based control of hysteresis and inter-axis coupling in piezoelectric fast steering mirrors

High-speed trajectory tracking of Piezoelectric Fast Steering Mirrors (PFSM) is severely limited by inherent rate-dependent hysteresis and strong inter-axis coupling dynamics. Existing Single-Input Single-Output (SISO) control approaches fail to address the complex inter-axis interactions in two-dimensional scanning tasks. To overcome these challenges, this paper proposes a Dual-Axis Long Short-Term Memory (LSTM) neural network to establish a high-fidelity inverse dynamic model of the PFSM. Unlike traditional non-recurrent models or SISO-based architectures, the proposed Multi-Input Multi-Output (MIMO) framework explicitly learns the coupled inverse dynamics, enabling simultaneous compensation of hysteresis and inter-axis interference. A composite control strategy combining the LSTM feedforward controller with a PID feedback loop is further developed to ensure system stability and disturbance rejection. Extensive comparative experiments were conducted on a PFSM prototype. Results demonstrate that the proposed method significantly outperforms state-of-the-art benchmarks, including the Multiple Nonlinear Autoregressive Moving Average-Level 2 (Multi-NARMA-L2) method and Single-Axis LSTM models. Specifically, the proposed strategy eliminates the elliptical distortion observed in SISO methods during high-frequency circular and Lissajous trajectory tracking, and demonstrates superior generalization on non-periodic random signals. Furthermore, step disturbance tests confirm the robust stability of the composite controller against external perturbations. The proposed approach offers a robust and high-precision solution for complex nano positioning applications.