This paper presents model-based hysteresis and cross-coupling compensators designed for precise control of a piezoelectric fast steering mirror (FSM). The hysteresis compensators are developed by inversely modeling the variation in the force constant relative to various excitation voltages, enabling the system to maintain linear response characteristics across a broad range of input amplitudes. The cross-coupling compensator is formulated by creating a decoupling matrix that cancels out coupling effects, generating signals of equal magnitude and opposite phase for each axis. The implementation of these compensators reduces the hysteresis band and magnitude uncertainty in the FSM dynamics by over 89.6% and 74.2%, respectively, while also significantly suppressing cross-coupling effects by more than 85.5%. Furthermore, the performance of the proposed compensators is validated in a closed-loop control system, demonstrating a notable reduction in cross-axis vibrations and improved tracking performance in response to step reference inputs and highfrequency sinusoidal trajectories.
Lee et al. (Sun,) studied this question.