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.

Nonlinear hysteresis effects in piezoelectric fast steering mirrors (FSMs) are major culprits of deteriorating the servo performance and reducing the robustness of a control system. In order to compensate for such nonlinearities, this paper presents an identification and compensation method of piezoelectric hysteresis using frequency response measurements. The relationship between hysteresis curves and frequency response was analyzed using various amplitudes of input voltage and measured output displacements. Results proved that hysteresis curves could be reconstructed based on frequency response measurements. By utilizing an inverse function from reconstructed hysteresis curves, parameters for the compensation model were identified. Experimental results showed that the maximum range of output displacement at the nominal position due to hysteresis was significantly decreased by 76% when the hysteresis model identified by the proposed frequency-domain method was used. In addition, the compensated frequency response showed consistent results regardless of input amplitudes, implying that linear dynamics of the piezoelectric FSM could be separately measured.