Design of an MPC with hysteresis compensation for high-accuracy trajectory tracking of piezoelectric fast steering mirrors

Piezoelectric fast steering mirrors (PFSMs) are widely employed in beam pointing systems. However, achieving high-precision tracking of fast trajectories remains challenging due to biaxial cross-coupling and a limited input range. Based on a Hammerstein-structured PFSM model, this paper proposes a model predictive control (MPC) approach to decouple the multiple-input-multiple-output rate-dependent biaxial linear dynamics with system constraints, where the state vector is augmented with error integral variables to eliminate steady-state errors. Then an inverse hysteresis compensator is series-connected for the rate-independent nonlinearities. Furthermore, theoretical proofs of zero steady-state error and disturbance rejection for the proposed controller are provided. Tracking experiments on step, sinusoidal, and composite trajectories are conducted. Compared to proportional-integral-derivative model-free controller and various model-based approaches, including the direct inverse model feedforward, normalized least mean squares adaptive control, and adaptive sliding mode control, the proposed MPC achieves a 69% reduction in the root-mean-square error for 400Hz sinusoidal tracking relative to the baseline controllers, while also exhibiting robustness to frequency variations.