High-Accuracy Model Predictive Control with Inverse Hysteresis for High-Speed Trajectory Tracking of Piezoelectric Fast Steering Mirror

TL;DR

This paper introduces a model predictive control method with inverse hysteresis compensation for piezoelectric steering mirrors, achieving high-precision, robust, and high-speed trajectory tracking by addressing nonlinear hysteresis and cross-coupling.

Contribution

It presents a novel MPC approach combined with inverse hysteresis modeling for improved high-speed trajectory tracking of PFSMs, reducing steady-state errors and enhancing robustness.

Findings

Significantly improved tracking accuracy over traditional controllers.

Effective compensation of hysteresis nonlinearities.

Robust performance across various trajectory types.

Abstract

Piezoelectric fast steering mirrors (PFSM) are widely utilized in beam precision-pointing systems but encounter considerable challenges in achieving high-precision tracking of fast trajectories due to nonlinear hysteresis and mechanical dual-axis cross-coupling. This paper proposes a model predictive control (MPC) approach integrated with a hysteresis inverse based on the Hammerstein modeling structure of the PFSM. The MPC is designed to decouple the rate-dependent dual-axis linear components, with an augmented error integral variable introduced in the state space to eliminate steady-state errors. Moreover, proofs of zero steady-state error and disturbance rejection are provided. The hysteresis inverse model is then cascaded to compensate for the rate-independent nonlinear components. Finally, PFSM tracking experiments are conducted on step, sinusoidal, triangular, and composite trajectories. Compared to traditional model-free and existing model-based controllers, the proposed method significantly enhances tracking accuracy, demonstrating superior tracking performance and robustness to frequency variations. These results offer valuable insights for engineering applications.