A disturbance-observer-based two-degree-of-freedom fractional-order internal model PID control method for liquid crystal optical phased array

The liquid crystal optical phased array (LCOPA), as a non-mechanical beam steering device, offers advantages of fast response, compact size, low power consumption, and easy integration, showing broad prospects in LiDAR and free-space optical communication. However, due to the inherent relaxation characteristics of liquid crystal materials and external disturbances, its beam steering process suffers from slow response, large steady-state error, and poor robustness. To address these issues, this paper proposes a disturbance observer (DOB)-based two-degree-of-freedom (2-DOF) SP-FO-IMCPID beam steering method. Different from existing LCOPA control methods that usually focus on a single aspect such as delay compensation, disturbance suppression, or fractional-order control, the proposed method integrates these mechanisms into a unified closed-loop beam steering framework for simultaneous reduction of system-level settling time and improvement of pointing accuracy and robustness. The DOB estimates and compensates for model uncertainties and external disturbances in real time to enhance robustness. A Smith predictor is introduced to compensate for the time delay, mitigating overshoot caused by sluggish response. A 2-DOF internal model control (IMC) structure independently optimizes the target tracking and disturbance rejection performance. Fractional calculus theory is incorporated to increase controller order, improving parameter tuning flexibility and adaptability to dynamic processes. The Whale Optimization Algorithm (WOA) is employed for global optimization of controller parameters. Simulation and experimental validation were conducted on a constructed LCOPA beam steering platform, including step response tests, fixed-point tracking tests, and robustness verification experiments. Results demonstrate that compared with traditional integer-order PID, fractional-order PID (FOPID) and FMAESO-FOPID methods, the proposed method effectively shortens the settling time, suppresses overshoot, and improves beam deflection tracking accuracy and anti-disturbance capability. This study enhances the dynamic control performance and robustness of the LCOPA system, providing a reference for high-precision laser beam steering under complex working conditions.