Fractional-Order Composite Control Method for Beam Steering of Liquid Crystal Optical Phased Arrays

To address the slow response, low pointing accuracy, and degraded stability caused by the coexistence of fractional-order dynamics, dual-axis coupling, and system delay in liquid crystal optical phased array (LCOPA) beam control, a fractional-order composite control method is proposed. First, the LCOPA is modeled as a two-input two-output system, and a fractional-order time-delay dynamic model is established. A composite control architecture integrating a fractional-order controller, a diagonal decoupling compensator, and a Smith predictor is then designed to improve dynamic response, suppress cross-axis coupling, and mitigate delay-induced performance degradation. A multi-strategy improved sparrow search algorithm is used to optimize the dual-channel fractional-order controller parameters, and closed-loop stability is verified using characteristic roots and the Matignon criterion. Simulation results show that the settling times of both axes are 11.50 ms, reduced by 62.54%/62.30%, 57.09%/56.11%, and 51.68%/48.89% compared with the results for PID, FOPID, and ADRC, respectively. The maximum cross-axis deviations are reduced to 0.0036° and 0.0030°, respsectively. Experiments further show that the mean absolute pointing errors of the X- and Y-axes decrease from 0.0466° and 0.0362° to 0.0057° and 0.0045°, while the RMSEs under external disturbances are 0.0060° and 0.0044°, respectively. These results demonstrate improved response speed, pointing accuracy, decoupling performance, and disturbance rejection.