Construction and Parameter Identification of Two-Dimensional Coupled Fractional-Order Dynamic Model for LCOPA

Aiming at the limitation that the traditional integer-order dynamic model of a liquid crystal optical phased array (LCOPA) cannot simultaneously characterize the liquid crystal deformation memory effect, cross-coupling of two-dimensional deflection channels and time-delay characteristics, this paper proposes a two-dimensional coupled fractional-order dynamic modeling and parameter identification method based on fractional calculus. First, the two-dimensional beam deflection mechanism of LCOPA is analyzed to establish a static beam propagation model. Then, a fractional-order generalized Kelvin constitutive equation is adopted to construct a coupled dynamic model integrating multi-element coupling, channel cross-coupling and time-delay characteristics. A Legendre wavelet integral operational matrix is constructed to simplify fractional operations, combined with the least squares algorithm to achieve synchronous high-precision identification of multiple parameters. Finally, an experimental platform is built for verification. The results show that the proposed model achieves a fitting degree of 98% for beam deflection dynamics, with steady-state prediction error less than 0.15% and dynamic RMSE no more than 0.00020 rad, significantly outperforming integer-order models. This research provides theoretical support and engineering reference for modeling and controller design of high-precision non-mechanical beam steering systems.