Free-space optical (FSO) communication has attracted extensive attention in recent years. To maintain a reliable FSO link, two main issues need to be addressed: beam drift and vibration. In this paper, we demonstrate a non-mechanical self-alignment system based on a cascaded liquid crystal optical antenna, in which a frequency decoupled hybrid integration Kalman filter (FDHI-KF) method is proposed to achieve predictive beam drift tracking and vibration mitigation. By leveraging the integrated control on our lab-made liquid crystal phase modulation devices, and implementing the adaptive algorithm on a heterogeneous field programmable gate array (FPGA), this system is capable of realizing precise self-alignment without any moving parts. Experiments are conducted to verify its performance in practical applications. We envision it to set a benchmark for future liquid crystal non-mechanical beam-steering systems in FSO communications.