This paper introduces the CRL2RT algorithm, an advanced reinforcement learning method aimed at improving the real-time control performance of the Direct-Drive Tandem-Wing Experimental Platform (DDTWEP). Inspired by dragonfly flight, DDTWEP's tandem wing structure causes nonlinear and unsteady aerodynamic interactions, leading to complex load behaviors during pitch, roll, and yaw maneuvers. These complexities challenge stable motion control at high frequencies (2000 Hz). To overcome these issues, we developed the CRL2RT algorithm, which combines classical control elements with reinforcement learning-based controllers using a time-interleaved architecture and a rule-based policy composer. This integration ensures finite-time convergence and single-life adaptability. Experimental results under various conditions, including different flapping frequencies and yaw disturbances, show that CRL2RT achieves a control frequency surpassing 2500 Hz on standard CPUs. Additionally, when integrated with classical controllers like PID, Adaptive PID, and Model Reference Adaptive Control (MRAC), CRL2RT enhances tracking performance by 18.3% to 60.7%. These findings demonstrate CRL2RT's broad applicability and superior performance in complex real-time control scenarios, validating its effectiveness in overcoming existing control strategy limitations and advancing robust, efficient real-time control for biomimetic aerial vehicles.