This paper introduces a physics enhanced residual learning (PERL) framework for connected and automated vehicle (CAV) platoon control, addressing the dynamics and unpredictability inherent to platoon systems. The framework first develops a physics-based controller to model vehicle dynamics, using driving speed as input to optimize safety and efficiency. Then the residual controller, based on neural network (NN) learning, enriches the prior knowledge of the physical model and corrects residuals caused by vehicle dynamics. By integrating the physical model with data-driven online learning, the PERL framework retains the interpretability and transparency of physics-based models and enhances the adaptability and precision of data-driven learning, achieving significant improvements in computational efficiency and control accuracy in dynamic scenarios. Simulation and robot car platform tests demonstrate that PERL significantly outperforms pure physical and learning models, reducing average cumulative absolute position and speed errors by up to 58.5% and 40.1% (physical model) and 58.4% and 47.7% (NN model). The reduced-scale robot car platform tests further validate the adaptive PERL framework's superior accuracy and rapid convergence under dynamic disturbances, reducing position and speed cumulative errors by 72.73% and 99.05% (physical model) and 64.71% and 72.58% (NN model). PERL enhances platoon control performance through online parameter updates when external disturbances are detected. Results demonstrate the advanced framework's exceptional accuracy and rapid convergence capabilities, proving its effectiveness in maintaining platoon stability under diverse conditions.