The implementation of rigid-flexible coupled force-controlled actuators significantly enhance the performance of adaptive robotic grinding. Nonlinear friction disturbances greatly limit the improvement of force accuracy. Three key factors complicate friction compensation in force-controlled actuators: complex traditional friction models neglecting dynamic-to-static friction transitions, the lack of rapid and accurate parameter identification methods, and compensation based on force feedback. In this study, a novel continuous dynamic friction model, parameter identification, and compensation method are introduced to improve the performance of force-controlled actuators. First, by investigating the transitional characteristics between presliding and sliding friction, a dynamic continuous friction model is formulated by combining the hyperbolic tangent function with a first-order system, and its dynamic friction and continuous differentiability properties are simulated and validated theoretically. Second, a time-frequency domain friction identification method combined with optimization algorithms is applied to accurately determine the model parameters, significantly reducing the calculation time while ensuring precision and consistency. Finally, the proposed model compensation is introduced based on the identified parameters, and experimental results on a self-developed robotic grinding platform verify the effectiveness of the proposed friction modeling and compensation method, achieving better force control precision and final grinding accuracy.