Automating the sewing process presents significant challenges due to the inherent softness of fabrics and the limited control capabilities of sewing systems. To realize sewing automation, we propose a time-scaling modeling and control architecture of the robotic sewing system. By using the time-scaling modeling, the nonholonomic kinematics of the sewing process of the industrial sewing machine is linearized precisely. Based on this model, a two-layer real-time control architecture is proposed. The upper layer controls the sewn seam line trajectory using the model-based feedback control implemented in the time-scaling domain, while the lower layer controls the manipulator and the sewing machine using geometric-based trajectory generation and coordinated motion control of the robot and the sewing system in the time domain. The experimental results demonstrate that the sewing trajectories exponentially converge to the desired trajectories without overshooting under different initial conditions and sewing speeds. Besides, the same sewing trajectories under different sewing speeds are obtained for a given stitch size. The sewing results show the good performance and application potential of the proposed robotic sewing system.