Tension control system design using fractional-order adaptive ADRC and Lyapunov-based adaptation

During the prepreg winding process, the strong coupling between tension and speed, combined with nonlinear dynamics and high sensitivity to disturbances, often leads to tension fluctuations that degrade product performance. To address this issue, this paper proposes a composite tension control method that integrates fractional-order active disturbance rejection control (FO-ADRC) with a Lyapunov-based adaptive law. A nonlinear dynamic model incorporating the unwinding roller, winding roller, and dancer mechanism is developed, and a model-assisted extended state observer (MESO) is introduced to enable real-time disturbance estimation and compensation while reducing the dependence on observer bandwidth. In the controller design, a fractional-order proportional–derivative structure is employed to enhance frequency-domain regulation, while a Lyapunov-based adaptive law is used to adjust control gains online, thereby improving stability and robustness under uncertain operating conditions. Furthermore, D-decomposition analysis is applied to investigate the stability region of control parameters, providing theoretical guidelines for controller tuning. Simulation and experimental studies were conducted under typical operating conditions. The tension-switching simulations demonstrated that the proposed method significantly reduced overshoot and settling time across multiple reference tensions (20 N, 30 N, and 50 N), ensuring smooth transitions. Experimental validation under speed disturbances further confirmed its effectiveness: when the spindle speed increased stepwise from 60 r/min to 240 r/min, the peak tension overshoot decreased from approximately 3.0 N to within 1.2 N, while the steady-state error was reduced from ±2.0 N to ±0.5 N. These results verify the proposed method through stability analysis, simulation, and experimental validation, and show that it can achieve high-precision and robust tension control under complex conditions such as tension switching and speed disturbances.