Modeling of Accumulator in Roll-to-Roll Coating Equipment and Tension Control with Nonlinear PID

This paper addresses the issue of the high-precision control of substrate tension in an accumulator during the roll-to-roll coating process. First, a coupling model for tension errors in the substrate within the accumulator is established, along with dynamic models for the input-output rollers, carriage, and the thrust model of the ball screw. Based on these models, a simulation model is built in MATLAB/Simulink to analyze the main causes of substrate tension errors in the accumulator under uncontrolled conditions. Next, to tackle the tension errors caused by carriage displacement, a nonlinear proportional-integral-derivative (PID) controller is proposed, and a control strategy for substrate tension in the accumulator is designed. Finally, based on the established simulation model, experiments are conducted using the proposed nonlinear PID controller and the designed tension control strategy, and their performance is compared with that of a classical PID controller. The simulation results show that both the nonlinear PID controller and the classical PID controller, when combined with the proposed tension error control strategy, can reduce tension errors in the accumulator substrate. However, the nonlinear PID controller is more suitable for controlling substrate tension errors in the accumulator. On the one hand, the nonlinear PID controller has better anti-disturbance capability. In the anti-disturbance experiment, under PID control, the substrate tension error remains stable at around -1.6 N, with tension disturbances of ±0.2 N occurring at approximately 185 s and 135 s. On the other hand, the nonlinear PID controller demonstrates better robustness. In the robustness experiment, under the nonlinear PID controller, the substrate tension error fluctuates within the range of 0 to 0.02 N, showing excellent robustness.