# A Parameter Self-Tuning Decoupling Controller Based on an Improved ADRC for Tension Systems
## 1 Introduction  
A roll-to-roll coating machine is an excellent option for producing printed electronic devices in a green, efficient, and continuous manner due to its thick coating and stable process. For the manufacturing of flexible electronic devices, it is crucial to maintain steady-state tension, with substrate tension control accuracy being required to be within \(\pm 5\%\). The accuracy of substrate tension control affects the quality of flexible electronic devices, causing defects such as folds, collapse, and slip. Therefore, tension control accuracy is critical for substrates. However, due to the tension system having multiple inputs and outputs, strong coupling, and parameters that vary with time, precise tension control is challenging. When it comes to modeling the tension systems of roll-to-roll coating machines, scholars take into account factors such as motor speed difference, bearing misalignment, shaft roundness error, and the impact of drying temperature on the substrate's elastic modulus. They then study and establish a serial coupling model of the tension system based on these factors. At the same time, many scholars have proposed new control strategies to improve tension control accuracy in roll-to-roll coating manufacturing in response to increasing accuracy requirements. [PERSON] et al. first proposed a multi-span tension model based on the law of mass conservation [1]. [PERSON] et al. introduced thermal deformation and equivalent elastic modulus into the multi-span tension model, and they researched and analyzed the changes these two factors made to the substrate tension [2]. [PERSON] et al. analyzed the factors that contribute to the variation oftension in a roll-to-roll system and developed a tension model for each section, which successfully predicted the tension applied to the system [3]. [PERSON] et al. established a heat transfer model capable of predicting the temperature distribution of the substrate [4]. [PERSON] et al., based on the energy approach and the heat conduction equation, considering the effect of deformation, derived the nonlinear vibrational equations of an axially traveling flexible printing electronic membrane coupled with temperature under the function of a nonlinear electrostatic excitation force [5]. [PERSON] et al. established a mathematical model to express the transverse motion of the multi-span substrate [6]. [PERSON] et al. trained a special neural network model to dynamically update rewinding roll tension with the radius of the roll [7]. [PERSON] et al. proposed a model for estimating web tension and tension distribution by measuring the local contact force on the substrate [8]. Research on tension control strategy has also been greatly developed. Based on research on the modeling of the tension system, [PERSON] et al. proposed a coordinated and optimized control method for multiple rolls, in which the speed of the drive roll of the next unit was adjusted to maintain the low tension condition of the substrate when the speed of the drive roll of the previous unit changes [9]. [PERSON] et al. proposed a nonlinear model predictive control scheme to eliminate tension perturbations in roll-to-roll systems [10]. [PERSON] et al. proposed a feed-forward controller that employed finite element method (FEM)-based web temperature distribution inputs to enhance tension control performance during the drying span [11]. [PERSON] et al. proposed a parameter self-tuning and self-anti-turbulence control strategy based on an RBF neural network by integrating feed-forward, RBF, and an ADRC, which improved the accuracy of the tension control [12]. [PERSON] et al. proposed a feed-forward improved PID parameter self-tuning and decoupling controller, which realized the steady-state control of tension [13]. [PERSON] et al. proposed a perturbed machine model that made it possible to handle both nonlinearities and parameter variations of a machine using simple static and first-order dynamic compensators [14]. [PERSON] et al.