# Multi-Span Tension Control for Printing Systems in Gravure Printed Electronic Equipment
## 1 Introduction  
Printed electronics technology involves the process of layering and depositing various electronic materials in the form of ink through printing methods, thereby forming electronic devices or circuit systems with diverse functions. [PERSON] studied the key technology to attain a high degree of TFT integration through R2R gravure printing [1]. [PERSON] developed a R2R processing system with gravure printing and coating functions for manufacturing printed electronic devices on flexible substrates [2]. [PERSON] analyzed the rheological properties of silver inks in the R2R printing process [3]. [PERSON] provided a potential strategy for commercially fabricating flexible perovskite solar cells (f-PSCs) via a scalable and efficient R2R printing process [4]. Compared with traditional manufacturing techniques for electronic devices and circuits, printed electronics technology boosts numerous advantages, including the absence of a corrosion process, environmental friendliness, minimal material and energy consumption, as well as the capability for large-scale production [5, 6]. Gravure printed electronic equipment is an essential piece of machinery for producing roll-to-roll (R2R) gravure-printing electronic products. While gravure-printing electronic products share similar production processes with traditional gravure printing of image-text materials, the former necessitates higher performance standards for the gravure-printing equipment, including greater accuracy in web tension and registration [7]. The tension system, which serves as the core of gravure printed electronic equipment, comprises three subsystems: unwinding, printing, and rewinding, as shown in Figure 1. The primary function of the unwinding tension system is specifically to ensure that theweb enters the printing section at a consistent speed while minimizing tension fluctuations. The purpose of the printing tension system is not only to maintain a constant web tension but also to ensure higher tension accuracy. This tension system is intimately coupled with the register system in the printing section, serving as its foundation. The rewinding tension system controls the web tension, ensuring that it varies vary according to a predetermined law (e.g., taper tension) during the rewinding process, thereby ensuring rewind quality and preventing wrinkles in the rolled material. The tension system of gravure printed electronic equipment has a complex structure and variable working conditions, and it is influenced by numerous factors that make the tension system exhibit nonlinear, strong coupling, and strong interference characteristics. The tension model serves as the foundation of tension control. Numerous scholars have been studying tension system models with the aim of devising mathematical models capable of accurately reflecting the intricate relationships among inputs, outputs, and various disturbances. In the unwinding and rewinding processes of gravure printed electronic equipment, significant tension fluctuations arise due to the continual changes in the radius and moment of inertia of the material roll, as well as the utilization of dancer roller mechanisms and material changing devices. Consequently, this topic has garnered substantial attention within the field of tension research. Many scholars have concentrated their efforts on studying models of key components or subsystems within tension systems. [PERSON] established a dynamic model of the non-continuous unwinding tension-control system to research the tension characteristics of non-continuous film unwinding systems [9]. [PERSON] proposed a mathematical model of the R2R system and described the effect of transmission backlash on web tension [10]. [PERSON] established the nonlinear coupling model of winding tension system by the coupling method [11]. The factors influencing changes in the tension of a roll-to-roll system were analyzed, and a tension model was developed for each section to predict the tension by [PERSON] [12].