# Study on Multi-Span Tension Coupling Relationship of Gravure Printed Electronic Equipment  
Kui He  
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Pengbo He  
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Shifa Li  
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Jian Li  
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Compared to traditional image and text gravure printed equipment, printing electronics have higher requirements for tension systems, such as smaller tension fluctuations and stronger anti-interference capabilities. In order to improve the accuracy of tension control, an accurate mathematical model that can reflect the multivariable coupling relationships must be established. Additionally, the multi-span coupling relationships within the tension system must be thoroughly analyzed and studied. There are many studies on the tension system of gravure printed equipment, and these research works mainly focus on two parts: model and control, with more research on control methods and algorithms. Some researchers have combined PID control algorithm with other control algorithms to devise a synthetic control method for tension control. [PERSON] designed a variable gain PID to control the tension of the unwinding system [5]. [PERSON] adopted a second-order PI control to achieve the comprehensive control of tension and speed in the tension system and designed a feedforward control strategy to improve control accuracy for known disturbances in the system [6; 7]. Recently, advanced control methods such as robust control, fuzzy control, and neural network control have also been studied and applied to tension systems. [PERSON] adopted the Hoo robust control algorithm in the tension control of the winding system, which has a good interference suppression effect in the simulation results [8]. [PERSON] achieved robust control of the unwinding tension subsystem by designing a disturbance observer [9]. [PERSON] proposed an adaptive fuzzy control algorithm for tension systems, which can automatically adjust control parameters to adapt to changes in system parameters and structural uncertainties [10]. [PERSON] used multi-layer neural networks to achieve the semi-decoupling control of speed and tension [11]. [PERSON] designed a backstepping control strategy for a tension control system, and simulation showed that it can achieve high tension control accuracy [12]. [PERSON] proposed a decoupling controller based on active disturbance rejection control to address the tension control problem of the rewinding tension system in gravure printed machines, achieving a high-precision control of the rewinding tension system [13]. He studied the application of active disturbance rejection control technology in rewinding tension [14]. He designed a high-precision reduced-order observer-based LQR control method for roll-to-roll systems [15]. [PERSON] introduced an advanced observer-based single-loop feedback system for roll-to-roll machine tension control applications, and the simulation results numerically validated the feasibility of the proposed solution [16]. The relevant studies on tension models are as follows. The mechanism of tension generation is the foundation of tension systems, but only a few researchers have studied the tension mechanism. [PERSON] and [PERSON] analyzed the mechanism of tension generation between two rollers [17; 18]. [PERSON] conducted a dynamic study on the film and guide rollers in the film transport system of gravure printing [19; 20]. He analyzed the mechanism of tension generation in detail, established a mathematical model for a single span, and further studied the influence mechanism of the drying system on tension in printed electronic equipment [21; 22]. [PERSON] developed a tension model for flexible electronics that enables accurate and precise tension control [23]. [PERSON] also considered the influence of temperature in system modeling [24]. The unwinding and rewinding tension systems of electronic-shaft gravure printed equipment are hot topics in tension research.