# Multi-Span Tension Control for Printing Systems in Gravure Printed Electronic Equipment
## 5 Conclusions  
This article conducts in-depth research on the tension-control problem within the printing system of gravure printed electronic equipment. The main accomplishments and conclusions derived from this research are as follows:  
1. The structure and characteristics of the printing tension system were analyzed, and, subsequently, the control system structure of the printing tension system was constructed. Notably, the printing tension system is a typical multi-span coupled system,  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Performance Index** & **PID Control** & **ADRC Decoupling Control** & **Comparison Results** \\ \hline Decoupling performance & \multicolumn{1}{c}{Cannot decouple} & \multicolumn{1}{c}{Completely decoupled} & \multicolumn{1}{c}{Excellent} \\ Steady-state accuracy & \(\pm\)1.1 N (\(\pm\)2.2\%) & \(\pm\)0.7 N (\(\pm\)1.4\%) & \multicolumn{1}{c}{Increase by 36.4\%} \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance comparison of printing tension-control systems.  
Figure 10: Performance experiment of ADRC decoupling control for the printing tension system.  
which adopts a constant tension-control mode and controls the speed of the discharge rollers for each span.
2. A static decoupling control model for the printing tension system was established, and an active disturbance rejection control (ADRC) controller was designed for each tension span. The ADRC controller adopts a first-order form, omitting the tracking differentiator (TD), and the nonlinear state error feedback (NLSEF) component employs a proportional adjustment method. These designs greatly reduce the computational complexity of the tension-control system and improve control efficiency. The extended state observer (ESO) can quickly track the system output, estimate the total disturbance of the current span, and quickly compensate for the controller output.
3. Simulation and experimental studies were conducted on the ADRC decoupling controller of the printing tension system. The research results indicate that the designed ADRC decoupling controller can effectively decouple the multi-span coupled tension system and suppress system disturbances effectively. The multi-span tension system achieves a steady-state tension-control accuracy of \(\pm\)1.4%, which is significantly lower than the tension-control accuracy index of \(\pm\)5% for traditional image-text gravure printing. Compared with traditional PID control, the designed ADRC decoupling controller exhibits better decoupling performance, anti-interference ability, and steady-state accuracy, thus enhancing the overall performance of gravure printed electronic equipment.  
Conceptualization, K.H. and J.L.; methodology, K.H.; data curation, S.L. and P.H.; writing--original draft, K.H. and X.W.; writing--review and editing, J.L. and X.W.; funding acquisition, K.H. and J.L. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Key R&D Program of China (grant number 2023 YFB4605105) and the Key Research Projects of Henan Province (grant number 222102220044).  
Not applicable.  
The data presented in this study are available in the article.  
The authors declare no conflicts of interest.