# Multi-Span Tension Control for Printing Systems in Gravure Printed Electronic Equipment
## 4 Performance Study of the ADRC Decoupling Controller for the Printing Tension System  
### Experimental Conditions  
In order to verify the control performance of the ADRC decoupling controller for the multi-span printing tension system, the designed control system was simulated on MATLAB/Simulink and experimentally studied on a dedicated experimental platform, with its performance compared to that of the traditional PID controller.  
The gravure printed electronic experimental platform is shown in Figure 5. It comprises a comprehensive system, primarily featuring an unwinding unit, a dedicated unwinding traction unit, a quartet of printing units, a rewinding traction unit, a rewinding unit, two dancer roller mechanisms, and a total of five load cells for accurate measurements.  
The electrical system is based on an industrial computer and controls eight servo motors, specifically two HF-SP102s and six HF-SE52 JW1-500s, through an 8-axis motion controller, the GTS-X800-PV-PCI. Five LX-015 TD load cells are used to detect the tensions of the web in each printing span, and the tension data is transmitted to the industrial computer via the LM-10 TA tension amplifier. The monitoring software for the experimental platform is written in Visual C# and primarily encompasses functions such as motion control, data acquisition, and data storage. The system data sampling period and control period are both 10 ms, and the sampled data are not filtered.  
The key indicators of the experimental platform are presented in Table 1.  
Figure 5: Photograph of the gravure printed electronic experimental platform.  
The structure of the PID control system is illustrated in Figure 6, where the controller PIDi outputs a control quantity \(\omega_{pi}\) that is specifically designed to regulate the web tension \(T_{pi}\) of the printing span i.  
The simulation parameters of the printing tension system are identical to those of the experimental platform, as shown in Table 1. Due to the absence of a drying system, the Young's modulus of elasticity at the drying temperature is assumed to be the same as that at ambient temperature. The parameters of the PID controller and the ADRC controller are adjusted under the condition of a steady-state printing speed of 100 r/min and do not change during operation. The parameters of the PID controller and the ADRC decoupling controller for the printing tension system are listed in Tables 2 and 3, respectively. The simulation employs a fixed-step mode with a control period of 10 ms.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline Groups of printing units & 4 & group \\ Maximum web width & 300 & mm \\ Printing roller diameter & 60 & mm \\ Tension range & 10\(\sim\)150 & N \\ Maximum unwinding and rewinding & 350 & mm \\ \multicolumn{3}{c}{Web material} & PET & / \\ Web length in a span & 350 & mm \\ Cross-section area of web & 10 & mm\({}^{2}\) \\ Young’s modulus of PET(25 °C) & \(4.89\times 10^{9}\) & Pa \\ \hline \hline \end{tabular}
\end{table}
Table 1: Main technical indicators of the experimental platform.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Controller** & **Parameter** \\ \hline PID1 & \(K_{P1}=15\); \(K_{I1}=200\); \(K_{D1}=0.12\) \\ PID2 & \(K_{P2}=15\); \(K_{I2}=200\); \(K_{D2}=0.12\) \\ PID3 & \(K_{P3}=15\); \(K_{I3}=200\); \(K_{D3}=0.12\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of the PID controllers for the printing tension system.  
Figure 6: PID control structure of the printing tension system.