# A Parameter Self-Tuning Decoupling Controller Based on an Improved ADRC for Tension Systems
## 4 Simulation and Analysis of Decoupled Controller for Global Tension System
### Simulation and Analysis of Decoupled Controller for Global Tension System
#### 4.2.2 Anti-Interference Capability Analysis  
When the system is in a steady state, the system was made to generate a velocity disturbance of 0.2 m/min for \(v_{0}\) in the 4 ths (\(v_{0}=\omega_{0}R_{0}\)); \(v_{4}\) was made to generate a velocity disturbance of 0.2 m/min in the 8 ths (\(v_{4}=\omega_{4}R_{4}\)). Then, \(T_{02}\) is made to generate a random disturbance of size \(\pm\)5 N in 1\(\sim\) 5 s time, and \(T_{04}\) is made to generate a random disturbance of size \(\pm\)5 N in 6\(\sim\)10 s time, and the results of simulation using parameter self-tuning decoupling controller based on improved ADRC for tension system and PID controller are shown in Figure 8.  
Figure 7: Comparison of decoupling performance simulation results.  
Observing the curves of Group (a) in Figure 8, it is evident that when \(v_{0}\) generates speed disturbance, \(T_{1}\) generates a tension disturbance of 0.16%. Similarly, when \(v_{4}\) generates speed disturbance, \(T_{4}\) and \(T_{5}\) generate tension disturbances of 0.4% and 0.06%, respectively. In the case of Group (b) curves, it can be observed that when \(v_{0}\) generates speed disturbance, \(T_{1}\), \(T_{2}\), \(T_{3}\), \(T_{4}\), and \(T_{5}\) generate tension perturbations of 16%, 3.1%, and 1.2%, 4%, and 0.6%, respectively. Likewise, when \(v_{4}\) generates velocity disturbance, \(T_{4}\) and \(T_{5}\) generate tension perturbations of 17% and 6%, respectively. The curves of Group (c) suggest that when \(T_{02}\) generates sustained tension perturbation, \(T_{1}\) generates a sustained tension perturbation of 0.01%. Similarly, when \(T_{04}\) generates sustained tension perturbation, \(T_{5}\) generates a sustained tension perturbation of 0.016%. Lastly, the Group (d) curves suggest that \(T_{02}\) produces a sustained tension perturbation, \(T_{3}\) produces a sustained tension perturbation of 0.6%, and \(T_{5}\) produces a sustained tension perturbation of 0.1%. Similarly, \(T_{04}\) produces a sustained tension perturbation, and \(T_{5}\) produces a sustained tension perturbation of 3%.  
The above results show that under speed disturbance, when using the parameter self-tuning decoupling controller based on improved ADRC for tension system, the maximum relative error of the tension unit is 0.4%; when using the traditional PID controller for tension control, the maximum relative error of the tension unit is 17%; under tension disturbance: when using the parameter self-tuning decoupling controller based on improved ADRC for tension system, the maximum relative error of the tension unit is 0.016%; when using the traditional PID controller for tension control, the maximum relative error of the tension unit is 3%. Compared with the traditional PID control, the parameter self-tuning decoupling controller based on improved ADRC for tension system has better anti-interference ability.  
Several researchers have conducted studies on designing decoupled controllers for tension systems. In this paper, the evaluation of the tension control performance of different  
Figure 8: Comparison of anti-interference simulation results.  
controllers is based on the relative tension error. Table 10 presents a comparison of the tension control effect of these controllers.  
Table 10 shows that under tension disturbance, the maximum relative error of FOPID controller is 4.63%, the REKF-PID controller is 3.74%, and the decoupled controller of tension system designed in this paper is 0.016%; under speed disturbance, the maximum relative error of RD-\(H\infty\) controller is 3.86%, and the decoupled controller of tension system designed in this paper is 0.4%. Therefore, the designed decoupling controller in this paper has a better control effect compared with FOPID, REKF-PID, and RD-\(H\infty\) controllers under tension disturbance and speed disturbance.