# Oscillation Suppression Method of Digital Proportional Valve Based on Fuzzy Intelligent PID Control
## 4 Control Method Design
### Fuzzy Intelligent PID Controller Design
When the position deviation E of the main valve spool is large and the deviation rate EC is small, \(f\mathrm{k}_{\mathrm{p}}\) is relatively large, while \(f\mathrm{k}_{\mathrm{i}}\) and \(f\mathrm{k}_{\mathrm{d}}\) are relatively small, aiming to accelerate the system response speed. When E is large and the deviation rate EC is also large, \(f\mathrm{k}_{\mathrm{p}}\) and \(f\mathrm{k}_{\mathrm{d}}\) are relatively small and \(f\mathrm{k}_{\mathrm{i}}\) is relatively large, with the purpose of reducing the overshoot. Figure 6: The membership function of E.  
Figure 7: The membership function of \(f\mathrm{k}_{\mathrm{P}}\). When E is small and EC is large, \(\beta_{\rm F}\)\({}_{\rm p}\) is relatively small and \(\beta_{\rm i}\) is relatively large to enhance the system's steady-state performance. When both E and EC are small, \(\beta_{\rm d}\) is relatively large to speed up the response and improve the system's steady-state performance. The fuzzy rule base is designed as shown in Table 2.  
The fuzzy quantities of \(\beta_{\rm p}\), \(\beta_{\rm i}\), and \(\beta_{\rm d}\) were obtained using fuzzy control rules, and the accurate values of \(\beta_{\rm p}\), \(\beta_{\rm i}\), and \(\beta_{\rm d}\) were calculated by the area center method. The values of \(\beta_{\rm p}\), \(\beta_{\rm i}\), and \(\beta_{\rm d}\) are shown in Figure 8.  
Obviously, \(\beta_{\rm F}\)\({}_{\rm p}\) is larger when E is larger and EC is smaller, \(\beta_{\rm i}\) is larger when E is smaller and EC is larger, and \(\beta_{\rm d}\) is larger when E is smaller. Considering the main spool displacement change rate \({\rm d}x\) (\(t\))/\({\rm d}t\) as the control condition, when \({\rm d}x\) (\(t\))/\({\rm d}t\geq 0\), a smaller proportional coefficient is adopted, and when \({\rm d}x\) (\(t\))/\({\rm d}t<0\), a larger proportional coefficient is used. Figure 9 shows the structural block diagram of the fuzzy intelligent PID controller. The specific control flowchart of the DPV is shown in Figure 5:0 \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{\(\beta_{\rm p}\)/\(\beta_{\rm i}\)/\(\beta_{\rm i}\)/\(\beta_{\rm d}\)i & \multicolumn{4}{c}{E} \\ \cline{3-8} \multicolumn{2}{c}{} & **NB** & **NM** & **NS** & **ZO** & **PS** & **PM** & **PB** \\ \hline \multirow{8}{*}{EC} & NB & PS/PM/Z & PS/PM/PS & PS/PB/PM & PS/PB/PM & PS/PB/PM & PM/Z/PS & PM/NB/Z \\  & NM & PS/PM/Z & PS/PM/PS & PS/PB/PM & PS/PB/PM & PS/PB/PM & PM/Z/Z & PM/NB/Z \\  & NS & PM/PS/PS & PM/PS/PS & PS/PS/PM & PM/PB/PM & PM/PS/PM & PB/NB/PS & PB/NB/PS \\  & ZO & PB/Z/PS & PM/Z/PS & PM/PS/PM & PM/PS/PM & PM/PS/PM & PB/Z/PS & PB/Z/PS \\  & PS & PB/NB/PS & PB/NB/PS & PM/PB/PM & PM/PB/PM & PM/PS/PM & PM/PS/PN & PM/PS/PS \\  & PM & PM/Z/Z & PM/Z/Z & PS/PB/PM & PS/PB/PM & PS/PB/PM & Z/PM/Z & Z/PM/Z \\  & PB & PM/Z/Z & PM/Z/Z & Z/PB/PM & Z/PB/PM & Z/PB/PM & PS/PM/Z & PS/PM/Z \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The fuzzy rule base. Figure 9: Structural block diagram of the fuzzy intelligent PID controller.