# Oscillation Suppression Method of Digital Proportional Valve Based on Fuzzy Intelligent PID Control
## 5 Simulation Results and Discussion
### Effectiveness Analysis
#### 5.1.1 Step Input Response  
When the reference displacement is a step input of 7-3.5 mm, the step response of the DPV is measured, and the results are shown in Figure 12. We have observed that the step response curve under the position-based full-bridge compensation control method depicted in Figure 12 coincides with the experimental results presented in Figure 4a. This demonstrates that the simulation results are reliable and can be utilized for subsequent simulation analysis.  
As shown in Figure 12, the main spool produces oscillation at the position of 3.5 mm in the control of full-bridge complementary method, while oscillation disappeared in the  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline \(m\) (kg) & 0.3 \\ \(K\) (N/mm) & 25 \\ \(x_{0}\) (mm) & 5 \\ _The diameter of main spool_ (mm) & 18 \\ _Leakage clearance_\(C_{r}\) (mm) & 0.01 \\ \(p_{K}\) (MPa) & 10 \\ \(V_{5}\) (mm\({}^{3}\)) & \(4\times 10^{3}\) \\ \(V_{4}\) (mm\({}^{3}\)) & \(1.8\times 10^{4}\) \\ \(\beta\) (MPa) & 1700 \\ \(p_{p}\) (MPa) & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Simulation parameters.  
Figure 12: Step response of the proportional valve: (**a**) Displacement step response of the main valve spool; (**b**) displacement tracking error; (**c**) control input of HSVB; (**d**) pressure of the two control chambers of the main spool.  
control of half-bridge method, and the main spool shows a better performance of the proposed controller than the PID controller. For comparison purposes, the response results of step input from 0 mm to 7 mm are summarized for the performance indices shown in Table 4. As we can see from Figure 12, the proposed control method can respond to the input signal quickly when the position error occurs. At the initial stage, the position error is a larger value in the positive direction, so that the HSV 1 and 3 have a larger duty cycle, and the pressure in the left chamber (\(p_{5}\)) rises rapidly; therefore, the spool moves to the position of 7 mm. When receiving a stepping input signal of 3.5 mm, the HSV 2 and 4 have a larger duty cycle control signal, and the pressure on the right side of the main spool increases and the left side reduces. The main spool is pushed and stabilized at the desired position after a short adjustment time. Then, the oscillation is suppressed.  
As can be seen from the simulation results summarized in Table 4, it is concluded that the rising time for the proposed method is 121 ms, which is longer than PID of half-bridge control, while the steady state error is 0.016 mm, which is much less than PID of half-bridge control of 0.243 mm, and a reduction of 26.2% is obtained in the overshoot for the proposed method. In addition, we have carried out an integral square error (ISE) analysis of the proposed control method and the PID of half-bridge control method within the time interval from 3 s to 5 s, and the results are presented in the last column of Table 4. The tracking error of the proposed method is significantly smaller than that of the traditional PID control method, suggesting that the proposed method exhibits a more precise and reliable tracking performance for step inputs.  
In summary, compared with the full-bridge control methods, the proposed half-bridge-based fuzzy intelligent PID control can quickly predict and adjust the control signals of the four HSV according to the position error and error change rate, so that the pressure in the left and right control chambers of the main spool can be quickly balanced. The proposed control method can suppress the oscillation of the main spool of the proportional valve for the step response.