# Oscillation Suppression Method of Digital Proportional Valve Based on Fuzzy Intelligent PID Control
## 4 Control Method Design
### Fuzzy Intelligent PID Controller Design  
The structure of control chambers at both ends of the main spool of the DPV is asymmetric, which produces different control effects in different movement directions. By optimizing the existing full-bridge-based control methods, the following half-bridge-based fuzzy intelligent PID control method is proposed. The parameters of fuzzy logic include the universe of discourse of input and output variables, fuzzy sets and membership functions, the fuzzy rule base, and the defuzzification method. The universe of discourse of input and output variables is set according to the specific parameters of the system. For the fuzzy sets and membership functions, the methods commonly used in literature and textbooks are adopted. There is a total of seven intervals for the fuzzy sets (NB, NM, NS, ZO, PS, PM, and PB). When NB and PB are at the maximum error, the stable and smooth Gaussian function is used, and for the others, the triangular membership function with higher sensitivity is used. The fuzzy rule base is designed based on experience and the system. The commonly used centroid method is chosen as the defuzzification method because it takes comprehensive information into account, the output results are relatively smooth, it has relatively high accuracy, and it is applicable to various types of membership functions. We have already opened or closed different HSVs according to the variations in input signals and errors. The usage details of the four HSVs are presented in Table 1. Additionally, to enhance the control accuracy, different control parameters are employed when the main spool moves in different directions. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Input Signal \(x_{in}\)** & **Position Error e** & \\
**Condition** & **Condition** & **Way to Control the Main Spool** \\ \hline \(x_{in}>0\) & e \(>0\) & Use HSV 1 and 3 \\ \(x_{in}>0\) & e \(\leq 0\) & Use HSV 2 and 4 \\ \(x_{in}<0\) & e \(\leq 0\) & Use HSV 2 and 4 \\ \(x_{in}<0\) & e \(>0\) & Use HSV 1 and 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Switching combinations of HSVs. Figure 5: Control structure block diagram of the DPV. The fuzzy intelligent PID control rule is designed as follows:  
\[\mathfrak{u}=(K_{p}+fk_{p})e(t)+(K_{i}+fk_{i})\int e(t)dt+(K_{d}+fk_{d})\frac{de(t )}{dt} \tag{7}\]  
where \(K_{p}\), \(K_{i}\), and \(K_{\mathrm{d}}\) represent the initial parameters of PID, and \(f\mathrm{k}_{p}\), \(f\mathrm{k}_{i}\), and \(f\mathrm{k}_{\mathrm{d}}\) represent the three output parameters of a fuzzy intelligent controller. The fuzzy intelligent controller takes the position error \(e\left(t\right)\) and the error change rate \(\mathrm{d}e\left(t\right)/\mathrm{d}t\) of the main spool as input parameters and takes three PID adjustment parameters \(f\mathrm{k}_{p}\), \(f\mathrm{k}_{i}\), and \(f\mathrm{k}_{\mathrm{d}}\) as outputs. The position error and error change rate of the main spool were quantified into fuzzy domains E [\(-\)1,1] and EC [\(-\)6,6], respectively. **Assumption 1**. : \(e_{i}\) _and \(ec_{i}\) are uniformly distributed regular convex fuzzy sets on domains E and EC, which are described by seven linguistic values. Their membership functions are stable and smooth Gaussian functions when the E and EC are NB and PB, and they are all trigonometric functions in other cases. The membership function is shown in Figure 6._  
**Assumption 2**. : \(f\mathrm{k}_{p}\)_, \(f\mathrm{k}_{i}\), and \(f\mathrm{k}_{d}\) are described by seven linguistic values. Their membership functions are all Gaussian functions, as shown in Figure 7._  
Based on the above assumptions, the implication relationship between each rule is as follows:  
\[\mathrm{R}i=(e_{i}\mathrm{and}ec_{i})\to fk_{\mathrm{pi}},fk_{\mathrm{i}i},fk_{ \mathrm{d}i}(i=1,2,\ldots,7) \tag{8}\]  
Fuzzy rules are determined based on experience and system requirements.