## 3 Design of the Master and Auxiliary Compound Control
### Variable Universe Fuzzy PID Controller
#### 3.1.1 Adaptive Fuzzy PID Control Module  
Adaptive fuzzy PID control is a combination of fuzzy control and PID control. The main idea is to first establish the fuzzy relationship between the three parameters of PID and the deviation \(e\) and deviation change rate \(ec\), and then the real-time monitoring of \(e\) and \(ec\) and, according to the fuzzy logic PID controller of proportion, the integral and differential online adjustments. The design of a fuzzy PID controller mainly consists of four parts: fuzzification, determination of membership function, the establishment of fuzzy control rules and defuzzification. 1. Fuzzification of input and output  
The structure of the fuzzy controller is a two-dimensional structure with two inputs and three outputs. The difference between the measured main pipe pressure and the coordinated set value is \(e\). The deviation \(e\) and the deviation change rate \(ec\) are inputs, and the PID parameter adjustment values \(\Delta K_{p}\), \(\Delta K_{i}\) and \(\Delta K_{d}\) are output. First, the deviation, deviation change rate, proportional coefficient increment, integral coefficient increment and differential coefficient increment are fuzzy processed, the quantization domains corresponding to them are determined, and the fuzzy language is used to express them. Through the experiment, the deviation range of the main pipe pressure under different working conditions is \(-0.06\) to \(0.06\), and the deviation change rate range is \(-0.9\) to \(0.9\). In the test process, the PID parameters are roughly tested according to the trial and error method, and the basic domain of the proportional adjustment can be obtained ([\(-3\), \(3\)]). The basic domains of the integral coefficient and the differential coefficient adjustment are [\(-3\), \(3\)] and [\(-10\), \(10\)], respectively. The quantization domains corresponding to the input and output are both [\(-6\), \(6\)]. The fuzzy language variables are divided into seven levels, which are negative big (NB), negative medium (NM), negative small (NS), zero (ZO), positive small (PS), positive medium (PM), positive big (PB). The input and output variables are summarized in Table 3.  
(2) Determination of membership function  
To obtain the analysis results quickly, reduce the complexity of the control system and improve the operation efficiency, the membership function adopts the triangular membership function. Given the characteristics of different working conditions of MCCS, the membership function is set to be sparse at both ends of the input universe and dense in the middle to meet the requirements of the rapid response of large deviations and the accurate regulation of small deviations. The membership functions of the input domain and the output domain are shown in Figure 11. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Variable**} & \multicolumn{2}{c}{**Basic Domain**} & \multicolumn{2}{c}{**Quantization**} & \multicolumn{2}{c}{**Fuzzy Language**} \\ \hline \multirow{2}{*}{Input} & \(e\) & [\(-0.06\), \(0.06\)] & [\(-6\), \(6\)] & [NB, NM, NS, ZO, PS, PM, PB] \\  & \(ec\) & [\(-0.9\), \(0.9\)] & [\(-6\), \(6\)] & [NB, NM, NS, ZO, PS, PM, PB] \\ \hline \multirow{2}{*}{Output} & \(\Delta K_{p}\) & [\(-3\), \(3\)] & [\(-6\), \(6\)] & [NB, NM, NS, ZO, PS, PM, PB] \\  & \(\Delta K_{i}\) & [\(-3\), \(3\)] & [\(-6\), \(6\)] & [NB, NM, NS, ZO, PS, PM, PB] \\  & \(\Delta K_{d}\) & [\(-10\), \(10\)] & [\(-6\), \(6\)] & [NB, NM, NS, ZO, PS, PM, PB] \\ \hline \hline \end{tabular}  
Negative big (NB); negative medium (NM); negative small (NS); zero (ZO); positive small (PS); positive medium (PM); positive big (PB).  
\end{table} 
Table 3: Variables and domain.