## 3 Design of the EASIST Transmission System
### The Controller
#### 3.2.1 ANFIS PID Controller  
The RBF neural network, first proposed by [PERSON] et al., is a local approximation network, which can approximate any nonlinear function with any accuracy and has the significant advantage of fast learning speed [40]. This paper designs the ANFIS controller by combining it with Fuzzy. The controller structure is shown in Figure 8, which consists of four layers: input layer, fuzzy layer, fuzzy reasoning layer, and output layer [41].  
The input layer includes \(e\) and \(ec\). The second layers describe the premise module IF in fuzzy rules. The third layer corresponds to the fuzzy reasoning module. And the output  
Figure 8: ANFIS PID control system structure.  
Figure 7: Structure diagram of the control system.  
layer is \(k_{p}\), \(k_{i}\) and \(k_{d}\) variables. The configuration of ANFIS is 2-14-49-3. The input variables \(e\) and \(ec\) are blurred into \(E\), \(EC\) and divided into fuzzy subsets of the following form:  
\[E=\{\text{NB, NM, NS, ZO, PS, PM, PN}\},\]  
\[EC=\{\text{NB, NM, NS, ZO, PS, PM, PN}\}.\]  
* The first layer: the input layer.  
The input quantity is imported into the ANFIS, and the input variables of this layer are \(e\) and \(ec\).  
\[\left\{\begin{array}{l}x_{1}=e(t)\\ x_{2}=ec(t)\\ O_{1}(i)=[x_{1},x_{2}]\end{array}\right. \tag{1}\]  
where \(i=1,2\).  
* The second layer: the fuzzy layer.  
The function of this layer is to fuzzy the input variables and calculate the membership function of each input variable. There are 14 nodes in this layer, corresponding to \(E\) and \(EC\) language variables: NB, NM, NS, ZO, PS, PM, and PN. This layer corresponds to the premise of the fuzzy rule, which is the IF part.  
\[O_{2}(i,j)=\exp\left(\frac{-\left[O_{1}(i)-C_{ij}\right]^{2}}{\left(b_{ij} \right)^{2}}\right) \tag{2}\]  
where \(i=1,2;j=1,2,\ldots,7\).  
* The third layer: the fuzzy reasoning layer.  
The function of this layer is to describe the fuzzy rules and form the fuzzy reasoning decisions. According to the input variables number and fuzzy subsets of each variable, the number of nodes in this layer is 49. Each node represents a fuzzy rule. The output of this layer corresponds to the conclusion of the fuzzy rules, which is the THEN part.  
\[O_{3}(i)=O_{2}(1,k_{1})O_{2}(2,k_{2}) \tag{3}\]  
where \(k_{1}=1,2,\ldots,7;k_{2}=1,2,\ldots,7;i=1,2,\ldots,49\).  
* The fourth layer: the output layer.  
The function of this layer is to defuzzify. The results obtained by the previous layer are weighted and output to the PID controller. The output variables are the setting results of \(k_{p}\), \(k_{i}\), and \(k_{d}\).  
\[O_{4}(i)=\sum_{j=1}^{9}O_{3}(j)\omega_{ij} \tag{4}\]  
where \(i=1,2,3\).  
\[\left\{\begin{array}{l}O_{4}(1)=k_{p}\\ O_{4}(2)=k_{i}\\ O_{4}(  
The center \(c_{ij}\) and width \(b_{ij}\) of the Gaussian function of ANFIS, and the weight \(w_{ij}\) between the fuzzy reasoning layer and output layer adopt a gradient descent method.  
\[\Delta c_{ij}=\eta\frac{\partial E(k)}{\partial c_{ij}}+\alpha\Delta c_{ij} \tag{7}\]  
\[\Delta b_{ij}=\eta\frac{\partial E(k)}{\partial b_{ij}}+\alpha\Delta b_{ij} \tag{8}\]  
\[\Delta\omega_{ij}=\eta\frac{\partial E(k)}{\partial\omega_{ij}}+\alpha\Delta \omega_{ij} \tag{9}\]  
where \(\eta\) is the learning efficiency, \(\alpha\) is the inertia coefficient.