# Bionic Intelligent Algorithms Used in Helicopter Individual Blade Control Optimization
## 2 Methods
### Fuzzy Neural Network Combined with PID Controller
#### 2.2.3 Fuzzy Neural Network  
A new method was established by combining the characteristics of fuzzy control and the artificial neural network together. The learning ability of the neural network was introduced into the fuzzy system, and four parts of the fuzzy system were represented by the distributed neural network [11]. The Figure 9 showed the structure of the fuzzy neural network. The input layer passed the value of the input variable \(x_{i}\) to the next layer. The second layer, the fuzzification layer, received the values passed from the input layer and performs as fuzzification processing. Each node in this layer represented the value of a language variable and acted as a membership function to calculate the input variables. The membership degree was: \(\mu_{i}^{j}(i=1,2,\ldots,n;j=1,2,\ldots,m)\), with the Gaussian function, as the membership function is as follows:  
\[\mu_{i}^{j}=e^{-\frac{(x_{i}-x_{i})^{2}}{\sigma_{ij}^{2}}} \tag{27}\]  
Among the equation, \(c_{ij}\) represented the center of the Gaussian membership function, \(\sigma_{ij}\) represented the width of the Gaussian membership function, the connection weight of this layer was 1, and the number of nodes in this layer was \(N_{2}=\sum_{i=1}^{n}m_{i}\). The third layer was the fuzzy inference layer, where each node corresponded to a fuzzy control rule. The neurons of the fuzzy inference layer corresponded to the antecedents of the fuzzy rules, and the applicability of each fuzzy rule was calculated in the form of a product. The expression is as follows:  
\[ \begin{gathered}\alpha_{j}=\mu_{1}^{i1}\mu_{2}^{i2}\cdots\mu_{n}^{ in}\\ i_{1},i_{2},\cdots,i_{n}\in\{1,2,\cdots,m\};\quad j=1,2,\cdots,m;m= \prod\limits_{m}^{n}m_{i}\end{gathered}  \tag{28}\]  
The connection weights of the fuzzy inference layer were all 1. When the input to this layer was constant, only the linguistic variable values around the input had a larger membership function value, and the membership function values far away from the linguistic variable area are relatively large. If it was small, it would be treated as \(0\) during the calculation. The function of the fourth layer was to convert a dimensional expression into a dimensionless expression in the inference process of the fuzzy neural network. The number of nodes in this layer was the same as that in the fuzzy inference layer. The expression is as follows:  
\[\beta_{j}=\alpha_{j}/\sum\limits_{j}^{m}\alpha_{j}\qquad j=1,2,\cdots,m \tag{29}\]  
Figure 9: Diagram of Mamdani fuzzy neural network structure. The fifth layer was the defuzzification layer with the function to convert the fuzzy amount into a precise amount; the expression is as follows:  
\[y_{i}=\sum_{j=1}^{r}\omega_{ij}\hat{\beta}_{j} \tag{30}\]  
Among the equation, \(\omega_{ij}\) represented the connection weight between the fourth layer and the fifth layer. The fuzzy neural network combined the advantages of the language variable description of the fuzzy controller and the advantages of the self-learning ability of ANN in the structure of the fuzzy neural network. The center value \(c_{ij}\), width value \(\sigma_{ij}\) of the Gaussian membership function, and the connection weight \(\omega_{ij}\) could be adjusted automatically. A fuzzy neural network was established. The following work is to combine the fuzzy neural network with the classical PID control together. The fuzzy neural network was used to adjust the PID control parameters automatically. Combined with the rotor aerodynamic model established in Section 2.1, the optimization process is shown in Figure 10:  
In this system, the input \(r_{in}(k)\) was the increment of the second-order harmonic cosine component, and the output \(y_{out}(k)\) was the 3/rev component of the vertical force on the rotor hub. The expected value was the minimal vertical load of the rotor hub, which was set according to a specific requirement.