## 5 Semi-Active Control Analysis of the Multi-DOF Seat Damping Suspension
### Design of the Semi-Active Controller
#### 5.1.3 Optimization of the Control Algorithm  
The control rules and reasoning mechanism of a designed fuzzy controller cannot be adjusted, but the quantization factors \(K_{a}\) and \(K_{v}\) and the scale factor \(K_{u}\) can be adjusted, which significantly influences the controller's performance. The experience-based selection of those factors was based on trial and error; it was challenging to obtain an optimum. Therefore, the best combination of the quantization factors \(K_{a}\) and \(K_{v}\) and the scale factor \(K_{u}\) of the fuzzy controller were searched using an optimized algorithm to obtain better control.  
The grey wolf optimizer (GWO) algorithm is an intelligent population optimization algorithm that was first proposed by [PERSON] in 2014 [25]. The GWO algorithm has a simple principle, uses fewer adjustment parameters, and little calculation, and has been applied in face recognition, traffic flow prediction, power system control, and other fields. Therefore, we used the GWO algorithm to quantify factors \(K_{a}\) and \(K_{v}\) and the scale factor \(K_{u}\), to obtain the best control effect.  
The optimization process of the GWO algorithm is described below.  
The GWO algorithm defines the best result, second best result, and the third best result as \(\alpha\) wolf, \(\beta\) wolf, and \(\delta\) wolf, respectively, which guide hunting; other candidate results are defined as \(\omega\) wolf, which follows \(\alpha\) wolf, \(\beta\) wolf, and \(\delta\) wolf. The predation behavior of gray wolves is divided into encircling, hunting, and attacking. Hunting by the gray wolf is expressed as follows [25]:  
\[\left\{\begin{array}{l}D=\left|C\cdot X_{p}(t)-X(t)\right|\\ X(t+1)=X_{p}(t)-A\cdot D\end{array}\right. \tag{16}\]  
where \(D\) is the distance between the wolf and its prey; \(X(t)\) and \(X_{p}(t)\) are the current positions of the wolf and prey, respectively; \(t\) is the current number of iterations; and \(A\) and \(C\) are the coefficient vectors.  
The specific definitions of \(A\) and \(C\) are as follows:  
\[\left\{\begin{array}{l}A=2a\cdot rand1-a\\ C=2\cdot rand2\end{array}\right. \tag{17}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\(v_{s}\)} & \multicolumn{5}{c}{\(v_{rel}\)} \\ \cline{2-6}  & **NB** & **NS** & **ZE** & **PS** & **PB** \\ \hline NB & B & M & S & **ZE** & **ZE** \\ NS & M & S & **ZE** & **ZE** & **ZE** \\ ZE & S & **ZE** & **ZE** & **ZE** & **S** \\ PS & **ZE** & **ZE** & **ZE** & **S** & **M** \\ PB & **ZE** & **ZE** & **S** & **M** & **B** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Fuzzy control rule table.  
Figure 22: Structure of fuzzy controller.  
where \(a\) is a linearly decreasing vector from 2 to 0. \(rand1\) and \(rand2\) are a randomly generated vector assignment in the interval [0, 1].  
\[\left\{\begin{array}{l}D_{\alpha}=\left|C_{1}\cdot X_{\alpha}-X\right|\\ D_{\beta}=\left|C_{2}\cdot X_{\beta}-X\right|\\ D_{\delta}=\left|C_{3}\cdot X_{\delta}-X\right|\end{array}\right. \tag{18}\]  
\[\left\{\begin{array}{l}X_{1}=X_{\alpha}-A_{1}D_{\alpha}\\ X_{2}=X_{\beta}-A_{2}D_{\beta}\\ X_{3}=X_{\delta}-A_{3}D_{\delta}\end{array}\right. \tag{19}\]  
\[X(t+1)=(X_{1}+X_{2}+X_{3})/3 \tag{20}\]  
In these formulas, \(D_{\alpha}\), \(D_{\beta}\), and \(D_{\delta}\) are the distances of \(\alpha\), \(\beta\), and \(\delta\) wolf from other gray wolves, respectively; \(X_{\alpha}\), \(X_{\beta}\), and \(X_{\delta}\) are the positions of \(\alpha\), \(\beta\), and \(\delta\) wolf, respectively; \(A_{1}\), \(A_{2}\), and \(A_{3}\) are coefficient vectors; \(C_{1}\), \(C_{2}\), and \(C_{3}\) are random vectors; and \(X\) is the position of the current gray wolf individual.  
Finally, the wolf pack assaults the prey. The value of the convergence factor a in Formula 17 linearly decreases from 2 to 0 with the value of \(a\). If \(\left|A\right|\leq 1\), the wolf pack assaults the prey, highlighting the local search; if \(A>1\), the wolf pack gives up hunting the current prey and spreads out, highlighting the global search.