# Design of Multi-Cell Cooperative Control Algorithm Based on Fuzzy Brain Emotional Learning
## 5 Simulation Results
### Control Multiple Cells  
The holographic optical tweezers system can place and control different optical traps at the same time. According to its advantages, this section will simulate the experiment of using holographic optical tweezers to manipulate multiple cells for cooperative control through MATLAB simulation experiments to verify the cell coordination based on FBELNN. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data Type** & **Main Controller** & **X-Axis** & **Y-Axis** \\ \hline \multirow{5}{*}{RMSE of Single-cell manipulation} & PI & \(8.2016\times 10^{-6}\) & \(5.0930\times 10^{-6}\) \\  & PID & \(7.7955\times 10^{-6}\) & \(4.8561\times 10^{-6}\) \\ \cline{1-1}  & BP & \(3.5697\times 10^{-6}\) & \(2.9983\times 10^{-6}\) \\ \cline{1-1}  & RBFNN & \(3.5188\times 10^{-6}\) & \(2.9389\times 10^{-6}\) \\ \cline{1-1}  & FCMNN & \(3.2798\times 10^{-6}\) & \(2.6285\times 10^{-6}\) \\ \cline{1-1}  & This work & \(2.8583\times 10^{-6}\) & \(2.1381\times 10^{-6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Root mean square error (RMSE) of single-cell manipulation. Figure 9: The trajectory error on the \(Y\)-axis (single cell manipulation): (**a**) Use PI as a controller. (**b**) Use PID as a controller. (**c**) Use BP as a controller. (**d**) Use RBFNN as a controller. (**e**) Use FCMNN as a controller. (**f**) Use FBELNN as a controller. Controller performance and effectiveness for multicellular manipulation control. Configure the same solution environment parameters and controller parameters as in Section 5.1 for simulation experiments. The ideal trajectory for the experiment is designed as:  
\[\left\{ \begin{matrix}X_{\mathrm{x}}{}^{d}=35+t\\ X_{y}{}^{d}=30+35\sin(0.1t)\times\cos(0.06t)\end{matrix} \right. \tag{36}\]  
Set the ideal cell formation to vertical formation. The formation matrix \(\chi\) is \(\left[ \begin{matrix}0&0\\ 0&20\\ 0&-20\end{matrix} \right]\). The initial position of captured cells are shown in Table 3.  
Figure 10 demonstrates the effect of multi-cell control using the FRELNN-based cell cooperative controller. It can be seen from the figure that each yeast cell can be manipulated from different initial positions to desired trajectories and form expected desired cell formations. At the same time, the cells can still maintain the preset desired formation during the process of being manipulated to move on the desired trajectory. Figure 11 shows the relative distances of the three yeast cells in the direction of the \(X\)-axis and the direction of the \(Y\)-axis during the process of being manipulated. In the direction of the \(X\) axis, the initial positions of each cell are similar, and they can move to the expected position at almost the same time. In the direction of the \(Y\) axis, since the distance between cell 2 and cell 3 is closer to the expected trajectory, the convergence speed is faster. \begin{table}
\begin{tabular}{c c} \hline \hline
**Captured Cell** & **Initial Position (\(\mu\)m)** \\ \hline Yeast cell 1 & (2.65, 5) \\ Yeast cell 2 & (8.16, 61.5) \\ Yeast cell 3 & (15, 0) \\ \hline \hline \end{tabular} The effect of multi-cell cooperative control is shown in Figure 10.  
\end{table} 
Table 3: Initial position of the controlled cells. Figure 10: The effect of multi-cell cooperative control. Cell 1, whose initial position is further away from the desired trajectory, converges slightly slower than the other two cells, but still moves to the desired position in a short time. The effectiveness of the proposed FBELNN-based cell cooperative controller is confirmed. Figures 12 and 13 show the trajectory errors in the \(X\)-axis direction and the \(Y\)-axis direction when using different controllers for multi-cell manipulation. It can be clearly seen that the three cells have different trajectory errors during the manipulation control process. When the PI and PID controllers are used, the trajectory errors of the three yeast cells in both directions shake violently before convergence.