# Design of Optical Tweezers Manipulation Control System Based on Novel Self-Organizing Fuzzy Cerebellar Model Neural Network

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model of NSOFCMNN

#### 2.1. Fuzzy Rules of the NSOFCMNN

#### 2.2. Structure of the NSOFCMNN

#### 2.3. Updating Law

#### 2.4. Novel Self-Organizing Adjustment Mechanism

## 3. Cell Manipulation Control

#### 3.1. Holographic Optical Tweezers System

#### 3.2. Cell Dynamics Model

#### 3.3. Cell Manipulation Control System

#### 3.4. Lyapunov Convergence Analysis

## 4. Simulation Results

**Hypothesis**

**1.**

**Hypothesis**

**2.**

**Hypothesis**

**3.**

#### 4.1. Case (1): Holographic Optical Tweezers Manipulate Control for Single Cells

**K**= [0.3x

_{1},0.3x

_{2}]

^{T}. In the PI controller, ${k}_{p}$ = 20, ${k}_{i}$ = 0.5. The number of hidden layer nodes of the BP neural network is 3, the number of neurons of the RBF neural network is 3, the number of layers of the FCMNN is fixed to 3, and the number of blocks is fixed to 3. The initial number of layers and initial blocks of the NSOFCMNN are both 3, and the self-organizing structure adjustment parameter ${T}_{n}$ = 0.01, ${T}_{m}$= 0.0001, ${T}_{k}$= 0.32.

^{−15}and 2.0 × 10

^{−16}, respectively, which are smaller than the RMSE and MAE when PI, BP and RBF are used as the main controllers, respectively, and the control accuracy is relatively high. Compared with the FCMNN main controller, the RMSE and MAE of the proposed NSOFCMNN are only 0.1–1% of the former. It can be concluded that the single-cell manipulation control of the NSOFCMNN main controller has better control performance than the other main controller, and even in the presence of interference factors, it can also have better robustness.

#### 4.2. Case (2): Holographic Optical Tweezers Manipulate Control for Multiple Cells

^{−6}, 5.1 × 10

^{−6}], [2.7 × 10

^{−10}, 1.2 × 10

^{−7}] and [3.3 × 10

^{−8}, 7.7 × 10

^{−8}], respectively. The corresponding MAE is in the interval of [4.0 × 10

^{−6}, 3.1 × 10

^{−5}], [4.0 × 10

^{−8}, 7.2 × 10

^{−6}] and [7.9 × 10

^{−9}, 2.8 × 10

^{−8}], respectively. As the main controller, FCMNN still has better control performance than the first three neural networks. The RMSE and MAE are between [1.9 × 10

^{−19}, 12.4 × 10

^{−10}] and [7.9 × 10

^{−9}, 2.8 × 10

^{−8}], respectively. The proposed NSOFCMNN as the main controller, as well as its RMSE and MAE, are both smaller than FCMNN due to the addition of self-organizing structure adjustment rules. The minimum RMSE and the minimum MAE of NSOFCMNN are only 1% of that of FCMNN. It can be concluded that the NSOFCMNN main controller has much more powerful control performance in the multi-cell manipulation of holographic optical tweezers, and it enables more precise manipulation of cells to expected positions.

## 5. Conclusions and Outlook

## Author Contributions

## Funding

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 12.**Comparison between the actual trajectories and the expected trajectories of four controlled cells.

Cell Velocity (μm/s) | ±5 | ±7.5 | ±10 |
---|---|---|---|

$\delta /k\left(\mathrm{s}\right)$ | 0.09 | 0.1 | 0.09 |

Data Type | Main Controller | X-Axis | Y-Axis |
---|---|---|---|

RMSE of single-cell manipulation | PI | 7.0 × 10^{−6} | 1.8 × 10^{−6} |

BP | 3.2 × 10^{−6} | 8.4 × 10^{−8} | |

RBF | 6.2 × 10^{−10} | 4.0 × 10^{−12} | |

FCMNN | 5.3 × 10^{−15} | 4.2 × 10^{−16} | |

This work | 7.4 × 10^{−18} | 3.3 × 10^{−18} | |

MAE of single-cell manipulation | PI | 5.5 × 10^{−5} | 3.7 × 10^{−6} |

BP | 1.3 × 10^{−5} | 5.8 × 10^{−8} | |

RBF | 2.5 × 10^{−11} | 2.1 × 10^{−13} | |

FCMNN | 2.0 × 10^{−16} | 2.1 × 10^{−17} | |

This work | 3.0 × 10^{−19} | 1.3 × 10^{−19} |

Cell 1 | Cell 2 | Cell 3 | Cell 4 | Virtual Cell | |
---|---|---|---|---|---|

initial position (μm) | [−15, 15] | [20, 10] | [−10, 10] | [5, 5] | [15, 20] |

Data Type | Main Controller | Cell 1 | Cell 2 | Cell 3 | Cell 4 |
---|---|---|---|---|---|

RMSE of each cell in the X-axis direction | PI | 4.7 × 10^{−6} | 5.1 × 10^{−6} | 4.7 × 10^{−6} | 5.0 × 10^{−6} |

BP | 2.2 × 10^{−6} | 2.7 × 10^{−6} | 2.2 × 10^{−6} | 2.7 × 10^{−6} | |

RBF | 7.0 × 10^{−8} | 5.0 × 10^{−8} | 6.4 × 10^{−10} | 7.0 × 10^{−8} | |

FCMNN | 8.4 × 10^{−15} | 1.4 × 10^{−19} | 2.4 × 10^{−10} | 2.1 × 10^{−12} | |

This work | 2.1 × 10^{−20} | 1.8 × 10^{−20} | 2.8 × 10^{−15} | 2.1 × 10^{−15} | |

RMSE of each cell in the Y-axis direction | PI | 2.2 × 10^{−6} | 2.1 × 10^{−6} | 1.9 × 10^{−6} | 2.0 × 10^{−6} |

BP | 2.1 × 10^{−7} | 2.1 × 10^{−7} | 1.2 × 10^{−7} | 1.2 × 10^{−7} | |

RBF | 3.3 × 10^{−8} | 5.0 × 10^{−8} | 5.1 × 10^{−8} | 7.7 × 10^{−8} | |

FCMNN | 2.7 × 10^{−15} | 1.9 × 10^{−19} | 7.5 × 10^{−11} | 7.1 × 10^{−12} | |

This work | 3.1 × 10^{−20} | 9.0 × 10^{−21} | 1.6 × 10^{−15} | 2.1 × 10^{−15} |

Data Type | Main Controller | Cell 1 | Cell 2 | Cell 3 | Cell 4 |
---|---|---|---|---|---|

MAE of each cell in the X-axis direction | PI | 2.6 × 10^{−5} | 3.1 × 10^{−5} | 2.5 × 10^{−5} | 2.9 × 10^{−5} |

BP | 6.5 × 10^{−6} | 7.2 × 10^{−6} | 6.5 × 10^{−6} | 7.2 × 10^{−6} | |

RBF | 1.5 × 10^{−8} | 2.1 × 10^{−8} | 8.9 × 10^{−9} | 2.8 × 10^{−8} | |

FCMNN | 3.4 × 10^{−16} | 3.8 × 10^{−20} | 9.9 × 10^{−12} | 4.8 × 10^{−14} | |

This work | 5.4 × 10^{−21} | 4.6 × 10^{−21} | 1.1 × 10^{−16} | 8.5 × 10^{−18} | |

MAE of each cell in the Y-axis direction | PI | 5.7 × 10^{−6} | 5.2 × 10^{−6} | 4.0 × 10^{−6} | 4.0 × 10^{−6} |

BP | 2.1 × 10^{−7} | 2.1 × 10^{−7} | 4.1 × 10^{−8} | 4.0 × 10^{−8} | |

RBF | 7.9 × 10^{−9} | 1.7 × 10^{−8} | 1.7 × 10^{−8} | 2.5 × 10^{−8} | |

FCMNN | 1.1 × 10^{−16} | 7.6 × 10^{−21} | 3.0 × 10^{−12} | 2.9 × 10^{−13} | |

This work | 5.6 × 10^{−23} | 3.0 × 10^{−23} | 6.4 × 10^{−17} | 8.4 × 10^{−17} |

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**MDPI and ACS Style**

Zhao, J.; Hou, H.; Huang, Q.-Y.; Zhong, X.-G.; Zheng, P.-S.
Design of Optical Tweezers Manipulation Control System Based on Novel Self-Organizing Fuzzy Cerebellar Model Neural Network. *Appl. Sci.* **2022**, *12*, 9655.
https://doi.org/10.3390/app12199655

**AMA Style**

Zhao J, Hou H, Huang Q-Y, Zhong X-G, Zheng P-S.
Design of Optical Tweezers Manipulation Control System Based on Novel Self-Organizing Fuzzy Cerebellar Model Neural Network. *Applied Sciences*. 2022; 12(19):9655.
https://doi.org/10.3390/app12199655

**Chicago/Turabian Style**

Zhao, Jing, Hui Hou, Qi-Yu Huang, Xun-Gao Zhong, and Peng-Sheng Zheng.
2022. "Design of Optical Tweezers Manipulation Control System Based on Novel Self-Organizing Fuzzy Cerebellar Model Neural Network" *Applied Sciences* 12, no. 19: 9655.
https://doi.org/10.3390/app12199655