# New Sliding Mode Control Based on Tracking Differentiator and RBF Neural Network

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## Abstract

**:**

## 1. Introduction

## 2. System Modelling

## 3. Design of New Sliding Mode Control Method

#### 3.1. Design of a New Approach to Law

#### 3.2. Design of a New Sliding Mode Speed Controller Based on RBF Neural Network

#### 3.3. Fastest Tracking Differentiator

## 4. Algorithm Simulation and Result Analysis

- The simulation running time is 2 s, the initial motor speed is 900 r/min, and the PMSM is started with a constant load of 10 N∙m. In order to better compare with traditional control, the PI, SMC (based on the traditional exponential approach to law), NSMC, and NSMC methods based on the TD and RBF neural network are used in this paper. The motor speed curve with three control methods is shown in Figure 5.

- 2.
- To verify the response speed and tracking ability of the new control method in the presence of load disturbance when the load disturbance exists. The simulation running time is 2 s, the initial speed of the electrode is 900 r/min, the PMSM is started when the load is 10 N∙m, and the load is suddenly increased to 20 N∙m in 0.8 s, runs to 1.2 s, and suddenly reduces the load to 15 N∙m. The load variation curve is shown in Figure 6. The comparison of the motor speed curves using the four control methods is shown in Figure 7.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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The Parameter | Value |
---|---|

$\mathrm{The}\mathrm{stator}\mathrm{resistance}R/\Omega $ | 0.0918 |

$\mathrm{Magnetic}\mathrm{chain}\psi /wb$ | 0.1688 |

$\mathrm{D}\mathrm{axis}\mathrm{inductance}L/mH$ | 0.000975 |

$\mathrm{Q}\mathrm{axis}\mathrm{inductance}L/mH$ | 0.000975 |

$\mathrm{Number}\mathrm{of}\mathrm{pole}\mathrm{pairs}{p}_{n}$ | 4 |

$\mathrm{The}\mathrm{moment}\mathrm{of}\mathrm{inertia}\mathrm{J}/\mathrm{kg}\cdot {\mathrm{m}}^{2}$ | 0.003945 |

$\mathrm{Coefficient}\mathrm{of}\mathrm{viscous}\mathrm{friction}\mathrm{kg}/\mathrm{s}$ | 0.0004924 |

Compare the Item | PI | SMC | NSMC | TDRBF-NSMC |
---|---|---|---|---|

Overshoot volume/% | 13.67 | 12.87 | 10.67 | 0.17 |

Speed decrease/% | 1.67 | 1.44 | 0.33 | 0.17 |

Speed recovery time/s | 0.26 | 0.223 | 0.116 | 0.043 |

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**MDPI and ACS Style**

Qu, C.; Hu, Y.; Guo, Z.; Han, F.; Wang, X. New Sliding Mode Control Based on Tracking Differentiator and RBF Neural Network. *Electronics* **2022**, *11*, 3135.
https://doi.org/10.3390/electronics11193135

**AMA Style**

Qu C, Hu Y, Guo Z, Han F, Wang X. New Sliding Mode Control Based on Tracking Differentiator and RBF Neural Network. *Electronics*. 2022; 11(19):3135.
https://doi.org/10.3390/electronics11193135

**Chicago/Turabian Style**

Qu, Chunyu, Yongzhuang Hu, Ziqi Guo, Fangxu Han, and Xiuping Wang. 2022. "New Sliding Mode Control Based on Tracking Differentiator and RBF Neural Network" *Electronics* 11, no. 19: 3135.
https://doi.org/10.3390/electronics11193135