# Research on the dq-Axis Current Reaction Time of an Interior Permanent Magnet Synchronous Motor for Electric Vehicle

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## Abstract

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## 1. Introduction

## 2. Mathematical Model of the Current Loop of IPMSM

## 3. Controller Design of Current-Loop Decoupling of IPMSM

#### 3.1. PI Controller Design

#### 3.2. IMC-PI Controller Design

#### 3.3. The Modulation Parameter Selection of IMC-PI

## 4. Simulation Analysis and Experimental Verification

#### 4.1. Simulation Analysis

#### 4.2. Hardware Experimentation

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The PI current-loop structure of IPMSM: (

**a**) d-axis PI current-loop structure; (

**b**) q-axis PI current-loop structure.

**Figure 6.**The simulation analysis results of the dq-axis current reaction time of IPMSM (${T}_{pwm}=0.001s$): (

**a**) PI method; (

**b**) IMC-PI method.

**Figure 7.**The simulation analysis results of the dq-axis current reaction time of IPMSM (${T}_{pwm}=0.01s$): (

**a**) PI method; (

**b**) IMC-PI method.

**Figure 8.**The simulation analysis results of the dq-axis current reaction time of IPMSM (${T}_{pwm}=0.1s$): (

**a**) PI method; (

**b**) IMC-PI method.

**Figure 9.**Experimental test of the dq-axis current reaction time of IPMSM: (

**a**) IPMSM’s structure; (

**b**) test platform.

**Figure 10.**The hardware test results of the dq-axis current reaction time of IPMSM (${T}_{pwm}=0.001s$): (

**a**) PI method; (

**b**) IMC-PI method.

**Figure 11.**The hardware test results of the dq-axis current reaction time of IPMSM (${T}_{pwm}=0.01s$): (

**a**) PI method; (

**b**) IMC-PI method.

Parameters | Descriptions |
---|---|

$R\left(s\right)$ | System’s input signal |

$C\left(s\right)$ | Feedback controller |

$\widehat{D}\left(s\right)$ | Feedback signal |

${G}_{IMC}\left(s\right)$ | IMC controller |

${G}_{p}\left(s\right)$ | System’s model |

${\widehat{G}}_{p}\left(s\right)$ | Internal model |

$D\left(s\right)$ | Interference signal |

$Y\left(s\right)$ | System’s output signal |

Item | Value | Unit |
---|---|---|

Number of phases | 3 | - |

Power | 1.5 | kW |

Rated line voltage | 220 | V |

Rated line current | 4.5 | A |

Rated speed | 2000 | r/min |

Number of stator slots | 18 | - |

Number of rotor poles | 8 | - |

Air-gap length | 0.5 | mm |

Phase resistance | 2.92 | Ω |

D-axis inductance | 8.96 | mH |

Q-axis inductance | 12.29 | mH |

Excitation flux linkage | 0.955 | Wb |

Item | ${\mathit{T}}_{\mathit{p}\mathit{w}\mathit{m}}=0.001\mathit{s}$ | ${\mathit{T}}_{\mathit{p}\mathit{w}\mathit{m}}=0.01\mathit{s}$ | ${\mathit{T}}_{\mathit{p}\mathit{w}\mathit{m}}=0.1\mathit{s}$ | |
---|---|---|---|---|

PI method | ${K}_{pq}$ | 6.145 | 0.6145 | 0.06145 |

${K}_{iq}$ | 1460 | 146 | 14.6 | |

${K}_{pd}$ | 4.48 | 0.448 | 0.0448 | |

${K}_{id}$ | 1460 | 146 | 14.6 | |

IMC-PI method | ${K}_{pq\left(IMC\right)}$ | 18.3 | 18.3 | 18.3 |

${K}_{iq\left(IMC\right)}$ | 4356 | 4356 | 4356 | |

${K}_{pd\left(IMC\right)}$ | 13.3 | 13.3 | 13.3 | |

${K}_{id\left(IMC\right)}$ | 4356 | 4356 | 4356 |

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**MDPI and ACS Style**

Huang, A.; Chen, Z.; Wang, J.
Research on the dq-Axis Current Reaction Time of an Interior Permanent Magnet Synchronous Motor for Electric Vehicle. *World Electr. Veh. J.* **2023**, *14*, 196.
https://doi.org/10.3390/wevj14070196

**AMA Style**

Huang A, Chen Z, Wang J.
Research on the dq-Axis Current Reaction Time of an Interior Permanent Magnet Synchronous Motor for Electric Vehicle. *World Electric Vehicle Journal*. 2023; 14(7):196.
https://doi.org/10.3390/wevj14070196

**Chicago/Turabian Style**

Huang, Anxue, Zhongxian Chen, and Juanjuan Wang.
2023. "Research on the dq-Axis Current Reaction Time of an Interior Permanent Magnet Synchronous Motor for Electric Vehicle" *World Electric Vehicle Journal* 14, no. 7: 196.
https://doi.org/10.3390/wevj14070196