# Current Control Method of Vehicle Permanent Magnet Synchronous Motor Based on Active Disturbance Rejection Control

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## Abstract

**:**

## 1. Introduction

## 2. Design and Improvement of ADRC Current Regulator

#### 2.1. Traditional ADRC Current Regulator

#### 2.2. Observation Error Compensation

#### 2.3. Utilization of Model Information

#### 2.4. Anti-Windup

## 3. Simulation Analysis

#### 3.1. Establishment of Simulink Model

#### 3.2. Analysis of Simulation Results

## 4. Bench Test

#### 4.1. Introduction to the Test Bench

#### 4.2. Analysis of Test Results

#### 4.2.1. Torque Step Test

^{−1}, and test the step response of the maximum demand torque of the PMSM to be tested. Under this working condition, the demand current of q-axis is 495 A, and the demand current of d-axis is −546 A (according to the motor inductance contour diagram shown in Appendix A, the inductance parameters under this working condition are approximately ${L}_{d}=0.522\mathrm{mH}$, ${L}_{q}=1.056\mathrm{mH}$). Tune the parameters of PI and ADRC, respectively, until they have the same steady-state performance (the PI parameters are: ${k}_{pd}=0.6$, ${k}_{id}=40$, ${k}_{pq}=0.5$, ${k}_{iq}=20$; the ADRC parameters are: ${\omega}_{d}={\omega}_{q}=250$, ${k}_{d}={k}_{q}=200$, ${b}_{d}=1618$, ${b}_{q}=507$). The dq-axis current waveforms of the two current regulators are shown in Figure 7. In terms of response speed, there is little difference between the two regulators; however, in terms of overshoot, the q-axis current under the PI regulator has an approximately 7% overshoot, while the ADRC regulator can ensure no overshoot. This shows that the ADRC regulator can alleviate the contradiction between response speed and overshoot to a certain extent.

#### 4.2.2. Dynamic Test

^{−1}, and then the speed is accelerated to 3000 r·min

^{−1}(PMSM peak speed) in 15 s. During this process, the motor’s operating point moves along the external characteristics. As shown in Figure 9, ADRC parameters under this working condition are shown in Appendix B.

^{−1}, the amplitude of the demand voltage vector reaches the limit value of the voltage vector modulus length, which indicates that the regulator will have integral saturation. At this time, anti-windup measures play a role, and the error before and after amplitude limiting is eliminated through negative feedback regulation. The module length of the voltage vector can be limited below the limit value, which ensures that the dq-axis current follows the demand value to the maximum extent, without generating excessive current error or causing the system to be out of control. Since the anti-windup measure only works when integral saturation occurs, it is equivalent to that when integral saturation occurs; the control structure of ADRC changes, which causes fluctuations in the observed values of dq-axis current and total disturbance, thus causing some fluctuations in the demand voltage vector.

## 5. Discussion

- (1)
- Compared with reference [11], the proposed algorithm in this paper has fewer parameters to be tuned, less computational effort, and is more suitable for engineering application;
- (2)
- Compared with [12,14], this paper pays more attention to the robustness of the current regulator when the motor parameters change. First, the robustness of the ADRC current regulator when the motor parameters change during operation is verified through simulation, and through bench experiments, a variety of working conditions are designed for this verification;
- (3)
- (4)
- In order to improve the safety of the algorithm under extreme operating conditions, the anti-windup measures of ADRC are also designed and bench tested under high dynamic conditions, which has not been found in the existing research on ADRC as PMSM current regulator.

- (1)
- Although according to the literature [16], the two gains of LESO can be expressed in the form of observer bandwidth, which reduces the number of parameters to a certain extent. However, compared with PI current regulator, ADRC still has more parameters to be tuned, which limits the application of ADRC to a certain extent. Finding a simpler parameter tuning method is the focus of the next research;
- (2)
- When ADRC is applied to some occasions with high system bandwidth (such as high-speed motors), in order to obtain faster convergence speed and higher observation accuracy, the bandwidth of LESO will inevitably be tuned to a larger value, which will lead to the reduction of noise suppression ability. Therefore, how to reduce the noise impact when the LESO gain is large will be the focus of future research.

## 6. Conclusions

- (1)
- The performance of LESO is analyzed using the frequency domain method, and the traditional ADRC algorithm is improved in three aspects: observation error compensation, model information utilization and anti windup;
- (2)
- The simulation results show that the improved ADRC current regulator is more robust than the PI current regulator when the parameters change;
- (3)
- The bench test results show that the improved ADRC current regulator has a fast step response without overshoot, good tracking performance and robustness when the load changes and the parameters change. In addition, the anti-windup performance is also verified.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

## Appendix B

Speed/r·min^{−1} | ${\mathit{\omega}}_{\mathit{d}}$ | ${\mathit{\omega}}_{\mathit{q}}$ | ${\mathit{k}}_{\mathit{d}}$ | ${\mathit{k}}_{\mathit{q}}$ | ${\mathit{b}}_{\mathit{d}}$ | ${\mathit{b}}_{\mathit{q}}$ |
---|---|---|---|---|---|---|

0 | 250 | 250 | 200 | 200 | 1618 | 507 |

200 | 250 | 250 | 200 | 200 | ||

400 | 250 | 250 | 200 | 200 | ||

600 | 250 | 250 | 200 | 200 | ||

800 | 400 | 400 | 200 | 200 | ||

1000 | 450 | 450 | 200 | 200 | ||

1200 | 500 | 500 | 200 | 200 | ||

1400 | 500 | 500 | 200 | 200 | ||

1600 | 500 | 500 | 100 | 100 | ||

1800 | 500 | 500 | 100 | 100 | ||

2000 | 500 | 500 | 50 | 50 | ||

2200 | 500 | 500 | 50 | 50 | ||

2400 | 500 | 500 | 50 | 50 | ||

2600 | 500 | 500 | 50 | 50 | ||

2800 | 650 | 650 | 25 | 25 | ||

3000 | 650 | 650 | 25 | 25 |

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**Figure 2.**Bode diagram of observation error transfer function: (

**a**) ${G}_{{e}_{d1/q1}}\left(s\right)$; (

**b**) ${G}_{{e}_{d2/q2}}\left(s\right)$.

Parameter Name | Parameter Value |
---|---|

Number of phases | 3 |

Rated DC voltage/V | 540 |

Rated/peak power/kW | 130/260 |

Rated/peak current/Arms | 230/525 |

Rated/peak speed/(r·min^{−1}) | 1350/3000 |

Rated/peak torque/N·m | 955/2800 |

Rated d-axis inductance/mH | 0.618 |

Rated q-axis inductance/mH | 0.197 |

Flux linkage/Wb | 0.344 |

Stator resistance/Ω | 0.035 |

Number of pole pairs | 6 |

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## Share and Cite

**MDPI and ACS Style**

Wang, J.; Miao, Q.; Zhou, X.; Sun, L.; Gao, D.; Lu, H.
Current Control Method of Vehicle Permanent Magnet Synchronous Motor Based on Active Disturbance Rejection Control. *World Electr. Veh. J.* **2023**, *14*, 2.
https://doi.org/10.3390/wevj14010002

**AMA Style**

Wang J, Miao Q, Zhou X, Sun L, Gao D, Lu H.
Current Control Method of Vehicle Permanent Magnet Synchronous Motor Based on Active Disturbance Rejection Control. *World Electric Vehicle Journal*. 2023; 14(1):2.
https://doi.org/10.3390/wevj14010002

**Chicago/Turabian Style**

Wang, Jinyu, Qiang Miao, Xiaomin Zhou, Lipeng Sun, Dawei Gao, and Haifeng Lu.
2023. "Current Control Method of Vehicle Permanent Magnet Synchronous Motor Based on Active Disturbance Rejection Control" *World Electric Vehicle Journal* 14, no. 1: 2.
https://doi.org/10.3390/wevj14010002