# Research on Dynamic Identification of Servo Motor Load Inertia Based on the Error Gain Factor Model

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## Abstract

**:**

## 1. Introduction

## 2. Establishment of PMSM Moment of Inertia Identification Model

#### 2.1. Motion Model of PMSM

#### 2.2. MRAS Identification Model

#### 2.3. MRAS Based on Error Gain Factor (EGF-MRAS)

## 3. Simulation of EGF-MRAS Identification Algorithm

#### 3.1. Simulation Design of Identification Algorithm

#### 3.2. Simulation Analysis

## 4. Experimental Verification

#### 4.1. Construction of the Experimental Platform

#### 4.2. Design of the Experiment

#### 4.3. Experimental Results and Analysis

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Hsu, C.-J.; Lai, Y.-S. Novel Online Optimal Bandwidth Search and Autotuning Techniques for Servo Motor Drives. IEEE Trans. Ind. Appl.
**2017**, 53, 3635–3642. [Google Scholar] [CrossRef] - Huang, W.-S.; Liu, C.-W.; Hsu, P.-L.; Yeh, S.-S. Precision Control and Compensation of Servomotors and Machine Tools via the Disturbance Observer. IEEE Trans. Ind. Electron.
**2009**, 57, 420–429. [Google Scholar] [CrossRef] - Kim, S. Moment of Inertia and Friction Torque Coefficient Identification in a Servo Drive System. IEEE Trans. Ind. Electron.
**2019**, 66, 60–70. [Google Scholar] [CrossRef] - Choi, J.-W.; Lee, S.-C.; Kim, H.-G. Inertia identification algorithm for high-performance speed control of electric motors. IEE Proc.-Electr. Power Appl.
**2006**, 153, 379–386. [Google Scholar] [CrossRef] - Fujita, K.; Sado, K. Instantaneous speed detection with parameter identification for AC servo systems. IEEE Trans. Ind. Appl.
**1992**, 28, 864–872. [Google Scholar] [CrossRef] - Chen, Y.; Yang, M.; Long, J.; Qu, W.; Xu, D.; Blaabjerg, F. A Moderate Online Servo Controller Parameter Self-Tuning Method via Variable-Period Inertia Identification. IEEE Trans. Power Electron.
**2019**, 34, 12165–12180. [Google Scholar] [CrossRef] - Wang, P.; Lin, K.; Lin, M.; Yang, A.; Fu, F.; Ai, J. Online multi-parameter estimation of permanent magnet synchronous machine with step-pulse injection. IET Electr. Power Appl.
**2021**, 15, 186–199. [Google Scholar] [CrossRef] - Liu, K.; Hou, C.; Hua, W. A Novel Inertia Identification Method and Its Application in PI Controllers of PMSM Drives. IEEE Access
**2019**, 7, 13445–13454. [Google Scholar] [CrossRef] - Campos-Delgado, D.U.; Arce-Santana, E.R.; Espinoza-Trejo, D.R. Edge optimisation for parameter identification of induction motors. IET Electr. Power Appl.
**2011**, 5, 668–675. [Google Scholar] [CrossRef] - Andoh, F. Moment of Inertia Identification Using the Time Average of the Product of Torque Reference Input and Motor Position. IEEE Trans. Power Electron.
**2007**, 22, 2534–2542. [Google Scholar] [CrossRef] - Lin, F.-J.; Chen, S.-G.; Li, S.; Chou, H.-T.; Lin, J.-R. Online Autotuning Technique for IPMSM Servo Drive by Intelligent Identification of Moment of Inertia. IEEE Trans. Ind. Inform.
**2020**, 16, 7579–7590. [Google Scholar] [CrossRef] - Wang, S.; Dinavahi, V.; Xiao, J. Multi-rate real-time model-based parameter estimation and state identification for induction motors. IET Electr. Power Appl.
**2013**, 7, 77–86. [Google Scholar] [CrossRef] - Li, S.; Liu, Z. Adaptive Speed Control for Permanent-Magnet Synchronous Motor System with Variations of Load Inertia. IEEE Trans. Ind. Electron.
**2009**, 56, 3050–3059. [Google Scholar] - Zhang, J.; Xu, H. Online Identification of Power System Equivalent Inertia Constant. IEEE Trans. Ind. Electron.
**2017**, 64, 8098–8107. [Google Scholar] [CrossRef] - Lee, K.; Ahmed, S.; Lukic, S.M. Universal Restart Strategy for High-Inertia Scalar-Controlled PMSM Drives. IEEE Trans. Ind. Appl.
**2016**, 52, 4001–4009. [Google Scholar] [CrossRef] - Chen, J.; Huang, J. Alternative Solution Regarding Problems of Adaptive Observer Compensating Parameters Uncertainties for Sensorless Induction Motor Drives. IEEE Trans. Ind. Electron.
**2019**, 67, 5879–5888. [Google Scholar] [CrossRef] - Lee, K.; Ahmed, S.; Lukic, S.M. Restart Strategy for Scalar (V/f) Controlled Synchronous Reluctance Machine Driving a High-Inertia Load. IEEE Trans. Ind. Appl.
**2019**, 55, 3834–3841. [Google Scholar] [CrossRef] - Nguyen, A.T.; Rafaq, M.S.; Choi, H.H.; Jung, J.-W. A Model Reference Adaptive Control Based Speed Controller for a Surface-Mounted Permanent Magnet Synchronous Motor Drive. IEEE Trans. Ind. Electron.
**2018**, 65, 9399–9409. [Google Scholar] [CrossRef] - Wang, D.-Q.; Liu, H.-B.; Ding, F. Fuzzy Least Squares for Identification of Individual Pharmacokinetic Parameters. IEEE Trans. Biomed. Eng.
**2009**, 23, 2796–2805. [Google Scholar] - Song, Z.; Mei, X.; Jiang, G. Inertia identification based on model reference adaptive system with variable gain for AC servo systems. In Proceedings of the 2017 IEEE International Conference on Mechatronics and Automation (ICMA), Takamatsu, Japan, 6–9 August 2017; pp. 188–192. [Google Scholar]
- Lian, C.; Xiao, F.; Gao, S.; Liu, J. Load Torque and Moment of Inertia Identification for Permanent Magnet Synchronous Motor Drives Based on Sliding Mode Observer. IEEE Trans. Power Electron.
**2019**, 34, 5675–5683. [Google Scholar] [CrossRef] - Li, S.; Gu, H. Fuzzy Adaptive Internal Model Control Schemes for PMSM Speed-Regulation System. IEEE Trans. Ind. Inform.
**2012**, 8, 767–779. [Google Scholar] [CrossRef] - Lee, K.B.; Yoo, J.Y.; Song, J.H.; Choy, I. Improvement of low speed operation of electric machine with an inertia identification using ROELO. IEE Proc.-Electr. Power Appl.
**2003**, 151, 116–120. [Google Scholar] [CrossRef] - Kim, H.; Kim, H.; Choi, J. Multiparameter identification for SPMSMs using NLMS adaptive filters and extended sliding-mode observer. IET Electr. Power Appl.
**2020**, 14, 533–543. [Google Scholar] [CrossRef]

Group | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

$\mathrm{J}(\mathrm{kg}\xb7{{m}}^{2}$) | 0.0003 | 0.0006 | 0.0009 | 0.0012 | 0.0015 |

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

Number of phases | 3 |

Pole pairs | 2 |

Back EMF waveform | Sinusoidal |

Rotor type | Round |

Mechanical input 1 | Torque T_{L} |

Mechanical input 2 | Inertia J |

Stator phase resistance/(ohm) | 0.8 |

Armature inductance/(H) | 3.95 × 10^{−4} |

Flux linkage/(Wb) | 0.1852 |

Group | Algorithm |
---|---|

(a) | EGF-MRAS algorithm |

(b) | MRAS algorithm |

(c) | Error integrator adaptive algorithm |

Groups | ${\mathit{P}}_{\mathit{\alpha}}$ | ${\mathit{P}}_{\mathit{\beta}}$ | ${\mathit{P}}_{\mathit{\gamma}}$ |
---|---|---|---|

a | 6.6% | 2.9% | 0.025 s |

b | - | 13.7% | 0.179 s |

c | 7.2% | 6.6% | 0.062 s |

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

motor type | ASM200-36-1250/2500 |

Excitation mode | Permanent magnet |

Number of Pole Pairs | 4 |

Line resistance | 0.33 Ω |

Line inductance | 0.9 mH |

Rated voltage | 36 V |

Rated torque | 1.276 N·m |

Rated current | 7.5 A |

Maximum speed | 3000 rpm |

Motor weight | 1.1 kg |

$\mathit{\omega}$ (rad/s) | 0 | 820 | 820 | 0 |
---|---|---|---|---|

t (s) | 0 | 0.052 | 1 | 1.051 |

Groups | ${\mathit{J}}_{\mathit{a}}$ | ${\mathit{J}}_{\mathit{d}}$ | $\overline{\mathit{J}}$ | ${\mathit{J}}_{\mathit{r}}$ |
---|---|---|---|---|

$\mathrm{J}$$(\times {10}^{-4}\mathrm{kg}\xb7{\mathrm{m}}^{2}$) | 6.34 | 6.24 | 6.29 | 6.30 |

Group | Algorithm |
---|---|

(a) | EGF-MRAS algorithm |

(b) | MRAS algorithm |

(c) | Error integrator adaptive algorithm |

**Table 9.**Calculation results of the accuracy parameters of Figure 9.

Groups | ${\mathit{P}}_{\mathit{\alpha}}$ | ${\mathit{P}}_{\mathit{\beta}}$ | ${\mathit{P}}_{\mathit{\gamma}}$ |
---|---|---|---|

(a) | 15.6% | 12.7% | 0.090 s |

(b) | 16.0% | 19.6% | 0.239 s |

**Table 10.**Calculation results of the accuracy parameters of Figure 10.

Groups | ${\mathit{P}}_{\mathit{\alpha}}$ | ${\mathit{P}}_{\mathit{\beta}}$ |
---|---|---|

(a) | 31.0% | 12.7% |

(b) | 128.7% | 28.6% |

**Table 11.**Calculation results of the accuracy parameters of Figure 11.

Groups | ${\mathit{P}}_{\mathit{\alpha}}$ | ${\mathit{P}}_{\mathit{\beta}}$ | ${\mathit{P}}_{\mathit{\gamma}}$ |
---|---|---|---|

(a) | 15.4% | 12.7% | 0.090 s |

(c) | 17.2% | 21.1% | 0.115 s |

**Table 12.**Calculation results of the accuracy parameters of Figure 12.

Groups | ${\mathit{P}}_{\mathit{\alpha}}$ | ${\mathit{P}}_{\mathit{\beta}}$ |
---|---|---|

(a) | 31.0% | 12.7% |

(c) | 77.3% | 21.1% |

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**MDPI and ACS Style**

Xie, F.; Yu, F.; An, C.
Research on Dynamic Identification of Servo Motor Load Inertia Based on the Error Gain Factor Model. *Energies* **2021**, *14*, 6664.
https://doi.org/10.3390/en14206664

**AMA Style**

Xie F, Yu F, An C.
Research on Dynamic Identification of Servo Motor Load Inertia Based on the Error Gain Factor Model. *Energies*. 2021; 14(20):6664.
https://doi.org/10.3390/en14206664

**Chicago/Turabian Style**

Xie, Fang, Fei Yu, and Chaochen An.
2021. "Research on Dynamic Identification of Servo Motor Load Inertia Based on the Error Gain Factor Model" *Energies* 14, no. 20: 6664.
https://doi.org/10.3390/en14206664