# Research on Position Sensorless Control of RDT Motor Based on Improved SMO with Continuous Hyperbolic Tangent Function and Improved Feedforward PLL

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## Abstract

**:**

## 1. Introduction

- (1)
- This study addresses SMO chattering by replacing the sign function with a continuous hyperbolic tangent function and selecting an appropriate boundary layer width. An observer based on the back-EMF model is developed to eliminate the LPF, reduce phase delay, and enhance the back-EMF signal estimation precision;
- (2)
- Through optimization of the traditional PLL structure and the addition of feedforward compensation, this study has successfully realized position extraction during bi-directional rotation of the motor, while significantly improving the accuracy of position extraction during acceleration and deceleration.

## 2. PMSM Mathematical Model

## 3. SMO Design for PMSM Rotor Position Estimation

**Theorem**

**1.**

**Proof**

**of**

**Theorem**

**1.**

**Theorem**

**2.**

**Proof**

**of**

**Theorem**

**2.**

## 4. Rotor Position and Speed Extraction

#### 4.1. Traditional PLL Analysis

#### 4.2. Improved PLL Analysis

- (1)
- Improve the inability of the conventional PLL to reliably extract position information during motor reversal;
- (2)
- During motor acceleration and deceleration, the conventional PLL’s error problem has been resolved.

## 5. Simulation Verification

#### 5.1. Steady-State Performance

#### 5.2. Dynamic Performance

#### 5.3. Forward and Reverse

#### 5.4. Performance under Ship Propeller Load

## 6. Conclusions and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 10.**Responses of the simulation with conventional SMO combined with conventional PLL (steady-state). (

**a**) Rotor speed. (

**b**) Rotor position. (

**c**) Estimation of the back-EMF.

**Figure 11.**Responses of the simulation with improved SMO combined with feedforward PLL (steady-state). (

**a**) Rotor speed. (

**b**) Rotor position. (

**c**) Estimation of the back-EMF.

**Figure 13.**Responses of simulation with conventional SMO combined with conventional PLL (dynamic). (

**a**) Rotor speed. (

**b**) Rotor position. (

**c**) Estimation of the back-EMF.

**Figure 14.**Responses of simulation with improved SMO combined with feedforward PLL (dynamic). (

**a**) Rotor speed. (

**b**) Rotor position. (

**c**) Estimation of the back-EMF.

**Figure 16.**Responses of the simulation with conventional SMO combined with conventional PLL (forward and reverse). (

**a**) Rotor speed. (

**b**) Rotor position. (

**c**) Estimation of the back-EMF.

**Figure 17.**Responses of simulation with the improved SMO combined with feedforward PLL (forward and reverse). (

**a**) Rotor speed. (

**b**) Rotor position. (

**c**) Estimation of the back-EMF.

**Figure 20.**Responses of the simulation with conventional SMO combined with conventional PLL (with propeller load). (

**a**) Rotor speed. (

**b**) Rotor position. (

**c**) Estimation of the back-EMF.

**Figure 21.**Responses of the simulation with improved SMO combined with feedforward PLL (with propeller load). (

**a**) Rotor speed. (

**b**) Rotor position. (

**c**) Estimation of the back-EMF.

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

number of pole pairs p | 4 |

stator resistance ${R}_{s}$ | 2.875 $\mathrm{\Omega}$ |

stator inductor ${L}_{s}$ | 8.5 $\mathrm{mH}$ |

rotational inertia J | 0.001 $\mathrm{kg}\xb7{\mathrm{m}}^{2}$ |

permanent magnet flux ${\psi}_{f}$ | 0.175 $\mathrm{Wb}$ |

DC voltage ${U}_{dc}$ | 311 $\mathrm{V}$ |

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

Propeller diameter ${D}_{p}$/m | 0.1 |

Hull mass ${M}_{s}$/kg | 100 |

Water attachment coefficient k | 1.1 |

Wake coefficient $\omega $ | 0.12285 |

Thrust derating coefficient t | 0.146 |

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## Share and Cite

**MDPI and ACS Style**

Bai, H.; Yu, B.; Gu, W.
Research on Position Sensorless Control of RDT Motor Based on Improved SMO with Continuous Hyperbolic Tangent Function and Improved Feedforward PLL. *J. Mar. Sci. Eng.* **2023**, *11*, 642.
https://doi.org/10.3390/jmse11030642

**AMA Style**

Bai H, Yu B, Gu W.
Research on Position Sensorless Control of RDT Motor Based on Improved SMO with Continuous Hyperbolic Tangent Function and Improved Feedforward PLL. *Journal of Marine Science and Engineering*. 2023; 11(3):642.
https://doi.org/10.3390/jmse11030642

**Chicago/Turabian Style**

Bai, Hongfen, Bo Yu, and Wei Gu.
2023. "Research on Position Sensorless Control of RDT Motor Based on Improved SMO with Continuous Hyperbolic Tangent Function and Improved Feedforward PLL" *Journal of Marine Science and Engineering* 11, no. 3: 642.
https://doi.org/10.3390/jmse11030642