# A Review of Position Sensorless Compound Control for PMSM Drives

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^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Compound Control Based on High-Frequency Injection Method

- High-frequency rotating injection method:

- 2.
- High-frequency pulsating injection method:

#### 2.1. HF Compounded with Model Reference Adaptive Method

#### 2.2. HF Compounded with Sliding Mode Observer

#### 2.3. HF Compounded with BEMF Integration Method or Flux Estimation

**ψ**

_{f}is the permanent magnet chain vector;

**ψ**

_{s}is the stator synthetic magnetic chain vector;

**U**

_{s}is the stator voltage vector;

**I**

_{s}is the stator current vector;

**L**

_{αβ}is the inductance matrix of the motor in the α-β coordinate system; and

**ψ**

_{fα}and

**ψ**

_{fβ}are the components of the rotor magnetic chain on the α-β axis, respectively. The basic structure is shown in Figure 9.

## 3. Compound Control Algorithm Based on I/F Control

_{q}* is the given current; J is the rotational inertia; T

_{L}is the load torque; and ω

_{re}is the rotor electric angular velocity.

#### 3.1. I/F Compounded with Sliding Mode Observer

#### 3.2. I/F Compounded with Flux Obsever

## 4. Switching Methods

#### 4.1. Weighting Factor Method

#### 4.2. Smooth Switching Method

_{L}, between it and the rotor synchronous coordinate system [69,70]. The process of smooth switching control strategy is actually the process of adjusting the phase difference θ

_{L}from an acute angle to close to zero. The phase angle difference θ

_{L}during I/F control preparation for switching cannot be equal to zero, otherwise it will cause the motor to miss-step [71,72,75]. The ideal control strategy is shown in Figure 14.

^{v}-axis current given indirectly to adjust the phase difference θ between the two coordinate systems at heavy load, and by adjusting the virtual q

^{v}-axis and virtual d-axis current given simultaneously at no load or light load. This improved switching strategy has a wider range of application, and at the same time, in this improved switching strategy, the synthetic current vectors of the q

^{v}and d

^{v}axes have a larger phase difference with the q-axis of the rotor synchronous coordinate system, such that this switching strategy is more resistant to disturbances and has a lower risk of motor miss-steps. The improved switching strategy is shown in Figure 15.

#### 4.3. Hysteresis Loop Switching Method

_{sw}. The switching process uses a smooth transition strategy as

## 5. Conclusions

- The high-frequency signal injection method has many advantages, but there are also problems of long convergence time, poor dynamic performance and small stability range. For compound control, the advantages of the high-frequency signal injection method inherit many disadvantages, which can have more or less impact on the estimation accuracy and other aspects in the compound control process. Therefore more advanced high-frequency signal injection methods should be studied to improve the reliability of the dynamic range of motor compound control estimation.
- I/F control is simple in structure, easy to implement, and has the advantages of smooth start-up and no current overcharge. It is the current start-up strategy for most position sensor-free control at medium and high speeds. However, the basic I/f control strategy is an open-loop scheme with disadvantages, such as the current amplitude and frequency cannot be automatically adjusted, and there is a tendency to lose steps, and the speed is easily disturbed, so its improvement will largely improve the performance of the compound control.
- There is a wide variety of control strategies for position sensorless control at high speeds, each with its own advantages, but also some shortcomings. So, the improvement of such algorithms will greatly improve the performance of the current compound control.
- Switching algorithms play a pivotal role in compound control. In the current research field of compound control, whether based on HF control or I/F control, switching strategies are required. Most of the switching algorithms commonly used today have the advantages of, for example, simpler methods and relatively stable algorithm switching, but their switching smoothness is not ideal, which means that the existing switching algorithms should be improved to achieve smoother and more stable switching, or smoother and more stable switching algorithms should be developed to meet the current high demand for motor position estimation.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**(

**a**) The relationship between the estimated rotor and the actual rotor synchronous rotation coordinate system; (

**b**) The control block diagram of the HF pulsating injection method.

**Figure 10.**The phase relation of virtual synchronous frame and rotor synchronous frame in IF control. (

**a**) Start state; (

**b**) Running state.

**Figure 13.**Operations of high-frequency pulse injection method and MRAS in each speed interval after improvement.

**Figure 15.**The block diagram of the improved smooth switching strategy. (

**a**) Motor positive rotation under heavy load; (

**b**) Motor negative rotation under heavy load; (

**c**) Motor positive rotation under light load; (

**d**) Motor negative rotation under light load.

Algorithms | Reference | Description |
---|---|---|

high frequency (HF) injection | [16,17,18,19,20,21,22,23] | The HF injection method is not reliant on the spatial protrusion of the tracking rotor rather than the mathematical equation of the motor, which addresses the sensitivity to the change in motor parameters and leads to a strong robustness. Yet the filter is needed, which has the defects of low signal-to-noise ratio and large phase lag in signal processing. |

including direct calculation | [24,25,26,27] | This method does not depend on the speed of the motor, but it needs to increase the integral circuit and increase the hardware complexity and may bring additional integral error. |

back-electromotive force (EMF) | [28,29,30] | The realization is simple, but the back EMF signal is small when the motor is low speed or static. The back EMF needs to be filtered, which will cause phase shift of the signal. |

flux estimation | [31,32] | The rotor flux of the motor cannot be detected directly. It is necessary to measure the phase voltage and current of the motor, and to establish the function equation, which is directly related to the rotor flux without relying on the rotor speed. The calculation is large. |

model reference adaptation system (MRAS) | [33,34,35,36,37,38] | The position observation is based on the accuracy of the reference model, and the accuracy of the parameters of the reference model itself directly affect the effectiveness of the identification. |

sliding mode observer (SMO) | [39,40,41,42] | It can solve the problem that the motor is difficult to control at high speed and heavy load, and has strong robustness, but it needs a large amount of operation. |

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**MDPI and ACS Style**

Li, Y.; Hu, H.; Shi, P.
A Review of Position Sensorless Compound Control for PMSM Drives. *World Electr. Veh. J.* **2023**, *14*, 34.
https://doi.org/10.3390/wevj14020034

**AMA Style**

Li Y, Hu H, Shi P.
A Review of Position Sensorless Compound Control for PMSM Drives. *World Electric Vehicle Journal*. 2023; 14(2):34.
https://doi.org/10.3390/wevj14020034

**Chicago/Turabian Style**

Li, Yong, Han Hu, and Peicheng Shi.
2023. "A Review of Position Sensorless Compound Control for PMSM Drives" *World Electric Vehicle Journal* 14, no. 2: 34.
https://doi.org/10.3390/wevj14020034