This study proposes an enhanced method for estimating the position of a permanent magnet synchronous motor (PMSM) using the Luenberger observer and phase-locked loop (PLL) algorithm. The main contribution to this research is the use of two low-pass filters (LPF) at the input of the PLL, which results in softer position reconstruction compared with conventional PLL. The proposed method is designed and simulated using the MATLAB/Simulink platform. The performance of the proposed method was evaluated and compared with conventional PLL and PLL with one LPF using several performance metrics such as estimation accuracy, convergence time, and stability. Simulation results show that the proposed method achieves better estimation accuracy and higher stability compared with the other methods. Additionally, the proposed method is robust to various disturbances such as load torque and parameter variations. Overall, the proposed method offers an effective and efficient solution for estimating the position of PMSM in various industrial applications.

Accurate estimation of the permanent magnet synchronous motors (PMSMs) position plays a crucial role in various industrial applications, ranging from robotics to electric vehicle propulsion systems [

The conventional phase-locked loop (PLL) algorithm has been widely used for estimating the position of PMSMs due to its simplicity and effectiveness. However, it suffers from certain limitations, such as sensitivity to noise and disturbances, which can affect its performance and stability [

To overcome these limitations, El Murr

This study focuses on the enhanced estimation of the PMSMs position using a combination of the Luenberger observer [

The study of enhanced estimation of the PMSMs position has attracted significant interest from researchers. WU

The LPF serves as a preprocessing stage in the position estimation algorithm, filtering out high-frequency noise and disturbances in the back-EMF signal [

In this study, comprehensive simulations were conducted using the MATLAB/Simulink platform to evaluate the performance and effectiveness of the proposed enhanced position estimation technique. A comparative analysis was conducted between the proposed method and conventional PLL-based approaches, considering key metrics such as estimation accuracy, convergence time, and stability. The results obtained from the simulations demonstrate the superiority of the proposed method. The incorporation of the LPF in the input of the PLL leads to a smoother back-EMF waveform, significantly reducing the impact of noise and disturbances on the position estimation process. Consequently, the enhanced position estimation technique achieves higher accuracy, faster convergence time, and improved stability, making it an attractive solution for real-world applications in motor control and industrial automation.

It is crucial to obtain the state-space model of the PMSM for the implementation of the Luenberger observer [

where R is the machine’s resistance, L is the machine’s inductance,

The derivative of

The state-space model of the PMSM in the α-β reference, considering

Based on Luo

Based on

Discretizing

After estimating the back-EMF based on the estimated current and the back-EMF observer gain, the rotor position can be estimated using the arctangent of the counter back-EMF, as shown in

According to

The PLL estimator for PMSM is a technique used to estimate the rotor position and velocity of the motor without the need for direct position sensors. The PLL estimator leverages the principles of phase and frequency synchronization to estimate the rotor position based on the back-EMF signal of the motor [

The basic idea behind the PLL observer is to compare the phase of the back-EMF signal from the Luenberger observer with a reference signal that is internally generated. This reference signal is typically derived from the estimated rotor angle using sine and cosine functions. By adjusting the phase and frequency of the reference signal, the observer aims to align it with the phase of the back-EMF signal. The

To achieve this alignment, a closed-loop system is used. The difference between the phase of the back-EMF signal and the reference signal is fed into a proportional integral (PI) controller, which adjusts the frequency and phase of the reference signal. The output of the PI controller is the estimated angular frequency that is integrated to generate the estimated rotor electrical angle. Hence, the estimated rotor angle is multiplied by sine and cosine functions to generate the reference signal.

By continuously adjusting the phase and frequency of the reference signal based on the phase difference between the back-EMF and reference signal, the PLL observer effectively tracks the rotor angle of the PMSM. This estimation process is conducted in a closed-loop manner, ensuring accurate and reliable angle estimation even in the presence of system disturbances and noise.

According to

Rewriting

Since the quantity

From

Thus, the transfer function of the PLL can be written as follows:

This study introduces an enhanced position estimation technique for PMSMs by incorporating two LPFs at the input of the PLL algorithm. This novel proposal aims to improve the estimation accuracy by reducing the impact of high-frequency noise and disturbances on the position estimation process.

The implementation of the proposed method involves using the dual LPF configuration to preprocess the input signal before it is fed into the PLL, as shown in

The LPFs effectively filter out unwanted high-frequency components, resulting in a smoother back-EMF waveform [

Applying the same principle as shown in

The cutoff frequency can be obtained as follows:

The proposed cutoff frequency can be obtained by considering it as follows:

Thus, the transfer function of the simplified enhanced PLL can be written as follows:

To ensure accurate control of the PMSM, we use the widely adopted field-oriented control (FOC) algorithm. The FOC algorithm enables the decoupled control of the motor’s torque and flux, enhancing its overall performance. The FOC algorithm incorporates the motor model, current controller, and sensor rotor angle. By precisely regulating the motor currents and controlling the flux orientation, the FOC algorithm optimizes the motor’s operation and response [

The diagram encompasses the PMSM model and the FOC controller block, which contains the Luenberger observer and the PLL algorithm, as shown in

The Luenberger observer and the enhanced PLL estimator obtain the estimated position and compare it with the sensor position when the reference position of the sensor is in conjunction with the FOC controller.

The system block diagrams for the Luenberger observer and the PLL estimator are shown in

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

Stator resistance |
0.15 | |

q-d Inductance | 0.16e-3 | |

Rated voltage | 52 | V |

Machine power | 1K | W |

Pole pair | 23 | – |

Electrical constant |
78.2 | Vp/Krpm |

Torque | 5 | N.M |

SV-PWM freq | 15K | Hz |

System sampling time | 50 | s |

Current observer gain |
8000 | – |

Back-EMF observer gain |
−21000 | – |

PLL |
105.5 | – |

PLL |
0.5 | – |

PLL |
0 | – |

LPF cutoff frequency | 840 | Hz |

These parameters were carefully selected to ensure realistic modeling of the PMSM system and accurate estimation of the motor’s position.

The results demonstrate the ability of our method to accurately estimate the rotor angle, providing valuable information for motor control and position tracking applications. The estimated rotor angle is in accordance with the literature [

The plot in

Parameter | Conventional PLL | Enhanced PLL | Unit |
---|---|---|---|

Phase delay (average) | 0.0018 | ||

Position error (average) | 3.2 | Degree |

In conclusion, the results obtained from the simulations demonstrate the effectiveness and superiority of the enhanced PLL algorithm with dual LPFs in improving the accuracy of estimating the PMSMs position.

Comparing the conventional PLL approach with the enhanced PLL, several key parameters were evaluated. The average phase delay for the conventional PLL was measured at 0.0018 s, whereas the enhanced PLL with the dual LPFs exhibited a slightly higher average phase delay of 0.0045 s. However, the increase in phase delay was outweighed by the significant reduction in position error.

The average position error for the conventional PLL was measured at 3.2 degrees, indicating a noticeable deviation from the actual rotor position. In contrast, the enhanced PLL with dual LPFs achieved a remarkable improvement, resulting in an average position error of only 0.9 degrees. This substantial reduction in position error signifies the enhanced accuracy and precision achieved by incorporating the dual LPFs into the PLL algorithm.

These results highlight the effectiveness of the proposed enhancement, showcasing the ability of the enhanced PLL to mitigate the impact of high-frequency noise and disturbances, leading to a more reliable and accurate position estimation. The reduced position error observed in the enhanced PLL is crucial for precise control and optimal performance in PMSM applications.

Overall, the enhanced PLL algorithm with dual LPFs presents a valuable contribution to the field of estimating the position of PMSMs. The results obtained validate the effectiveness of this approach in improving the accuracy and reliability of position estimation, offering potential benefits for various industrial applications where precise control and motion control are essential.

Future research may require further optimization and fine-tuning of the LPF parameters to strike an optimal balance between phase delay and position error. Additionally, experimental validation of the enhanced PLL algorithm on real-world PMSM systems proposed in this study will be valuable to confirm the results of the simulation and assess the challenges to its practical implementation.