# Overview of Position-Sensorless Technology for Permanent Magnet Synchronous Motor Systems

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Composition of PMSM Drive Systems Based on Sensorless Control

#### 2.1. Structure and Mathematical Model of PMSM Systems

_{d}, i

_{d}and ψ

_{d}represent the voltage, current, and magnetic flux on the d-axis, respectively; i

_{q}, u

_{q}and ψ

_{q}represent the current, voltage, and magnetic flux on the q-axis, respectively; ω

_{e}is the electrical angular velocity; and R is the stator resistance. ψ

_{q}and ψ

_{d}can be expressed as

_{d}and L

_{d}are the stator inductance of the dq axis, and ψ

_{f}is the permanent magnet flux linkage.

_{n}is the number of pole pairs, J is the rotational inertia, B is the damping coefficient, ω

_{m}is the mechanical angular velocity, and T

_{e}and T

_{L}are the electromagnetic torque and the load torque, respectively.

#### 2.2. Analysis of the Sensorless Control Principle

_{α}and i

_{α}represent the voltage and current on the α-axis, respectively; u

_{β}and i

_{β}represent the voltage and current on the β-axis, respectively; L

_{d}and L

_{q}are the inductance components of the dq axis; p is the differential operator; and E

_{α}and E

_{β}are the extended back-EMF. E

_{α}and E

_{β}can be expressed as

_{e}is the electrical angle.

_{e}is included in the extended back-EMF. Therefore, only by obtaining the back-EMF accurately can the information on the speed and position of the motor be calculated. In general, to obtain an accurate back-EMF, the sliding mode observer method or the model reference adaptive method can be used. Taking the sliding mode observer as an example, by designing the control law of the sliding mode observer, the error can be zero. At this time, the state variable of the observer reaches the sliding mode’s surface. According to the equivalent control principle of sliding mode control, the level of control at this time can be regarded as an equivalent level of control, that is, the estimated back-EMF is equal to the actual back-EMF.

_{e}, the rotor’s speed can be obtained. At this time, the information on the rotor’s position and the rotational speed of the motor are known quantities, and the motor can realize high-performance control.

_{d}+ L

_{q})/2 is the average inductance and ΔL = (Lq − Ld)/2 is half the differential inductance.

_{αβ}in the static coordinate system as

_{e}.

## 3. An Overview of the Recent Developments in Sensorless Methods of PMSM

#### 3.1. Model-Based Sensorless Methods

#### 3.1.1. Sliding Mode Observer

#### 3.1.2. Model Reference Adaptive Systems

#### 3.1.3. Extended Kalman Filter

#### 3.1.4. State Observer

#### 3.2. Saliency-Based Sensorless Methods

#### 3.2.1. Rotating Signal Injection

_{h}is the frequency of the injected high-frequency signal and U

_{in}is the amplitude of the high-frequency signal.

_{sp}and I

_{sn}are the positive and negative terms of the high-frequency response current, respectively.

#### 3.2.2. Pulsating Signal Injection

_{in}is the amplitude of the HF signal, and the symbol “^” indicates the components of the estimated rotor’s frame of reference.

#### 3.2.3. FPE-Based Methods

## 4. Future Directions

#### 4.1. High Dynamic Performance throughout the Full Speed Range

#### 4.2. Smooth Switching between Low Speed and High Speed

#### 4.3. Sensorless Control of Ultra-High-Speed PMSMs

#### 4.4. High Robustness under Heavy and Changing Loads

#### 4.5. High Robustness to Changes in the Motor’s Parameters

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Tian, X.; He, R.; Sun, X.; Cai, Y.; Xu, Y. An ANFIS-based ECMS for energy optimization of parallel hybrid electric bus. IEEE Trans. Veh. Technol.
**2020**, 69, 1473–1483. [Google Scholar] [CrossRef] - Sun, X.; Jin, Z.; Xue, M.; Tian, X. Adaptive ECMS with gear shift control by grey wolf optimization algorithm and neural network for plug-in hybrid electric buses. IEEE Trans. Ind. Electron.
**2023**, 71, 667–677. [Google Scholar] [CrossRef] - Sun, X.; Xue, M.; Cai, Y.; Tian, X.; Jin, Z.; Chen, L. Adaptive ECMS based on EF optimization by model predictive control for plug-in hybrid electric buses. IEEE Trans. Transp. Electrif.
**2023**, 9, 2153–2163. [Google Scholar] [CrossRef] - Choi, K.; Kim, Y.; Kim, S.-K.; Kim, K.-S. Current and position sensor fault diagnosis algorithm for PMSM drives based on robust state observer. IEEE Trans. Ind. Electron.
**2021**, 68, 5227–5236. [Google Scholar] [CrossRef] - Sun, X.; Cai, F.; Yang, Z.; Tian, X. Finite position control of interior permanent magnet synchronous motors at low speed. IEEE Trans. Power Electron.
**2022**, 37, 7729–7738. [Google Scholar] [CrossRef] - Novak, Z.; Novak, M. Adaptive PLL-based sensorless control for improved dynamics of high-speed PMSM. IEEE Trans. Power Electron.
**2022**, 37, 10154–10165. [Google Scholar] [CrossRef] - Sun, X.; Hu, C.; Lei, G.; Guo, Y.; Zhu, J. State feedback control for a PM hub motor based on gray wolf optimization algorithm. IEEE Trans. Power Electron.
**2020**, 35, 1136–1146. [Google Scholar] [CrossRef] - Yeam, T.-I.; Lee, D.-C. Design of sliding-mode speed controller with active damping control for single-inverter dual-PMSM drive systems. IEEE Trans. Power Electron.
**2021**, 36, 5794–5801. [Google Scholar] [CrossRef] - Li, T.; Sun, X.; Yao, M.; Guo, D.; Sun, Y. Improved finite control set model predictive current control for permanent magnet synchronous motor with sliding mode observer. IEEE Trans. Transp. Electrif.
**2023**. [Google Scholar] [CrossRef] - Woldegiorgis, A.T.; Ge, X.; Wang, H.; Zuo, Y. An active flux estimation in the estimated reference frame for sensorless control of IPMSM. IEEE Trans. Power Electron.
**2022**, 37, 9047–9060. [Google Scholar] [CrossRef] - Chen, L.; Xu, H.; Sun, X. A Novel Strategy of Control Performance Improvement for Six-Phase Permanent Magnet Synchronous Hub Motor Drives of EVs Under New European Driving Cycle. IEEE Trans. Veh. Technol.
**2021**, 70, 5628–5637. [Google Scholar] [CrossRef] - Lara, J.; Xu, J.; Chandra, A. Effects of Rotor Position Error in the Performance of Field-Oriented-Controlled PMSM Drives for Electric Vehicle Traction Applications. IEEE Trans. Power Electron.
**2016**, 63, 4738–4751. [Google Scholar] [CrossRef] - Candelo-Zuluaga, C.; Riba, J.-R.; Garcia, A. PMSM Parameter Estimation for Sensorless FOC Based on Differential Power Factor. IEEE Trans. Instrum. Meas.
**2021**, 70, 1504212. [Google Scholar] [CrossRef] - Sun, X.; Xiong, Y.; Yao, M.; Tang, X.; Tian, X. A unified control method combined with improved TSF and LADRC for SRMs using modified grey wolf optimization algorithm. ISA Trans.
**2022**, 131, 662–671. [Google Scholar] [CrossRef] [PubMed] - Kuruppu, S.S.; Abeyratne, S.G. Disambiguation of Uniform Demagnetization Fault From Position Sensor Fault in FOC PMSM Applications. IEEE Access
**2022**, 10, 103099–103110. [Google Scholar] [CrossRef] - Wu, Z.; Yang, Z.; Ding, K.; He, G. Transfer Mechanism Analysis of Injected Voltage Harmonic and its Effect on Current Harmonic Regulation in FOC PMSM. IEEE Trans. Power Electron.
**2022**, 37, 820–829. [Google Scholar] [CrossRef] - Sun, X.; Xu, N.; Yao, M.; Cai, F.; Wu, M. Efficient feedback linearization control for an IPMSM of EVs based on improved firefly algorithm. ISA Trans.
**2023**, 134, 431–441. [Google Scholar] [CrossRef] - Petkar, S.G.; Thippiripati, V.K. A Novel Duty-Controlled DTC of a Surface PMSM Drive With Reduced Torque and Flux Ripples. IEEE Trans. Ind. Electron.
**2023**, 70, 3373–3383. [Google Scholar] [CrossRef] - Sun, X.; Feng, L.; Zhu, Z.; Lei, G.; Diao, K.; Guo, Y.; Zhu, J. Optimal design of terminal sliding mode controller for direct torque control of SRMs. IEEE Trans. Transp. Electrif.
**2022**, 8, 1445–1453. [Google Scholar] - Wang, M.; Sun, D.; Zheng, Z.; Nian, H. A Novel Lookup Table Based Direct Torque Control for OW-PMSM Drives. IEEE Trans. Ind. Electron.
**2021**, 68, 10316–10320. [Google Scholar] [CrossRef] - Lemma, B.D.; Pradabane, S. Control of PMSM Drive Using Lookup Table Based Compensated Duty Ratio Optimized Direct Torque Control (DTC). IEEE Access
**2023**, 11, 19863–19875. [Google Scholar] [CrossRef] - Nasr, A.; Gu, C.; Wang, X.; Buticchi, G.; Bozhko, S.; Gerada, C. Torque-Performance Improvement for Direct Torque-Controlled PMSM Drives Based on Duty-Ratio Regulation. IEEE Trans. Power Electron.
**2022**, 37, 749–760. [Google Scholar] [CrossRef] - Sun, X.; Xiong, Y.; Yang, J.; Tian, X. Torque ripple reduction for a 12/8 switched reluctance motor based on a novel sliding mode control strategy. IEEE Trans. Transp. Electrif.
**2023**, 9, 359–369. [Google Scholar] [CrossRef] - Sun, D.; Chen, W.; Cheng, Y.; Nian, H. Improved Direct Torque Control for Open-Winding PMSM System Considering Zero-Sequence Current Suppression With Low Switching Frequency. IEEE Trans. Power Electron.
**2021**, 36, 4440–4451. [Google Scholar] [CrossRef] - Feng, L.; Sun, X.; Tian, X.; Diao, K. Direct torque control with variable flux for an SRM based on hybrid optimization algorithm. IEEE Trans. Power Electron.
**2022**, 37, 6688–6697. [Google Scholar] [CrossRef] - Ding, L.; Li, Y.W.; Zargari, N.R. Discrete-Time SMO Sensorless Control of Current Source Converter-Fed PMSM Drives With Low Switching Frequency. IEEE Trans. Ind. Electron.
**2021**, 68, 2120–2129. [Google Scholar] [CrossRef] - Sun, X.; Zhu, Y.; Cai, Y.; Yao, M.; Sun, Y.; Lei, G. Optimized-sector-based model predictive torque control with sliding mode controller for switched reluctance motor. IEEE Trans. Energy Convers.
**2023**. [Google Scholar] [CrossRef] - Zhao, K.; Yin, T.; Zhang, C.; He, J.; Li, X.; Chen, Y.; Zhou, R.; Leng, A. Robust Model-Free Nonsingular Terminal Sliding Mode Control for PMSM Demagnetization Fault. IEEE Access
**2019**, 7, 15737–15748. [Google Scholar] [CrossRef] - Filho, C.J.V.; Xiao, D.; Vieira, R.P.; Emadi, A. Observers for High-Speed Sensorless PMSM Drives: Design Methods, Tuning Challenges and Future Trends. IEEE Access
**2021**, 9, 56397–56415. [Google Scholar] [CrossRef] - Gong, C.; Hu, Y.; Gao, J.; Wang, Y.; Yan, L. An Improved Delay-Suppressed Sliding-Mode Observer for Sensorless Vector-Controlled PMSM. IEEE Trans. Ind. Electron.
**2020**, 67, 5913–5923. [Google Scholar] [CrossRef] - Yu, K.; Wang, Z. Improved Deadbeat Predictive Current Control of Dual Three-Phase Variable-Flux PMSM Drives With Composite Disturbance Observer. IEEE Trans. Power Electron.
**2022**, 37, 8310–8321. [Google Scholar] [CrossRef] - Kim, H.; Son, J.; Lee, J. A High-Speed Sliding-Mode Observer for the Sensorless Speed Control of a PMSM. IEEE Trans. Ind. Electron.
**2011**, 58, 4069–4077. [Google Scholar] - Feng, L.; Sun, X.; Guo, D.; Yao, M.; Diao, K. Advanced torque sharing function strategy with sliding mode control for switched reluctance motors. IEEE Trans. Transp. Electrif.
**2023**. [Google Scholar] [CrossRef] - Abu-Ali, M.; Berkel, F.; Manderla, M.; Reimann, S.; Kennel, R.; Abdelrahem, M. Deep Learning-Based Long-Horizon MPC: Robust, High Performing, and Computationally Efficient Control for PMSM Drives. IEEE Trans. Power Electron.
**2022**, 37, 12486–12501. [Google Scholar] [CrossRef] - Sun, X.; Li, T.; Zhu, Z.; Lei, G.; Guo, Y.; Zhu, J. Speed Sensorless Model Predictive Current Control Based on Finite Position Set for PMSHM Drives. IEEE Trans. Transp. Electrif.
**2021**, 7, 2743–2752. [Google Scholar] [CrossRef] - Wu, M.; Sun, X.; Zhu, J.; Lei, G.; Guo, Y. Improved Model Predictive Torque Control for PMSM Drives Based on Duty Cycle Optimization. IEEE Trans. Magn.
**2021**, 57, 8200505. [Google Scholar] [CrossRef] - Xu, S.; Sun, Z.; Yao, C.; Zhang, H.; Hua, W.; Ma, G. Model Predictive Control With Constant Switching Frequency for Three-Level T-Type Inverter-Fed PMSM Drives. IEEE Trans. Ind. Electron.
**2022**, 69, 8839–8850. [Google Scholar] [CrossRef] - Xue, C.; Zhou, D.; Li, Y. Finite-Control-Set Model Predictive Control for Three-Level NPC Inverter-Fed PMSM Drives With LC Filter. IEEE Trans. Ind. Electron.
**2021**, 68, 11980–11991. [Google Scholar] [CrossRef] - Tian, X.; Cai, Y.; Sun, X.; Zhu, Z.; Xu, Y. A novel energy management strategy for plug-in hybrid electric buses based on model predictive control and estimation of distribution algorithm. IEEE/ASME Trans. Mechatron.
**2022**, 27, 4350–4361. [Google Scholar] [CrossRef] - Zhang, X.; Bai, H.; Cheng, M. Improved Model Predictive Current Control With Series Structure for PMSM Drives. IEEE Trans. Ind. Electron.
**2022**, 69, 12437–12446. [Google Scholar] [CrossRef] - Xu, T.; Wang, X.; Xiao, D.; Meng, X.; Mao, Y.; Wang, Z. A Novel Two-Mode Inverter-Based Open-Winding PMSM Drive and Its Modulation Strategies. IEEE Trans. Power Electron.
**2023**, 38, 8762–8774. [Google Scholar] [CrossRef] - Chen, L.; Xu, H.; Sun, X.; Cai, Y. Three-Vector-Based Model Predictive Torque Control for a Permanent Magnet Synchronous Motor of EVs. IEEE Trans. Transp. Electrif.
**2021**, 7, 1454–1465. [Google Scholar] [CrossRef] - Luo, Y.; Yang, K.; Zheng, Y. Luenberger Observer-Based Model Predictive Control for Six-Phase PMSM Motor With Localization Error Compensation. IEEE Trans. Ind. Electron.
**2023**, 70, 10800–10810. [Google Scholar] [CrossRef] - Sun, X.; Li, T.; Tian, X.; Zhu, J.G. Fault-tolerant operation of a six-phase permanent magnet synchronous hub motor based on model predictive current control with virtual voltage vectors. IEEE Trans. Energy Convers.
**2022**, 37, 337–346. [Google Scholar] [CrossRef] - Liang, D.; Li, J.; Qu, R. Sensorless Control of Permanent Magnet Synchronous Machine Based on Second-Order Sliding-Mode Observer With Online Resistance Estimation. IEEE Trans. Ind. Appl.
**2017**, 53, 3672–3682. [Google Scholar] [CrossRef] - Sun, X.; Cao, J.; Lei, G.; Guo, Y.; Zhu, J. A robust deadbeat predictive controller with delay compensation based on composite sliding mode observer for PMSMs. IEEE Trans. Power Electron.
**2021**, 36, 10742–10752. [Google Scholar] [CrossRef] - Apte, A.; Joshi, V.A.; Mehta, H.; Walambe, R. Disturbance-Observer-Based Sensorless Control of PMSM Using Integral State Feedback Controller. IEEE Trans. Power Electron.
**2020**, 35, 6082–6090. [Google Scholar] [CrossRef] - Qiao, Z.; Shi, T.; Wang, Y.; Yan, Y.; Xia, C.; He, X. New Sliding-Mode Observer for Position Sensorless Control of Permanent-Magnet Synchronous Motor. IEEE Trans. Ind. Electron.
**2013**, 60, 710–719. [Google Scholar] [CrossRef] - Wang, G.; Hao, X.; Zhao, N.; Zhang, G.; Xu, D. Current Sensor Fault-Tolerant Control Strategy for Encoderless PMSM Drives Based on Single Sliding Mode Observer. IEEE Trans. Transp. Electrif.
**2020**, 6, 679–689. [Google Scholar] [CrossRef] - Li, Z.; Zhang, Z.; Feng, S.; Wang, J.; Guo, X.; Sun, H. Design of Model-Free Speed Regulation System for Permanent Magnet Synchronous Linear Motor Based on Adaptive Observer. IEEE Access
**2022**, 10, 68545–68556. [Google Scholar] [CrossRef] - Sun, X.; Hu, C.; Zhu, J.; Wang, S.; Zhou, W.; Yang, Z.; Lei, G.; Li, K.; Zhu, B.; Guo, Y. MPTC for PMSMs of EVs with multi-motor driven system considering optimal energy allocation. IEEE Trans. Magn.
**2019**, 55, 1–6. [Google Scholar] [CrossRef] - Zuo, Y.; Lai, C.; Iyer, K.L.V. A Review of Sliding Mode Observer Based Sensorless Control Methods for PMSM Drive. IEEE Trans. Power Electron.
**2023**, 38, 11352–11367. [Google Scholar] [CrossRef] - Kashif, M.; Singh, B. Modified Active-Power MRAS Based Adaptive Control With Reduced Sensors for PMSM Operated Solar Water Pump. IEEE Trans. Energy Convers.
**2023**, 38, 38–52. [Google Scholar] [CrossRef] - Sun, X.; Li, T.; Yao, M.; Lei, G.; Guo, Y.; Zhu, J. Improved finite-control-set model predictive control with virtual vectors for PMSHM drives. IEEE Trans. Energy Convers.
**2022**, 37, 1885–1894. [Google Scholar] [CrossRef] - Kivanc, O.C.; Ozturk, S.B. Sensorless PMSM Drive Based on Stator Feedforward Voltage Estimation Improved With MRAS Multiparameter Estimation. IEEE/ASME Trans. Mechatron.
**2018**, 23, 1326–1337. [Google Scholar] [CrossRef] - Badini, S.S.; Verma, V. A New Stator Resistance Estimation Technique for Vector-Controlled PMSM Drive. IEEE Trans. Ind. Appl.
**2020**, 56, 6536–6545. [Google Scholar] [CrossRef] - Kim, H.-W.; Youn, M.-J.; Cho, K.-Y. New voltage distortion observer of PWM VSI for PMSM. IEEE Trans. Ind. Electron.
**2005**, 52, 1188–1192. [Google Scholar] [CrossRef] - Sun, X.; Zhang, Y.; Tian, X.; Cao, J.; Zhu, J. Speed Sensorless Control for IPMSMs Using a Modified MRAS With Gray Wolf Optimization Algorithm. IEEE Trans. Transp. Electrif.
**2022**, 8, 1326–1337. [Google Scholar] [CrossRef] - Liu, Z.-H.; Nie, J.; Wei, H.-L.; Chen, L.; Li, X.-H.; Zhang, H.-Q. A Newly Designed VSC-Based Current Regulator for Sensorless Control of PMSM Considering VSI Nonlinearity. IEEE J. Emerg. Sel. Top. Power Electron.
**2021**, 9, 4420–4431. [Google Scholar] [CrossRef] - Chen, D.; Wang, J.; Zhou, L. Adaptive Second-Order Active-Flux Observer for Sensorless Control of PMSMs With MRAS-Based VSI Nonlinearity Compensation. IEEE J. Emerg. Sel. Top. Power Electron.
**2023**, 11, 3076–3086. [Google Scholar] [CrossRef] - Liu, Z.-H.; Nie, J.; Wei, H.-L.; Chen, L.; Wu, F.-M.; Lv, M.-Y. Second-Order ESO-Based Current Sensor Fault-Tolerant Strategy for Sensorless Control of PMSM With B-Phase Current. IEEE/ASME Trans. Mechatron.
**2022**, 27, 5427–5438. [Google Scholar] [CrossRef] - Chen, D.; Li, J.; Chen, J.; Qu, R. On-Line Compensation of Resolver Periodic Error for PMSM Drives. IEEE Trans. Ind. Appl.
**2019**, 55, 5990–6000. [Google Scholar] [CrossRef] - Zhu, Y.; Cheng, M.; Hua, W.; Zhang, B. Sensorless Control Strategy of Electrical Variable Transmission Machines for Wind Energy Conversion Systems. IEEE Trans. Magn.
**2013**, 49, 3383–3386. [Google Scholar] [CrossRef] - Kim, H.-W.; Youn, M.-J.; Cho, K.-Y.; Kim, H.-S. Nonlinearity estimation and compensation of PWM VSI for PMSM under resistance and flux linkage uncertainty. IEEE Trans. Control. Syst. Technol.
**2006**, 14, 589–601. [Google Scholar] - Jin, Z.; Yang, J.; Qiu, X.; Ge, H.; Bai, C. A High Torque Estimation Accuracy Direct Torque Control of Permanent Magnet Synchronous Motor Based on a Novel Iron Loss Resistance Observer. IEEE Access
**2021**, 9, 125822–125829. [Google Scholar] [CrossRef] - Sun, X.; Zhu, Y.; Cai, Y.; Xiong, Y.; Yao, M.; Yuan, C. Current fault tolerance control strategy for 3-phase switched reluctance motor combined with position signal reconstruction. IEEE Trans. Energy Convers.
**2023**. [Google Scholar] [CrossRef] - Bolognani, S.; Oboe, R.; Zigliotto, M. Sensorless full-digital PMSM drive with EKF estimation of speed and rotor position. IEEE Trans. Ind. Electron.
**1999**, 46, 184–191. [Google Scholar] [CrossRef] - Wang, Z.; Zheng, Y.; Zou, Z.; Cheng, M. Position Sensorless Control of Interleaved CSI Fed PMSM Drive With Extended Kalman Filter. IEEE Trans. Magn.
**2012**, 48, 3688–3691. [Google Scholar] [CrossRef] - Yang, H.; Yang, R.; Hu, W.; Huang, Z. FPGA-Based Sensorless Speed Control of PMSM Using Enhanced Performance Controller Based on the Reduced-Order EKF. IEEE J. Emerg. Sel. Top. Power Electron.
**2021**, 9, 289–301. [Google Scholar] [CrossRef] - Xiao, X.; Chen, C. Reduction of Torque Ripple Due to Demagnetization in PMSM Using Current Compensation. IEEE Trans. Appl. Supercond.
**2010**, 20, 1068–1071. [Google Scholar] [CrossRef] - Sun, X.; Tang, X.; Tian, X.; Wu, J.; Zhu, J. Position sensorless control of switched reluctance motor drives based on a new sliding mode observer using Fourier flux linkage model. IEEE Trans. Energy Convers.
**2022**, 37, 978–988. [Google Scholar] [CrossRef] - Zwerger, T.; Mercorelli, P. Using a Bivariate Polynomial in an EKF for State and Inductance Estimations in the Presence of Saturation Effects to Adaptively Control a PMSM. IEEE Access
**2022**, 10, 111545–111553. [Google Scholar] [CrossRef] - Quang, N.K.; Hieu, N.T.; Ha, Q.P. FPGA-Based Sensorless PMSM Speed Control Using Reduced-Order Extended Kalman Filters. IEEE Trans. Ind. Electron.
**2014**, 61, 6574–6582. [Google Scholar] [CrossRef] - Sun, X.; Cao, J.; Lei, G.; Guo, Y.; Zhu, J. A Composite Sliding Mode Control for SPMSM Drives Based on a New Hybrid Reaching Law With Disturbance Compensation. IEEE Trans. Transp. Electrif.
**2021**, 7, 1427–1436. [Google Scholar] [CrossRef] - Yang, Z.; Yan, Z.; Lu, Y.; Wang, W.; Yu, L.; Geng, Y. Double DOF Strategy for Continuous-Wave Pulse Generator Based on Extended Kalman Filter and Adaptive Linear Active Disturbance Rejection Control. IEEE Trans. Power Electron.
**2022**, 37, 1382–1393. [Google Scholar] [CrossRef] - Bolognani, S.; Tubiana, L.; Zigliotto, M. Extended Kalman filter tuning in sensorless PMSM drives. IEEE Trans. Ind. Appl.
**2003**, 39, 1741–1747. [Google Scholar] [CrossRef] - Li, X.; Kennel, R. General Formulation of Kalman-Filter-Based Online Parameter Identification Methods for VSI-Fed PMSM. IEEE Trans. Ind. Electron.
**2021**, 68, 2856–2864. [Google Scholar] [CrossRef] - Xiao, X.; Chen, C.; Zhang, M. Dynamic Permanent Magnet Flux Estimation of Permanent Magnet Synchronous Machines. IEEE Trans. Appl. Supercond.
**2010**, 20, 1085–1088. [Google Scholar] [CrossRef] - Li, X.; Zhang, S.; Cui, X.; Wang, Y.; Zhang, C.; Li, Z.; Zhou, Y. Novel Deadbeat Predictive Current Control for PMSM With Parameter Updating Scheme. IEEE J. Emerg. Sel. Top. Power Electron.
**2022**, 10, 2065–2074. [Google Scholar] [CrossRef] - Mwasilu, F.; Jung, J.-W. Enhanced Fault-Tolerant Control of Interior PMSMs Based on an Adaptive EKF for EV Traction Applications. IEEE Trans. Power Electron.
**2016**, 31, 5746–5758. [Google Scholar] [CrossRef] - Diao, S.; Diallo, D.; Makni, Z.; Marchand, C.; Bisson, J.-F. A Differential Algebraic Estimator for Sensorless Permanent-Magnet Synchronous Machine Drive. IEEE Trans. Energy Convers.
**2015**, 30, 82–89. [Google Scholar] [CrossRef] - Li, W.; Feng, G.; Li, Z.; Toulabi, M.S.; Kar, N.C. Extended Kalman Filter Based Inductance Estimation for Dual Three-Phase Permanent Magnet Synchronous Motors Under the Single Open-Phase Fault. IEEE Trans. Energy Convers.
**2022**, 37, 1134–1144. [Google Scholar] [CrossRef] - Smidl, V.; Peroutka, Z. Advantages of Square-Root Extended Kalman Filter for Sensorless Control of AC Drives. IEEE Trans. Ind. Electron.
**2012**, 59, 4189–4196. [Google Scholar] [CrossRef] - Sun, X.; Tang, X.; Tian, X.; Lei, G.; Guo, Y.; Zhu, J. Sensorless control with fault-tolerant ability for switched reluctance motors. IEEE Trans. Energy Convers.
**2022**, 37, 1272–1281. [Google Scholar] [CrossRef] - Zuo, S.; Hu, X.; Li, D.; Mao, Y.; Wu, Z.; Xiong, Y. Analysis and Suppression of Longitudinal Vibration of Electric Wheel System Considering Rotor Position Error. IEEE Trans. Transp. Electrif.
**2021**, 7, 671–682. [Google Scholar] [CrossRef] - Wu, Q.; Dong, S.; Zhang, W.-A.; Yu, L. Online Modeling of the CNC Engraving System With Dead-Zone Input Nonlinearity. IEEE Trans. Ind. Electron.
**2022**, 69, 774–782. [Google Scholar] [CrossRef] - Shi, Z.; Sun, X.; Cai, Y.; Yang, Z. Robust Design Optimization of a Five-Phase PM Hub Motor for Fault-Tolerant Operation Based on Taguchi Method. IEEE Trans. Energy Convers.
**2020**, 35, 2036–2044. [Google Scholar] [CrossRef] - Yang, J.; Zhou, J.; Zhou, H.; Yi, F.; Song, D.; Dong, M. High-Precision Harmonic Current Extraction for PMSM Based on Multiple Reference Frames Considering Speed Harmonics. IEEE Trans. Ind. Electron.
**2023**, 70, 9764–9776. [Google Scholar] [CrossRef] - Li, Z.; Feng, G.; Lai, C.; Banerjee, D.; Li, W.; Kar, N.C. Current Injection-Based Multi-parameter Estimation for Dual Three-Phase IPMSM Considering VSI Nonlinearity. IEEE Trans. Transp. Electrif.
**2019**, 5, 405–415. [Google Scholar] [CrossRef] - Brosch, A.; Wallscheid, O.; Böcker, J. Long-Term Memory Recursive Least Squares Online Identification of Highly Utilized Permanent Magnet Synchronous Motors for Finite-Control-Set Model Predictive Control. IEEE Trans. Power Electron.
**2023**, 38, 1451–1467. [Google Scholar] [CrossRef] - Zhou, Y.; Zhang, S.; Cui, X.; Zhang, C.; Li, X. An Accurate Torque Output Method for Open-End Winding Permanent Magnet Synchronous Motors Drives. IEEE Trans. Energy Convers.
**2021**, 36, 3470–3480. [Google Scholar] [CrossRef] - Sun, X.; Wu, M.; Yin, C.; Wang, S. Model Predictive Thrust Force Control for Linear Motor Actuator used in Active Suspension. IEEE Trans. Energy Convers.
**2021**, 36, 3063–3072. [Google Scholar] [CrossRef] - Sun, X.; Cao, J.; Lei, G.; Guo, Y.; Zhu, J. Speed sensorless control for permanent magnet synchronous motors based on finite position set. IEEE Trans. Ind. Electron.
**2020**, 67, 6089–6100. [Google Scholar] [CrossRef] - Yu, Y.; Huang, X.; Li, Z.; Wu, M.; Shi, T.; Cao, Y.; Yang, G.; Niu, F. Full Parameter Estimation for Permanent Magnet Synchronous Motors. IEEE Trans. Ind. Electron.
**2023**, 69, 4376–4386. [Google Scholar] [CrossRef] - Song, J.; Wang, Y.-K.; Zheng, W.X.; Niu, Y. Adaptive Terminal Sliding Mode Speed Regulation for PMSM Under Neural-Network-Based Disturbance Estimation: A Dynamic-Event-Triggered Approach. IEEE Trans. Ind. Electron.
**2023**, 70, 8446–8456. [Google Scholar] [CrossRef] - Liu, Z.L.H.W.X.L.K.; Zhong, Q. Global identification of electrical and mechanical parameters in PMSM drive based on dynamic self-learning PSO. IEEE Trans. Power Electron.
**2018**, 33, 10858–10871. [Google Scholar] [CrossRef] - Sun, X.; Wu, M.; Lei, G.; Guo, Y.; Zhu, J. An improved model predictive current control for PMSM drives based on current track circle. IEEE Trans. Ind. Electron.
**2021**, 68, 3782–3793. [Google Scholar] [CrossRef] - Xiao, Z.L.H.W.Q.Z.K.L.X.; Wu, L. GPU implementation of DPSO-RE algorithm for parameters identification of surface PMSM considering VSI nonlinearity. IEEE Trans. Emerg. Sel. Topics Power Electron.
**2017**, 5, 1334–1345. [Google Scholar] - Sun, X.; Shi, Z.; Lei, G.; Guo, Y.; Zhu, J. Multi-objective design optimization of an IPMSM based on multilevel strategy. IEEE Trans. Ind. Electron.
**2021**, 68, 139–148. [Google Scholar] [CrossRef] - Wang, Y.; Feng, Y.; Zhang, X.; Liang, J. A New Reaching Law for Antidisturbance Sliding-Mode Control of PMSM Speed Regulation System. IEEE Trans. Power Electron.
**2020**, 35, 4117–4126. [Google Scholar] [CrossRef] - Liu, C.; Shang, J. Sensorless Drive Strategy of Open-End Winding PMSM With Zero-Sequence Current Suppression. IEEE Trans. Energy Convers.
**2021**, 36, 2987–2997. [Google Scholar] [CrossRef] - Chen, S.; Ding, W.; Hu, R.; Wu, X.; Shi, S. Sensorless Control of PMSM Drives Using Reduced Order Quasi Resonant-Based ESO and Newton–Raphson Method-Based PLL. IEEE Trans. Power Electron.
**2023**, 38, 229–244. [Google Scholar] [CrossRef] - Zhang, M.; Xia, B.; Zhang, J. Parameter Design and Convergence Analysis of Flux Observer for Sensorless PMSM Drives. IEEE Trans. Energy Convers.
**2022**, 37, 2512–2524. [Google Scholar] [CrossRef] - Sun, X.; Zhang, Y.; Lei, G.; Guo, Y.; Zhu, J. An improved deadbeat predictive stator flux control with reduced-order disturbance observer for in-wheel PMSMs. IEEE/ASME Trans. Mechatron.
**2021**, 27, 690–700. [Google Scholar] [CrossRef] - Qu, L.; Qiao, W.; Qu, L. An Extended-State-Observer-Based Sliding-Mode Speed Control for Permanent-Magnet Synchronous Motors. IEEE J. Emerg. Sel. Top. Power Electron.
**2021**, 9, 1605–1613. [Google Scholar] [CrossRef] - Filho, C.J.V.; Vieira, R.P. Adaptive Full-Order Observer Analysis and Design for Sensorless Interior Permanent Magnet Synchronous Motors Drives. IEEE Trans. Ind. Electron.
**2021**, 68, 6527–6536. [Google Scholar] [CrossRef] - Sun, X.; Zhang, Y.; Cai, Y.; Tian, X. Compensated deadbeat predictive current control considering disturbance and VSI nonlinearity for in-wheel PMSMs. IEEE/ASME Trans. Mechatron.
**2022**, 27, 3536–3547. [Google Scholar] [CrossRef] - Liu, H.; Li, S. Speed Control for PMSM Servo System Using Predictive Functional Control and Extended State Observer. IEEE Trans. Ind. Electron.
**2012**, 59, 1171–1183. [Google Scholar] [CrossRef] - Filho, C.J.V.; Scalcon, F.P.; Gabbi, T.S.; Vieira, R.P. Adaptive observer for sensorless permanent magnet synchronous machines with online pole placement. In Proceedings of the 2017 Brazilian Power Electronics Conference (COBEP), Juiz de Fora, Brazil, 19–22 November 2017; pp. 1–6. [Google Scholar]
- Sun, X.; Shi, Z.; Cai, Y.; Lei, G.; Guo, Y.; Zhu, J. Driving-cycle oriented design optimization of a permanent magnet hub motor drive system for a four-wheel-drive electric vehicle. IEEE Trans. Transp. Electrif.
**2020**, 6, 1115–1125. [Google Scholar] [CrossRef] - Yang, M.; Lang, X.; Long, J.; Xu, D. Flux Immunity Robust Predictive Current Control With Incremental Model and Extended State Observer for PMSM Drive. IEEE Trans. Power Electron.
**2017**, 32, 9267–9279. [Google Scholar] - Xie, G.; Lu, K.; Dwivedi, S.K.; Rosholm, J.R.; Blaabjerg, F. Minimum-Voltage Vector Injection Method for Sensorless Control of PMSM for Low-Speed Operations. IEEE Trans. Power Electron.
**2016**, 31, 1785–1794. [Google Scholar] [CrossRef] - Wen, D.; Wang, W.; Zhang, Y. Sensorless Control of Permanent Magnet Synchronous Motor in Full Speed Range. Chin. J. Electr. Eng.
**2022**, 8, 97–107. [Google Scholar] [CrossRef] - Song, X.; Han, B.; Zheng, S.; Chen, S. A Novel Sensorless Rotor Position Detection Method for High-Speed Surface PM Motors in a Wide Speed Range. IEEE Trans. Power Electron.
**2018**, 33, 7083–7093. [Google Scholar] [CrossRef] - Wu, C.; Zhao, Y.; Sun, M. Enhancing Low-Speed Sensorless Control of PMSM Using Phase Voltage Measurements and Online Multiple Parameter Identification. IEEE Trans. Power Electron.
**2020**, 35, 10700–10710. [Google Scholar] [CrossRef] - Lin, H.; Liao, Y.; Yan, L.; Li, F.; Feng, Y. A Novel Modulation-Based Current Harmonic Control Strategy for PMSM Considering Current Measurement Error and Asymmetric Impedance. IEEE Access
**2022**, 10, 89346–89357. [Google Scholar] - Sun, X.; Hu, C.; Lei, G.; Yang, Z.; Guo, Y.; Zhu, J. Speed sensorless control of SPMSM drives for EVs with a binary search algorithm-based phase-locked loop. IEEE Trans. Veh. Technol.
**2020**, 69, 4968–4978. [Google Scholar] - Song, S.I.K.J.H.I.E.Y.; Kim, R.Y. A new rotor position estimation method of IPMSM using all-pass filter on high-frequency rotating voltage signal injection. IEEE Trans. Ind. Electron.
**2016**, 63, 6499–6509. [Google Scholar] - Shinnaka, R.H.S.; Nakamura, N. New sensorless vector control of PMSM by discrete-time voltage injection of PWM carrier frequency–sine- and cosine-form amplitudes extraction method. In Proceedings of the IECON 2016—42nd Annual Conference of the IEEE Industrial Electronics Society, Florence, Italy, 23–26 October 2016; pp. 2862–2867. [Google Scholar]
- Dietrich, L.C.G.G.S.; Hahn, I. Self-sensing control of permanent-magnet synchronous machines with multiple saliencies using pulse-voltage-injection. IEEE Trans. Ind. Appl.
**2016**, 52, 3480–3491. [Google Scholar] - Jin, Z.; Sun, X.; Lei, G.; Guo, Y.; Zhu, J. Sliding mode direct torque control of SPMSMs based on a hybrid wolf optimization algorithm. IEEE Trans. Ind. Electron.
**2022**, 69, 4534–4544. [Google Scholar] [CrossRef] - Corley, M.J.; Lorenz, R.D. Rotor position and velocity estimation for a salient-pole permanent magnet synchronous machine at standstill and high speeds. IEEE Trans. Ind. Appl.
**1998**, 34, 784–789. [Google Scholar] [CrossRef] [Green Version] - Medjmadj, S.; Diallo, D.; Mostefai, M.; Delpha, C.; Arias, A. PMSM drive position estimation: Contribution to the high-frequency injection voltage selection issue. IEEE Trans. Energy Convers.
**2015**, 30, 349–358. [Google Scholar] - Harke, D.R.M.C.; Lorenz, R.D. Robust magnet polarity estimation for initialization of PM synchronous machines with near-zero saliency. IEEE Trans. Ind. Appl.
**2008**, 44, 1199–1209. [Google Scholar] - Li, T.; Sun, X.; Lei, G.; Yang, Z.; Guo, Y.; Zhu, J. Finite-control-set model predictive control of permanent magnet synchronous motor drive systems—An overview. IEEE/CAA J. Autom. Sinica
**2022**, 9, 2087–2105. [Google Scholar] - Xu, P.L.; Zhu, Z.Q. Novel square-wave signal injection method using zero-sequence voltage for sensorless control of PMSM drives. IEEE Trans. Ind. Electron.
**2016**, 63, 7444–7454. [Google Scholar] [CrossRef] - Xu, P.L.; Zhu, Z.Q. Novel carrier signal injection method using zero-sequence voltage for sensorless control of PMSM drives. IEEE Trans. Ind. Electron.
**2016**, 63, 2053–2061. [Google Scholar] - Luo, X.; Tang, Q.; Shen, A.; Zhang, Q. PMSM Sensorless Control by Injecting HF Pulsating Carrier Signal Into Estimated Fixed-Frequency Rotating Reference Frame. IEEE Trans. Ind. Electron.
**2016**, 63, 2294–2303. [Google Scholar] - Zhang, X.; Li, H.; Yang, S.; Ma, M. Improved Initial Rotor Position Estimation for PMSM Drives Based on HF Pulsating Voltage Signal Injection. IEEE Trans. Ind. Electron.
**2018**, 65, 4702–4713. [Google Scholar] - Almarhoon, A.H.; Zhu, Z.Q.; Xu, P.L. Improved Pulsating Signal Injection Using Zero-Sequence Carrier Voltage for Sensorless Control of Dual Three-Phase PMSM. IEEE Trans. Energy Convers.
**2017**, 32, 436–446. [Google Scholar] [CrossRef] - Tang, Q.; Shen, A.; Luo, X.; Xu, J. PMSM Sensorless Control by Injecting HF Pulsating Carrier Signal Into ABC Frame. IEEE Trans. Power Electron.
**2017**, 32, 3767–3776. [Google Scholar] [CrossRef] - Liu, J.M.; Zhu, Z.Q. Novel Sensorless Control Strategy With Injection of High-Frequency Pulsating Carrier Signal Into Stationary Reference Frame. IEEE Trans. Ind. Appl.
**2014**, 50, 2574–2583. [Google Scholar] - Xu, Z.; Zhang, J.; Cheng, M. Investigation of Signal Injection Methods for Fault Detection of PMSM Drives. IEEE Trans. Energy Convers.
**2022**, 37, 2207–2216. [Google Scholar] - Mai, Z.; Xiao, F.; Fu, K.; Liu, J.; Lian, C.; Li, K.; Zhang, W. HF Pulsating Carrier Voltage Injection Method Based on Improved Position Error Signal Extraction Strategy for PMSM Position Sensorless Control. IEEE Trans. Power Electron.
**2021**, 36, 9348–9360. [Google Scholar] - Xu, P.L.; Zhu, Z.Q. Carrier Signal Injection-Based Sensorless Control for Permanent-Magnet Synchronous Machine Drives Considering Machine Parameter Asymmetry. IEEE Trans. Ind. Electron.
**2016**, 63, 2813–2824. [Google Scholar] - Laborda, D.F.; Reigosa, D.D.; Fernández, D.; Sasaki, K.; Kato, T.; Briz, F. Enhanced Torque Estimation in Variable Leakage Flux PMSM Combining High and Low Frequency Signal Injection. IEEE Trans. Ind. Appl.
**2023**, 59, 801–813. [Google Scholar] - Reigosa, D.D.; Fernandez, D.; Yoshida, H.; Kato, T.; Briz, F. Permanent-Magnet Temperature Estimation in PMSMs Using Pulsating High-Frequency Current Injection. IEEE Trans. Ind. Appl.
**2015**, 51, 3159–3168. [Google Scholar] [CrossRef] - Basic, D.; Malrait, F.; Rouchon, P. Current Controller for Low-Frequency Signal Injection and Rotor Flux Position Tracking at Low Speeds. IEEE Trans. Ind. Electron.
**2011**, 58, 4010–4022. [Google Scholar] [CrossRef] [Green Version] - Wang, S.; Yang, K.; Chen, K. An Improved Position-Sensorless Control Method at Low Speed for PMSM Based on High-Frequency Signal Injection into a Rotating Reference Frame. IEEE Access
**2019**, 7, 86510–86521. [Google Scholar] [CrossRef] - Reigosa, D.D.; Fernandez, D.; Tanimoto, T.; Kato, T.; Briz, F. Sensitivity Analysis of High-Frequency Signal Injection-Based Temperature Estimation Methods to Machine Assembling Tolerances. IEEE Trans. Ind. Appl.
**2016**, 52, 4798–4805. [Google Scholar] - Reigosa, D.; Fernandez, D.; Tanimoto, T.; Kato, T.; Briz, F. Comparative Analysis of BEMF and Pulsating High-Frequency Current Injection Methods for PM Temperature Estimation in PMSMs. IEEE Trans. Power Electron.
**2017**, 32, 3691–3699. [Google Scholar] - Accetta, A.; Cirrincione, M.; Pucci, M.; Vitale, G. Sensorless Control of PMSM Fractional Horsepower Drives by Signal Injection and Neural Adaptive-Band Filtering. IEEE Trans. Ind. Electron.
**2012**, 59, 1355–1366. [Google Scholar] [CrossRef] - Lara, J.; Chandra, A. Performance Investigation of Two Novel HSFSI Demodulation Algorithms for Encoderless FOC of PMSMs Intended for EV Propulsion. IEEE Trans. Ind. Electron.
**2018**, 65, 1074–1083. [Google Scholar] [CrossRef] - Jin, X.; Ni, R.; Chen, W.; Blaabjerg, F.; Xu, D. High-Frequency Voltage-Injection Methods and Observer Design for Initial Position Detection of Permanent Magnet Synchronous Machines. IEEE Trans. Power Electron.
**2018**, 33, 7971–7979. [Google Scholar] [CrossRef] [Green Version] - Raca, D.; Garcia, P.; Reigosa, D.D.; Briz, F.; Lorenz, R.D. Carrier-Signal Selection for Sensorless Control of PM Synchronous Machines at Zero and Very Low Speeds. IEEE Trans. Ind. Appl.
**2010**, 46, 167–178. [Google Scholar] [CrossRef] - Fu, X.; Xu, Y.; He, H.; Fu, X. Initial Rotor Position Estimation by Detecting Vibration of Permanent Magnet Synchronous Machine. IEEE Trans. Ind. Electron.
**2021**, 68, 6595–6606. [Google Scholar] [CrossRef] - Wang, Z.; Cao, Z.; He, Z. Improved Fast Method of Initial Rotor Position Estimation for Interior Permanent Magnet Synchronous Motor by Symmetric Pulse Voltage Injection. IEEE Access
**2020**, 8, 59998–60007. [Google Scholar] [CrossRef] - Zhang, G.; Wang, G.; Wang, H.; Xiao, D.; Li, L.; Xu, D. Pseudo-random-frequency sinusoidal injection-based sensorless IPMSM drives with tolerance for system delays. IEEE Trans. Power Electron.
**2019**, 34, 3623–3632. [Google Scholar] [CrossRef] - Murakami, S.; Shiota, T.; Ohto, M.; Ide, K.; Hisatsune, M. Encoderless servo drive with adequately designed IPMSM for pulse-voltage-injection-based position detection. IEEE Trans. Ind. Appl.
**2012**, 48, 1922–1930. [Google Scholar] [CrossRef] - Wang, G.; Zhou, H.; Zhao, N.; Li, C.; Xu, D. Sensorless control of IPMSM drives using a pseudo-random phase-switching fixed-frequency signal injection scheme. IEEE Trans. Ind. Electron.
**2018**, 65, 7660–7671. [Google Scholar] [CrossRef] - Wang, G.; Zhou, H.; Zhao, N.; Li, C.; Xu, D. Sensorless control scheme of IPMSMs using HF orthogonal square-wave voltage injection into a stationary reference frame. IEEE Trans. Power Electron.
**2019**, 34, 2573–2584. [Google Scholar] [CrossRef] - Li, C.; Wang, G.; Zhang, G.; Xu, D.; Xiao, D. Saliency-based sensorless control for SynRM drives with suppression of position estimation error. IEEE Trans. Ind. Electron.
**2019**, 66, 5839–5849. [Google Scholar] [CrossRef] - Yang, S.C.; Yang, S.M.; Hu, J.H. Design consideration on the square-wave voltage injection for sensorless drive of interior permanent-magnet machines. IEEE Trans. Ind. Electron.
**2017**, 64, 159–168. [Google Scholar] [CrossRef] - Wang, G.; Yang, L.; Zhang, G.; Zhang, X.; Xu, D. Comparative investigation of pseudorandom high-frequency signal injection schemes for sensorless IPMSM drives. IEEE Trans. Power Electron.
**2017**, 32, 2123–2132. [Google Scholar] [CrossRef] - Wang, G.; Xiao, D.; Zhao, N.; Zhang, X.; Wang, W.; Xu, D. Low-frequency pulse voltage injection scheme-based sensorless control of IPMSM drives for audible noise reduction. IEEE Trans. Ind. Electron.
**2017**, 64, 8415–8426. [Google Scholar] [CrossRef] - Ni, R.; Xu, D.; Blaabjerg, F.; Lu, K.; Wang, G.; Zhang, G. Square-wave voltage injection algorithm for PMSM position sensorless control with high robustness to voltage errors. IEEE Trans. Power Electron.
**2017**, 32, 5425–5437. [Google Scholar] [CrossRef] - Kim, D.; Kwon, Y.C.; Sul, S.K.; Kim, J.H.; Yu, R.S. Suppression of injection voltage disturbance for high-frequency square-wave injection sensorless drive with regulation of induced high-frequency current ripple. IEEE Trans. Ind. Appl.
**2016**, 52, 302–312. [Google Scholar] [CrossRef] - Demmelmayr, F.; Troyer, M.; Schroedl, M. Advantages of PM-machines compared to induction machines in terms of efficiency and sensorless control in traction applications. In Proceedings of the IECON 2011—37th Annual Conference of the IEEE Industrial Electronics Society, Melbourne, VIC, Australia, 7–10 November 2011; pp. 2762–2768. [Google Scholar]
- Hofer, M.; Nikowitz, M.; Schroedl, M. Sensorless control of a reluctance synchronous machine in the whole speed range without voltage pulse injections. In Proceedings of the 2017 IEEE 3rd International Future Energy Electronics Conference and ECCE Asia (IFEEC 2017—ECCE Asia), Kaohsiung, Taiwan, 3–7 June 2017; pp. 1194–1198. [Google Scholar]
- Robeischl, E.; Schroedl, M. Optimized inform measurement sequence for sensorless PM synchronous motor drives with respect to minimum current distortion. IEEE Trans. Ind. Appl.
**2004**, 40, 591–598. [Google Scholar] [CrossRef] - Zhao, C.; Tanaskovic, M.; Percacci, F.; Mariéthoz, S.; Gnos, P. Sensorless position estimation for slotless surface mounted permanent magnet synchronous motors in full speed range. IEEE Trans. Power Electron.
**2019**, 34, 11566–11579. [Google Scholar] [CrossRef] - Hind, D.; Li, C.; Sumner, M.; Gerada, C. Realising robust low speed sensorless PMSM control using current derivatives obtained from standard current sensors. In Proceedings of the 2017 IEEE International Electric Machines and Drives Conference (IEMDC), Miami, FL, USA, 21–24 May 2017; pp. 1–6. [Google Scholar]
- Guan, D.Q.; Bui, M.X.; Xiao, D.; Rahman, M.F. Performance comparison of two FPE sensorless control methods on a direct torque controlled interior permanent magnet synchronous motor drive. In Proceedings of the 2016 19th International Conference on Electrical Machines and Systems (ICEMS), Chiba, Japan, 13–16 November 2016; pp. 1–6. [Google Scholar]
- Wang, G.; Kuang, J.; Zhao, N.; Zhang, G.; Xu, D. Rotor position estimation of PMSM in low-speed region and standstill using zero-voltage vector injection. IEEE Trans. Power Electron.
**2018**, 33, 7948–7958. [Google Scholar] [CrossRef] - Xie, G.; Lu, K.; Dwivedi, S.K.; Riber, R.J.; Wu, W. Permanent magnet flux online estimation based on zero-voltage vector injection method. IEEE Trans. Power Electron.
**2015**, 30, 6506–6509. [Google Scholar] [CrossRef] - Guan, D.Q.; Bui, M.X.; Xiao, D.; Rahman, M.F. Evaluation of an FPGA current derivative measurement system for the fundamental PWM excitation sensorless method for IPMSM. In Proceedings of the 2016 IEEE 2nd Annual Southern Power Electronics Conference (SPEC), Auckland, New Zealand, 5–8 December 2016; pp. 1–6. [Google Scholar]
- Xie, G.; Lu, K.; Kumar, D.S.; Riber, R.J. High bandwidth zero voltage injection method for sensorless control of PMSM. In Proceedings of the 2014 17th International Conference on Electrical Machines and Systems (ICEMS), Hangzhou, China, 22–25 October 2014; pp. 3546–3552. [Google Scholar]
- Al-Kaf, H.A.G.; Lee, K.-B. Low Complexity MPC-DSVPWM for Current Control of PMSM Using Neural Network Approach. IEEE Access
**2022**, 10, 132596–132607. [Google Scholar] [CrossRef] - Zhang, Z.; Wang, Z.; Wei, X.; Liang, Z.; Kennel, R.; Rodriguez, J. Space-Vector-Optimized Predictive Control for Dual Three-Phase PMSM With Quick Current Response. IEEE Trans. Power Electron.
**2022**, 37, 4453–4462. [Google Scholar] - Fuentes, E.; Silva, C.A.; Kennel, R.M. MPC Implementation of a Quasi-Time-Optimal Speed Control for a PMSM Drive, with Inner Modulated-FS-MPC Torque Control. IEEE Trans. Ind. Electron.
**2016**, 63, 3897–3905. [Google Scholar] - Lee, Y.; Sul, S.K. Model-based sensorless control of an IPMSM with enhanced robustness against load disturbances based on position and speed estimator using a speed error. IEEE Trans. Ind. Appl.
**2018**, 54, 1448–1459. [Google Scholar] - Lin, T.C.; Zhu, Z.Q.; Liu, J.M. Improved rotor position estimation in sensorless-controlled permanent-magnet synchronous machines having asymmetric-EMF with harmonic compensation. IEEE Trans. Ind. Electron.
**2015**, 62, 6131–6139. [Google Scholar] - Tuovinen, T.; Hinkkanen, M. Signal-injection-assisted full-order observer with parameter adaptation for synchronous reluctance motor drives. IEEE Trans. Ind. Appl.
**2014**, 50, 3392–3402. [Google Scholar] - Bao, D.; Pan, X.; Wang, Y.; Wang, X.; Li, K. Adaptive synchronous-frequency tracking-mode observer for the sensorless control of a surface PMSM. IEEE Trans. Ind. Appl.
**2018**, 54, 6460–6471. [Google Scholar] - Feng, Y.; Yu, X.; Han, F. High-order terminal sliding-mode observer for parameter estimation of a permanent-magnet synchronous motor. IEEE Trans. Ind. Electron.
**2013**, 60, 4272–4280. [Google Scholar] - Foo, G.; Rahman, M.F. Evaluation of velocity servo performance of IPMSM drive under high-performance sensorless operation. In Proceedings of the 8th International Conference on Power Electronics—ECCE Asia, Jeju, Republic of Korea, 30 May–3 June 2011; pp. 1–10. [Google Scholar]
- Scarcella, G.; Scelba, G.; Testa, A. High performance sensorless controls based on HF excitation: A viable solution for future AC motor drives? In Proceedings of the 2015 IEEE Workshop on Electrical Machines Design, Control and Diagnosis (WEMDCD), Turin, Italy, 26–27 March 2015; pp. 178–187. [Google Scholar]
- Gabriel, F.; De Belie, F.; Neyt, X.; Lataire, P. High-frequency issues using rotating voltage injections intended for position self-sensing. IEEE Trans. Ind. Electron.
**2013**, 60, 5447–5457. [Google Scholar] - Zhao, Y.; Qiao, W.; Wu, L. Improved rotor position and speed estimators for sensorless control of interior permanent-magnet synchronous machines. IEEE J. Emerg. Sel. Topics Power Electron.
**2014**, 2, 627–639. [Google Scholar] - Sato, S.; Iura, H.; Ide, K.; Sul, S.K. Three years of industrial experience with sensorless IPMSM drive based on high frequency injection method. In Proceedings of the 2011 Symposium on Sensorless Control for Electrical Drives, Birmingham, UK, 1–2 September 2011; pp. 74–79. [Google Scholar]
- Chen, Y.; Wang, X.; Meng, X.; He, M.; Xiao, D.; Wang, Z. A Universal Model Predictive Control Strategy for Dual Inverters Fed OW-PMSM Drives. IEEE Trans. Power Electron.
**2023**, 38, 7575–7585. [Google Scholar] - Friedmann, J.; Hoffmann, R.; Kennel, R. A new approach for a complete and ultrafast analysis of PMSMs using the arbitrary injection scheme. In Proceedings of the 2016 IEEE Symposium on Sensorless Control for Electrical Drives (SLED), Nadi, Fiji, 5–6 June 2016; pp. 1–6. [Google Scholar]
- Shi, Z.; Sun, X.; Cai, Y.; Yang, Z.; Lei, G.; Guo, Y.; Zhu, J. Torque analysis and dynamic performance improvement of A PMSM for EVs by skew angle optimization. IEEE Trans. Appl. Supercon.
**2019**, 29, 0600305. [Google Scholar] - Hosogaya, Y.; Kubota, H. Flux position estimation method of IPMSM by controlling current derivative at zero voltage vector. In Proceedings of the 2010 International Conference on Electrical Machines and Systems, Incheon, Republic of Korea, 10–13 October 2010; pp. 894–899. [Google Scholar]
- Sun, X.; Cao, Y.; Jin, Z.; Tian, X.; Xue, M. An adaptive ECMS based on traffic information for plug-in hybrid electric buses. IEEE Trans. Ind. Electron.
**2023**, 70, 9248–9259. [Google Scholar] - Shi, Z.; Sun, X.; Lei, G.; Tian, X.; Guo, Y.; Zhu, J. Multiobjective optimization of a five-phase bearingless permanent magnet motor considering winding area. IEEE/ASME Trans. Mechatron.
**2022**, 27, 2657–2666. [Google Scholar] - Bolognani, S.; Ortombina, L.; Tinazzi, F.; Zigliotto, M. Model sensitivity of fundamental-frequency-based position estimators for sensorless PM and reluctance synchronous motor drives. IEEE Trans. Ind. Electron.
**2018**, 65, 77–85. [Google Scholar] - Sun, X.; Xu, N.; Yao, M. Sequential subspace optimization design of a dual three-phase permanent magnet synchronous hub motor based on NSGA III. IEEE Trans. Transp. Electrif.
**2023**, 9, 622–630. [Google Scholar] - Yao, C.; Sun, Z.; Xu, S.; Zhang, H.; Ren, G.; Ma, G. ANN Optimization of Weighting Factors Using Genetic Algorithm for Model Predictive Control of PMSM Drives. IEEE Trans. Ind. Appl.
**2022**, 58, 7346–7362. [Google Scholar] - Andreescu, G.-D.; Pitic, C.I.; Blaabjerg, F.; Boldea, I. Combined Flux Observer With Signal Injection Enhancement for Wide Speed Range Sensorless Direct Torque Control of IPMSM Drives. IEEE Trans. Energy Convers.
**2008**, 23, 393–402. [Google Scholar] - Wang, G.; Yang, R.; Xu, D. DSP-Based Control of Sensorless IPMSM Drives for Wide-Speed-Range Operation. IEEE Trans. Ind. Electron.
**2013**, 60, 720–727. [Google Scholar] - Seilmeier, M.; Piepenbreier, B. Sensorless Control of PMSM for the Whole Speed Range Using Two-Degree-of-Freedom Current Control and HF Test Current Injection for Low-Speed Range. IEEE Trans. Power Electron.
**2015**, 30, 4394–4403. [Google Scholar] - Hong, D.-K.; Woo, B.-C.; Lee, J.-Y.; Koo, D.-H. Ultra High Speed Motor Supported by Air Foil Bearings for Air Blower Cooling Fuel Cells. IEEE Trans. Magn.
**2012**, 48, 871–874. [Google Scholar] - Zhao, L.; Ham, C.; Zheng, L.; Wu, T.; Sundaram, K.; Kapat, J.; Chow, L. A Highly Efficient 200 000 RPM Permanent Magnet Motor System. IEEE Trans. Magn.
**2007**, 43, 2528–2530. [Google Scholar] - Ahn, J.-H.; Choi, J.-Y.; Park, C.H.; Han, C.; Kim, C.-W.; Yoon, T.-G. Correlation Between Rotor Vibration and Mechanical Stress in Ultra-High-Speed Permanent Magnet Synchronous Motors. IEEE Trans. Magn.
**2017**, 53, 1–6. [Google Scholar]

**Figure 3.**Block diagram of a sensorless control system based on a disturbance observer [47].

Methods | Accuracy | Complexity | Advantage | Disadvantage |
---|---|---|---|---|

MRAS | Medium | Medium | Wide speed range | Sensitive to noise |

RLS | Medium | Medium | Easy to implement, the small amount of calculation | Low accuracy |

EKF | High | High | Less impact of measurement noise | Complex computation |

Neural network | High | High | High accuracy | Complex computation |

Method | Advantages | Disadvantages |
---|---|---|

Rotating signal injection | Does not require information on the initial location, good robustness | Only applicable to salient pole motors |

Pulsating sinusoidal injection | Low injection frequency. The influence of the inverter;s nonlinearity is small. | LPF affects the system’s bandwidth and has insufficient dynamic performance |

Pulsating square wave injection | High injection frequency. High-frequency signal extraction is simple, and the influence of the inverter’s nonlinearity is small | LPF affects the system’s bandwidth and has insufficient dynamic performance. It needs information on the initial location |

FPE-based methods | No external signal injection required, no high-frequency noise | High requirements of the current signal sampling circuit |

Categories | Speed Range | Advantages | Disadvantages |
---|---|---|---|

SMO | Medium and high speed | Good robustness | Chattering exists. Heavy calculation demands |

MRAS | Medium and high speed | Simple structure, easy to implement quick response | Depends on the motor’s parameters |

EKF | Medium and high speed | Strong anti-interference resistance to noise | Heavy calculation |

SO | Medium and high speed | Good robustness | Complex structure |

Rotating signal injection | Startup and low speed | Easy to implement, good robustness | High-frequency noise, torque ripple |

Pulsating signal injection | Startup and low speed | Suitable for salient pole and hidden pole motors | LPF affects the system’s bandwidth |

FPE-based methods | Startup and low-speed | No need to inject a signal | High requirements for the hardware detection circuit |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xu, Y.; Yao, M.; Sun, X.
Overview of Position-Sensorless Technology for Permanent Magnet Synchronous Motor Systems. *World Electr. Veh. J.* **2023**, *14*, 212.
https://doi.org/10.3390/wevj14080212

**AMA Style**

Xu Y, Yao M, Sun X.
Overview of Position-Sensorless Technology for Permanent Magnet Synchronous Motor Systems. *World Electric Vehicle Journal*. 2023; 14(8):212.
https://doi.org/10.3390/wevj14080212

**Chicago/Turabian Style**

Xu, Yulei, Ming Yao, and Xiaodong Sun.
2023. "Overview of Position-Sensorless Technology for Permanent Magnet Synchronous Motor Systems" *World Electric Vehicle Journal* 14, no. 8: 212.
https://doi.org/10.3390/wevj14080212