# Rotor Position Estimation Approaches for Sensorless Control of Permanent Magnet Traction Motor in Electric Vehicles: A Review

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## Abstract

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## 1. Introduction

## 2. Sensorless Control Scheme for Rotor Initial and Low Speed Position Detection

#### 2.1. Inductance Method

_{o}is the constant component of winding self-induction, the L

_{gm}is the m harmonic amplitude of self-inductance, the θ

_{e}is the rotor electrical angle.

#### 2.2. High Frequency (HF) Injection Method

#### 2.2.1. Rotating HF Injection Method

_{α}

_{i}and u

_{βi}are the α-β axis components of the HF response voltage, respectively.

#### 2.2.2. Pulse HF Injection Method

_{d}and u

_{q}are the d-q axis components of the stator voltage, respectively. i

_{d}and i

_{q}are the d-q axis components of the stator current, respectively. p is a differential operator. R

_{s}is the stator armature winding resistance. ω

_{e}is the electric angular velocity. ψ

_{f}is the permanent magnetic flux.

_{p}= (L

_{di}+ L

_{qi})/2, L

_{m}= (L

_{di}− L

_{qi})/2, Δθ = θ

_{e}− θ

_{e(est)}. i

_{di}and i

_{qi}are the d-q axis components of the HF response current, vi is the amplitude of the injected signal, ω

_{i}is the frequency of the injected signal, θ

_{e}is the rotor electrical angle. Injecting a HF pulse voltage signal on the d-axis of the virtual synchronous coordinate system and the stator winding current response carries the information on rotor position, see Equation (4). Since this method is proposed to indicate the spatial convex polarity of the rotor by adding a continuous HF excitation signal, which is irrelevant to the speed, it is possible to make an effective estimate of the speed at low speeds. Besides this, the 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.

_{α}

_{i}and i

_{βi}are the α-β axis components of the HF response current, respectively.

#### 2.3. Carrier Frequency Component Method

_{γ}

_{i}and u

_{δi}are the γ/δ axis components of the HF response voltage, respectively. i

_{γ}

_{i}and i

_{δi}are the γ/δ axis components of the HF response current.

#### 2.4. Method Based on Rotor Fretting

#### 2.5. Compound Method

## 3. Sensorless Control Scheme for Medium-High Speed Operation

#### 3.1. Back EMF Methods

#### 3.1.1. Back EMF Zero-Crossing Detection Method

#### 3.1.2. Back EMF Integration Method

_{e}is the back EMF coefficient, B[θ(t)] is the air gap flux density.

#### 3.1.3. Extended EMF (EEMF) Method

_{α}and E

_{β}are the α-β axis components of the EEMF, respectively.

#### 3.2. Third Harmonic Method

_{i}is the Fourier expansion term of i-th power harmonics.

_{HF}is the Fourier expansion term of higher frequency harmonic components.

#### 3.3. Flux Estimation Method

#### 3.4. State Observer Method

#### 3.4.1. Extened Kalman Filter (EKF) Method

#### 3.4.2. Sliding Mode Observer (SMO) Method

_{α}, e

_{β}is the back EMF in α-β coordinate system.

#### 3.4.3. Other Observers

_{αβ}. The error between the measured current and its estimated value was treated as a disturbance, which was fed back to the voltage model method for establishing a disturbance observer based on flux observation. In [107], a complex-vector-based discrete-time synchronous-frame full-order observer with a low-pulse width modulation (PWM) to operating fundamental frequency ratio was proposed, the direct pole assignment in the discrete-time domain was used to ensure the stability and dynamic performance with low-frequency ratios.

#### 3.5. Artificial Neural Network (ANN) Method

#### 3.6. Model Reference Adaptive System (MRAS)

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Li, Y.; Xu, X.; Sun, X.D.; Jiang, H.B.; Qu, Y.P. Review and Future Development of In-Wheel Motor Drive Technology. Electr. Mach. Control Appl.
**2017**, 44, 1–7. [Google Scholar] - Li, Y.; Wu, H.; Zhang, B.H. Frontier techniques and prospect of in-wheel motor for electric vehicle. J. Jiangsu Univ. Nat. Sci. Ed.
**2019**, 40, 261–268. [Google Scholar] - Tanwir, N.S.; Hamzah, M.I. Predicting Purchase Intention of Hybrid Electric Vehicles: Evidence from an Emerging Economy. World Electr. Veh. J.
**2020**, 11, 35. [Google Scholar] [CrossRef] [Green Version] - Yu, Y.; Jiang, J.; Min, Z.; Wang, P.; Shen, W. Research on Energy Management Strategies of Extended-Range Electric Vehicles Based on Driving Characteristics. World Electr. Veh. J.
**2020**, 11, 54. [Google Scholar] [CrossRef] - Sun, X.D.; Hu, C.C.; Lei, G.; Yang, Z.B.; Guo, Y.G.; Zhu, J.G. 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] [CrossRef] - Liu, C.H.; Luo, Y.X. Overview of Advanced Control Strategies for Electric Machines. Chin. J. Electr. Eng.
**2017**, 3, 53–61. [Google Scholar] - Sahoo, B.; Routray, S.K.; Rout, P.K. A novel sensorless current shaping control approach for SVPWM inverter with voltage disturbance rejection in a dc grid-based wind power generation system. Wind Energy
**2020**, 23, 986–1005. [Google Scholar] [CrossRef] - Zhang, H.; Liu, W.G.; Chen, Z.; Mao, S.; Meng, T.; Peng, J.C.; Jiao, N.F. A Time-Delay Compensation Method for IPMSM Hybrid Sensorless Drives in Rail Transit Applications. IEEE Trans. Ind. Electron.
**2019**, 66, 6715–6726. [Google Scholar] [CrossRef] - Liu, J.L.; Xiao, F.; Shen, Y.; Mai, Z.Q.; Li, C.R. Position-Sensorless Control Technology of Permanent-Magnet Synchronous Motor-a Review. Trans. China Electrotech. Soc.
**2017**, 32, 76–88. [Google Scholar] - Chen, S.H.; Liu, G.; Zhu, L.Q. Sensorless Startup Strategy for a 315-kW High-Speed Brushless DC Motor with Small Inductance and Nonideal Back EMF. IEEE Trans. Ind. Electron.
**2019**, 66, 1703–1714. [Google Scholar] [CrossRef] - Li, K.; Ling, F.; Sun, X.D.; Cai, Y.F.; Zhao, D.; Yang, Z.B. Displacement sensorless control for bearingless induction motor drives based on the MRAS method. Int. J. Appl. Electromagn. Mech.
**2020**, 62, 787–805. [Google Scholar] [CrossRef] - Shinnaka, S.; Takeuchi, S. A New Sensorless Drive Control System for Transmissionless EVs Using a Permanent-Magnet Synchronous Motor. World Electr. Veh. J.
**2007**, 1, 1–9. [Google Scholar] [CrossRef] - Lu, Q.; Zhu, X.Y.; Li, Q.; Zuo, Y.F.; Du, S.C. Rotor position estimation scheme with harmonic ripple attenuation for sensorless controlled permanent magnet synchronous motors. IET Electr. Power Appl.
**2018**, 12, 1200–1206. [Google Scholar] [CrossRef] - Sun, X.D.; Cao, J.H.; Lei, G.; Guo, Y.G.; Zhu, J.G. Speed Sensorless Control for Permanent Magnet Synchronous Motors Based on Finite Position Set. IEEE Trans. Ind. Electron.
**2020**, 67, 6089–6100. [Google Scholar] [CrossRef] - Zhang, L.; Zhu, X.Y.; Gao, J.; Mao, Y. Design and Analysis of New Five-Phase Flux-Intensifying Fault-Tolerant Interior-Permanent-Magnet Motor for Sensorless Operation. IEEE Trans. Ind. Electron.
**2020**, 67, 6055–6065. [Google Scholar] [CrossRef] - Scicluna, K.; Staines, C.S.; Raute, R. Sensorless Low/Zero Speed Estimation for Permanent Magnet Synchronous Machine Using a Search-Based Real-Time Commissioning Method. IEEE Trans. Ind. Electron.
**2020**, 67, 6010–6018. [Google Scholar] [CrossRef] - Wang, G.L.; Valla, M.; Solsona, J. Position Sensorless Permanent Magnet Synchronous Machine Drives—A Review. IEEE Trans. Ind. Electron.
**2020**, 67, 5830–5842. [Google Scholar] [CrossRef] - Ren, L.; Cui, R.H.; Wang, Z.P.; Cheng, Z. Saturation Effect of PMSM Windings Inductance. Trans. China Electrotech. Soc.
**2000**, 15, 21–25. [Google Scholar] - Wang, C.; Li, Z.; Kang, G.Q.; Zeng, C.Y. BLDC Motor Torque Ripple Control Using Self-Tuning PID Fuzzy Control System. Appl. Mech. Mater.
**2016**, 851, 459–463. [Google Scholar] [CrossRef] - Acarnley, P.P.; Watson, J.F. Review of position-sensorless operation of brushless permanent-magnet machines (Review). IEEE Trans. Ind. Electron.
**2018**, 53, 352–362. [Google Scholar] [CrossRef] - Shi, T.N.; Li, C.; Jiang, G.K.; Xia, C.L. Model free predictive control method to suppress commutation torqueripple for brushless DC motor. Trans. China Electrotech. Soc.
**2016**, 31, 54–61. [Google Scholar] - Wang, Z.H.; Lu, K.Y.; Ye, Y.Y. Initial position estimation method for permanent magnet synchronous motor based on improved pulse voltage injection. Proc. CSEE
**2011**, 31, 95–101. [Google Scholar] - Nakashima, S.; Inagaki, Y.Y.; Miki, I. Sensorless initial rotor position estimation of surface permanent-magnet synchronous motor. IEEE Trans. Ind. Appl.
**2000**, 36, 1598–1603. [Google Scholar] - Tang, N.P.; Cui, B. A high resolution detectingmethod for rotor zero initial position of sensorlessbrushless DC motor. Trans. China Electrotech. Soc.
**2013**, 28, 90–96. [Google Scholar] - Wang, Q.; Wang, Y.R.; Kong, D.M.; Xu, X.M. Initial rotor position estimation for non-salient polebrushless DC Motors. Proc. CSEE
**2012**, 32, 105–110. [Google Scholar] - Gambetta, D.; Ahfock, A. New sensorless commutationtechnique for brushless DC motors. IET Electr. Appl.
**2009**, 3, 40–49. [Google Scholar] [CrossRef] [Green Version] - Gong, J.; Liao, L.Q.; Ye, B.Q. Brushless DC Motor Starting Based on High Precision Inductance Method and Study on the Stability of BEMF Synchronous Detection. Trans. China Electrotech. Soc.
**2017**, 32, 105–112. [Google Scholar] - Meng, G.J.; Yu, H.T.; Huang, L.; Jiu, C.X.; Zhao, D.D. A Novel Initial Rotor Position Estimation Method for PMSM Based on Variation Behavior of Line Inductances. Trans. China Electrotech. Soc.
**2015**, 30, 1–9. [Google Scholar] - Sun, W.; Shen, J.X.; Li, P.; Wang, K. Iron Core Hysteresis-Based Position Sensorless Control of PM Brushless DC Motors. Appl. Mech. Mater.
**2013**, 416, 583–588. [Google Scholar] [CrossRef] - Tang, Q.P.; Shen, A.W.; Luo, X.; Xu, J.B. IPMSM Sensorless Control by Injecting Bidirectional Rotating HF Carrier Signals. IEEE Trans. Power Electron.
**2018**, 33, 10698–10707. [Google Scholar] [CrossRef] - Qin, F.; He, Y.K.; Liu, Y.; Zhang, W. Comparative investigation of sensorless control with two high-frequency signal injection schemes. Proc. CSEE
**2005**, 25, 118–123. [Google Scholar] - Lu, J.D.; Liu, J.L.; Wei, L.C. Estimation of the Initial Rotor Position for Permanent Magnet Synchronous Motors. Trans. China Electrotech. Soc.
**2015**, 30, 105–111. [Google Scholar] - Zhou, Y.J.; Cai, M.F. Initial rotor position inspection of PMSM based on rotating high frequency voltage signal injection. Electr. Mach. Control
**2010**, 14, 68–72. [Google Scholar] - Wang, G.L.; Zhang, G.Q.; Gui, X.G.; Xu, D.G. Hybrid Sensorless Control Strategy for Permanent Magnet Synchronous Motors. Proc. CSEE
**2012**, 32, 103–109. [Google Scholar] - Wang, G.L.; Yang, R.F.; Yu, Y.; Xu, D.G. Position Sensorless Control for Interior Permanent Magnet Synchronous Motor. Proc. CSEE
**2010**, 30, 93–98. [Google Scholar] - Kim, S.I.; Song, E.Y.; Im, J.H.; Kim, R.Y. A new rotorposition 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] [CrossRef] - Tian, B.; An, Q.T.; Sun, D.Y.; Sun, L.; Zhao, K. Initial Position Estimation for Surface Permanent Magnet Synchronous Motors Based on Magnetic Saturation Effect. Trans. China Electrotech. Soc.
**2016**, 31, 155–164. [Google Scholar] - Zhu, Z.Q.; Gong, L.M. Investigation of effectiveness of sensorless operation in carrier signal injection based sensorless control methods. IEEE Trans. Ind. Electron.
**2011**, 58, 3431–3439. [Google Scholar] [CrossRef] - Lin, T.C.; Zhu, Z.Q. Sensorless operation capability of surface-mounted permanent-magnet machine based on high-frequency signal injection methods. IEEE Trans. Ind. Appl.
**2015**, 51, 2161–2171. [Google Scholar] [CrossRef] - Liu, Y.; Zhou, B.; Li, S.; Feng, Y. Initial Rotor Position Detection of Surface Mounted Permanent Magnet Synchronous Motor. Proc. CSEE
**2011**, 31, 48–54. [Google Scholar] - Gong, L.M.; Zhu, Z.Q. Robust initial rotor position estimation of permanent-magnet brushless ac machines with carrier-signal-injection-based sensorless control. IEEE Trans. Ind. Appl.
**2013**, 49, 2602–2609. [Google Scholar] [CrossRef] - Liu, H.D.; Zhou, B.; Guo, H.H.; Liu, B.; Li, J.; Xu, X.H.; Shi, R.S. Error Analysis of High Frequency Pulsating Signal Injection Method. Trans. China Electrotech. Soc.
**2015**, 30, 38–44. [Google Scholar] - 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] [CrossRef] - Liu, J.M.; Zhu, Z.Q. Sensorless control strategy by square aveform high-frequency pulsating signal injection into stationary reference frame. IEEE J. Emerg. Sel. Top. Power Electron.
**2014**, 2, 171–180. [Google Scholar] [CrossRef] - Yoon, Y.D.; Sul, S.K.; Morimoto, S.; Ide, K. High-Bandwidth Sensorless Algorithm for AC Machines Based on Square-Wave-Type Voltage Injection. IEEE Trans. Ind. Appl.
**2011**, 47, 1361–1370. [Google Scholar] [CrossRef] - Zhang, G.Q.; Wang, G.L.; Xu, D.G. Filterless Square-Wave Injection Based Initial Position Detection for Permanent Magnet Synchronous Machines. Trans. China Electrotech. Soc.
**2017**, 32, 162–168. [Google Scholar] - Wang, G.L.; Yang, L.; Yuan, B.H. Pseudo-random high frequency square-wave voltage injection basedsensorless control of IPMSM drives for audible noisereduction. IEEE Trans. Ind. Electron.
**2016**, 63, 7423–7433. [Google Scholar] [CrossRef] - Li, W.Z.; Liu, J.L.; Chen, S.S. Permanent Magnet Synchronous Motor Rotor Position Detection Method Based on High-Frequency Square-Wave Signal Injection. Trans. China Electrotech. Soc.
**2018**, 33, 5821–5829. [Google Scholar] - Wu, T.; Wang, H.; Luo, D.R.; Shao, J.B. A New Initial Position Estimation Method for Interior Permanent Magnet Synchronous Motor. Trans. China Electrotech. Soc.
**2018**, 33, 3578–3585. [Google Scholar] - 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] - Zhu, J.; Tian, M.; Fu, R.B.; Liu, H.J. Research on rotor position of permanent magnet synchronous motor based on carrier frequency component. Power Syst. Prot. Control
**2015**, 43, 48–54. [Google Scholar] - Mamo, M.; Ide, K.; Sawamura, M.; Oyama, J. Novel rotor position extraction based on carrier frequency component method (CFCM) using two reference frames for IPM drives. IEEE Trans. Ind. Electron.
**2005**, 52, 508–514. [Google Scholar] [CrossRef] - Gao, H.W.; Yu, Y.J.; Chai, F.; Cheng, S.K. Position sensorless control of interior permanent magnet synchronous motor based on carrier frequency component method. Proc. CSEE
**2010**, 30, 91–96. [Google Scholar] - Li, Y.T.; Hu, H.F.; Qu, W.L.; Shuang, S. A novel initial rotor position estimation method for permanent magnet synchronous motors. Proc. CSEE
**2013**, 33, 75–82. [Google Scholar] - Wei, K.; Jin, X.H. Initial rotor position estimate technique on surface mounted permanent magnet synchronous motor. Proc. CSEE
**2006**, 26, 104–109. [Google Scholar] - Hong, K.; Liu, G.; Mao, K.; Lv, X.Y.; Zhou, X.X. Initial Position Detection of Surface Mounted Permanent Magnet Synchronous Machines Based on Novel High-Frequency Injection Method. Trans. China Electrotech. Soc.
**2018**, 33, 2914–2922. [Google Scholar] - Lv, X.Y.; Liu, J.; Mao, K.; Chen, B.D. Initial Position Detection of Permanent Magnet Motor Based on Virtual Pulsating High-Frequency Injection Method. Trans. China Electrotech. Soc.
**2017**, 32, 34–41. [Google Scholar] - Li, J.; Zhou, B.; Liu, B.; Wang, L.; Ni, T.H.; Xu, X.H.; Shi, R.S. A Novel Starting Strategy of Sensorless Control for Surface Mounted Permanent Magnet Synchronous Machines. Proc. CSEE
**2016**, 36, 2513–2520. [Google Scholar] - Damodharan, P.; Vasudevan, K. Sensorless Brushless DC Motor Drive Based on the Zero-Crossing Detection of Back Electromotive Force (EMF) From the Line Voltage Difference. IEEE Trans. Energy Convers.
**2010**, 25, 661–668. [Google Scholar] [CrossRef] - Zhang, G.Q.; Wang, G.L.; Xu, D.G.; Fu, Y.; Ni, R.G. Adaptive Notch Filter Based Rotor Position Estimation for Interior Permanent Magnet. Proc. CSEE
**2016**, 36, 2521–2527. [Google Scholar] - Wang, D.F.; Zhu, Y.Q.; Jin, Y.; Liu, Z.Q. A novel research on detecting position of brushless DC motors. Trans. China Electrotech. Soc.
**2013**, 28, 139–144. [Google Scholar] - Shen, J.X.; Iwasaki, S. Sensorless control of ultrahigh-speed PM brushless motor using PLL and third-harmonic back EMF. IEEE Trans. Ind. Electron.
**2006**, 53, 421–428. [Google Scholar] [CrossRef] - Wang, D.F.; Zhu, Y.Q.; Jin, Y.; Zhao, G.Y. Tentative Strategy of Starting Sensorless BLDCM with the Method of Integrating the Back EMF. Trans. China Electrotech. Soc.
**2012**, 27, 178–184. [Google Scholar] - Gupta, N.; Pandey, D.A.K. A Review: Sensorless Control of Brushless DC Motor; Esrsa Publications: Auckland, New Zealand, 2012. [Google Scholar]
- Chen, Z.Q.; Tomita, M.; Doki, S. An extended electromotive force model for sensorless control of interior permanent- magnet synchronous motors. IEEE Trans. Ind. Electron.
**2003**, 50, 288–295. [Google Scholar] [CrossRef] - Zhang, B.; Ge, Q.X.; Liu, J.X.; Wang, X.X.; Li, Y.H. Research on Speed Sensorless Control of long Stator Linear Synchronous Motor Based on EEMF. Trans. China Electrotech. Soc.
**2017**, 32, 91–99. [Google Scholar] [CrossRef] - Jae, L.Y.; Bak, Y.; LEE, K.B. Restarting Method for EEMF Based Sensorless Permanent Magnet Synchronous Motor Drive Systems. Trans. Korean Inst. Power Electron.
**2019**, 23, 127–133. [Google Scholar] - Wang, G.L.; Ding, L.; Li, Z.M.; Xu, J.; Zhang, G.Q.; Zhan, H.L.; Ni, R.G.; Xu, D.G. Enhanced Position Observer Using Second-Order Generalized Integrator for Sensorless Interior Permanent Magnet Synchronous Motor Drives. IEEE Trans. Energy Convers.
**2014**, 29, 486–495. [Google Scholar] - Song, X.D.; Han, B.C.; Wang, K. Sensorless Drive of High-Speed BLDC Motors Based on Virtual Third-Harmonic Back EMF and High-Precision Compensation. IEEE Trans. Power Electron.
**2018**, 34, 8787–8796. [Google Scholar] [CrossRef] - Song, X.D.; Han, B.C.; Zheng, S.Q.; Chen, S.H. A Novel Sensorless Rotor Position Detection Method for High-Speed Surface PM Motors in a Wide Speed Range. IEEE Trans. Power Electron.
**2017**, 33, 7083–7093. [Google Scholar] [CrossRef] - Liu, J.M.; Zhu, Z.Q. Improved sensorless control of permanent-magnet synchronous machine based on third-harmonic back EMF. IEEE Trans. Ind. Appl.
**2014**, 50, 1861–1870. [Google Scholar] [CrossRef] - Liu, J.M.; Zhu, Z.Q. Rotor position error compensation based on third harmonic back-EMF in flux observer sensorless control. In Proceedings of the International Conference on Electrical Machine, Berlin, Germany, 2–5 September 2014. [Google Scholar]
- Lee, K.G.; Lee, J.S.; Lee, K.B. Wide-range sensorless control for SPMSM using an improved full-order flux observer. J. Power Electron.
**2015**, 15, 721–729. [Google Scholar] [CrossRef] [Green Version] - Qiu, T.F.; Wen, X.H.; Zaho, F.; Wang, Y.X. Design Strategy of Permanent Magnet Flux Linkage Adaptive Observer for Permanent Magnet Synchronous Motor. Proc. CSEE
**2015**, 35, 2287–2294. [Google Scholar] - Boldea, I.; Paicu, M.C.; Andreescu, G.D.; Blaabjerg, F. “Active flux” DTFC-SVM sensorless control of IPMSM. IEEE Trans. Energy Convers.
**2009**, 24, 314–322. [Google Scholar] [CrossRef] - Abdelmaksoud, H.; Zaky, M. Design of an Adaptive Flux Observer for Sensorless Switched Reluctance Motors Using Lyapunov Theory. Adv. Electr. Comput. Eng.
**2020**, 20, 123–130. [Google Scholar] [CrossRef] - Ji, J.H.; Jiang, Y.; Zhao, W.X.; Chen, Q.; Yang, A.C. Sensorless Control of Linear Vernier Permanent-Magnet Motor Based on Improved Mover Flux Observer. IEEE Trans. Power Electron.
**2019**, 35, 3869–3877. [Google Scholar] [CrossRef] - Zhao, Q.; Yang, Z.B.; Sun, X.D.; Ding, Q.F. Speed-sensorless control system of a bearingless induction motor based on iterative central difference Kalman filter. Int. J. Electron.
**2020**, 1524–1542. [Google Scholar] [CrossRef] - Xiao, X.; Chen, C.M.; Zhang, M. Dynamic permanent magnet flux estimation of permanent magnet synchronous machines. IEEE Trans. Appl. Supercond.
**2010**, 20, 1085–1088. [Google Scholar] [CrossRef] - Zhang, M.; Xiao, X. Speed and flux linkage observer for permanent magnet synchronous motor based on EKF. Proc. CSEE
**2007**, 27, 36–40. [Google Scholar] - Jiang, B. A Novel Algorithm Based on EKF to Estimate Rotor Position and Speed for Sensorless PMSM Drivers. In Proceedings of the International Conference on Information Engineering and Computer Science, Wuhan, China, 19–20 December 2009. [Google Scholar]
- Yu, P.Q.; Lu, Y.H.; Wang, Y.; Yang, W.M.; Chen, Z.C. Research on Permanent Magnet Linear Synchronous Motor Position Sensorless Control System. Proc. CSEE
**2007**, 27, 53–57. [Google Scholar] - Yu, P.Q.; Wang, Y.; Yang, W.M.; Lu, H.C.; Chen, Z.C. Application of UKF in positionless sensor control of permanent magnet linear synchronous motor. J. Mech. Eng.
**2007**, 11, 149–153. [Google Scholar] [CrossRef] - Li, J.; Li, J.Z. Speed Sensorless SVM-DTC for Pemanent Magnet Synchronous Motors. Proc. CSEE
**2007**, 27, 28–34. [Google Scholar] - Quang, N.K.; Hieu, N.T. FPGA-based sensorless PMSM speed control using reduced-order extended Kalman filters. IEEE Trans. Ind. Electron.
**2014**, 61, 6574–6582. [Google Scholar] [CrossRef] - Xu, B.; Shen, X.K.; Ji, W.; Shi, G.D. Adaptive Nonsingular Terminal Sliding Model Control for Permanent Magnet Synchronous Motor Based on Disturbance Observer. IEEE Access
**2018**, 6, 48913–48920. [Google Scholar] [CrossRef] - Chen, M.S.; Hwang, Y.R.; Tomizuka, M. A state-dependent boundary layer design for sliding mode control. IEEE Trans. Autom. Control
**2010**, 47, 1677–1681. [Google Scholar] [CrossRef] - Zhang, X.; Guo, L.L.; Yang, S.Y.; Cao, R.X. Speed Sensorless Control of Permanent Magnet Synchronous Generators. Proc. CSEE
**2014**, 34, 3440–3447. [Google Scholar] - Su, J.Y.; Li, T.C.; Yang, G.J. PMSM sensorless control based on four-order hybrid sliding mode observer. Proc. CSEE
**2009**, 29, 98–103. [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. Top. Power Electron.
**2014**, 2, 627–639. [Google Scholar] [CrossRef] - Mansouri, S.A.; Ahmarinejad, A.; Javadi, M.S.; Heidari, R.; Catalao, J.P.S. Improved double-surface sliding mode observer for flux and speed estimation of induction motors. IET Electr. Power Appl.
**2020**, 14, 1002–1010. [Google Scholar] [CrossRef] - Ye, S.C. Fuzzy sliding mode observer with dual SOGI-FLL in sensorless control of PMSM drives. ISA Trans.
**2019**, 85, 161–176. [Google Scholar] [CrossRef] - Peng, S.Q.; Song, Y.Y. Sensorless vector control of PMSM based on adaptive fuzzy sliding mode observer. Control Des.
**2018**, 33, 644–648. [Google Scholar] - Huang, L.; Zhao, G.Z.; Nian, H. Sensorless Control of interior Pemanent Magnet Synchronous Motor by Estimation of an Extended Electromotive Force, motive Force. IET Electr. Power Appl.
**2007**, 9, 59–63. [Google Scholar] - Wu, S.F.; Zhang, J.W.; Chai, B.B. Adaptive super-twisting sliding mode observer based robust backstepping sensorless speed control for IPMSM. ISA Trans.
**2019**, 92, 155–165. [Google Scholar] [CrossRef] [PubMed] - Zhang, Q.; Li, D. Adaptive second-order sliding mode observer with parameter identification for PMSM sensorless vector control. Control Decis.
**2019**, 34, 1385–1393. [Google Scholar] - Kim, H.; Son, 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] - Saadaoui, O.; Khlaief, A.; Abassi, M.; Tlili, I.; Chaari, A.; Boussak, M. A New Full-Order Sliding Mode Observer Based Rotor Speed and Stator Resistance Estimation for Sensorless Vector Controlled Pmsm Drives. Asian J. Control
**2019**, 21, 1318–1327. [Google Scholar] [CrossRef] - Wang, Y.Q.; Feng, Y.T.; Qin, M.; Li, M.H. Full-Order Sliding Mode Observation and Control Strategy for Surface Permanent Magnet Synchronous Motor. Trans. China Electrotech. Soc.
**2018**, 33, 5688–5699. [Google Scholar] - Lu, W.Q.; Hu, Y.W.; Du, X.Y.; Huang, W.X. Sensorless Vector Control Using a Novel Sliding Mode Observer for PMSM Speed Control System. Proc. CSEE
**2010**, 30, 78–83. [Google Scholar] - Lu, X.Q.; Lin, H.Y.; Han, J.L. Position Sensorless Control of Permanent Magnet Synchronous Machine Using a Disturbance Observer. Proc. CSEE
**2016**, 36, 1387–1394. [Google Scholar] - Zhao, W.X.; Jiao, S.; Chen, Q.; Xu, D.Z.; Ji, J.H. Sensorless Control of Linear Permanent-Magnet Motor Based on Improved Disturbance Observer. IEEE Trans. Ind. Electron.
**2018**, 65, 9291–9300. [Google Scholar] [CrossRef] - Aoshima, I.; Yoshikawa, M.; Ohnuma, N.; Shinnaka, S. Development of Electric Scooter Driven by Sensorless Motor Using D-State-Observer. World Electr. Veh. J.
**2009**, 3, 48–54. [Google Scholar] [CrossRef] [Green Version] - Zhu, X.H.; Li, Y.H.; Chen, Y.B. Sensorless Vector Control for PMSM Based on Nonlinear State Observer. Trans. China Electrotech. Soc.
**2010**, 25, 50–57. [Google Scholar] - Guven, S.; Usta, M.A.; Okumus, H.I. An improved sensorless DTC-SVM for three-level inverter-fed permanent magnet synchronous motor drive. Electr. Eng.
**2018**, 100, 2553–2567. [Google Scholar] [CrossRef] - Zhao, W.X.; Yang, A.C.; Ji, J.H.; Zhu, J.H. Modified Flux Linkage Observer for Sensorless Direct Thrust Force Control of Linear Vernier Permanent Magnet Motor. IEEE Trans. Power Electron.
**2018**, 99, 7800–7811. [Google Scholar] [CrossRef] - Zhang, G.Q.; Wang, G.L.; Xu, D.G.; Yu, Y. Discrete-Time Low-Frequency-Ratio Synchronous-Frame Full-Order Observer for Position Sensorless IPMSM Drives. IEEE J. Emerg. Sel. Top. Power Electron.
**2017**, 5, 870–879. [Google Scholar] [CrossRef] - Sun, X.D.; Chen, L.; Yang, Z.B.; Zhu, H.Q. Speed-sensorless vector control of a bearingless induction motor with artificial neural network inverse speed observer. IEEE/ASME Trans. Mechatron.
**2013**, 18, 1357–1366. [Google Scholar] [CrossRef] - Alsofyani, I.M.; Idris, N.R.N. A review on sensorless techniques for sustainable reliablity and efficient variable frequency drives of induction motors. Renew. Sustain. Energy Rev.
**2013**, 24, 111–121. [Google Scholar] [CrossRef] - Xiao, L.; Sun, H.X.; Gao, F. Position Sensorless Control System of SRM Based on Improved BP Neural Network. Adv. Mater. Res.
**2012**, 1670, 2187–2192. [Google Scholar] [CrossRef] - Xia, C.L.; Wen, D.; Fan, J.; Yang, X.J. Based on RBF Neural Network Position Sensorless Control for Brushless DC Motors. Trans. China Electrotech. Soc.
**2002**, 17, 26–29. [Google Scholar] - Li, H.R.; Gu, S.S. Neural-network-based adaptive observer of position and speed of PMSM. Proc. CSEE
**2002**, 12, 33–36. [Google Scholar] - Xia, C.L.; Wang, M.C.; Shi, T.N.; Guo, P.J. Position sensorless control for switched reluctance motors using neural network. Proc. CSEE
**2005**, 25, 123–128. [Google Scholar] - Bao, D.Y.; Wang, H.; Wang, X.J.; Zhang, C.R. Sensorless speed control based on the improved Q-MRAS method for induction motor drives. Energies
**2018**, 11, 235. [Google Scholar] - Zhu, Y.; Cheng, M.; Hua, W.; Zhang, B.F.; Wang, W. Sensorless control for electrical variable transmission based on sliding mode model reference adaptive system. Trans. China Electrotech. Soc.
**2015**, 30, 64–72. [Google Scholar] - Rai, R.; Shukla, S.; Singh, B. Electromagnetic Torque-Based Model Reference Adaptive System Speed Estimator for Sensorless Surface Mount Permanent Magnet Synchronous Motor Drive. IEEE Trans. Ind. Inform.
**2020**, 16, 4714–4725. [Google Scholar] [CrossRef] - Hu, W.H.; Wang, Y.; Li, M.X.; Li, M.; Wang, Z.A. Research on sensorless control strategy of direct drive multiphase PMSG wind power generation system based on MRAS. Power Syst. Prot. Control
**2014**, 42, 118–124. [Google Scholar] - Wang, Q.L.; Zhang, C.W.; Zhang, X. Variable- structure MRAS speed identification for permanent magnet synchronous motor. Proc. CSEE
**2008**, 28, 71–75. [Google Scholar] - Zhang, H.S.; Wang, P.; Han, B.C. Rotor Position Measurement for High-speed Permanent Magnet Synchronous Motors Based on Fuzzy PI MRAS. Proc. CSEE
**2014**, 34, 1889–1896. [Google Scholar]

**Figure 5.**Waveforms of sensorless estimation at zero-low speed. (Initial rotor angle: (

**a**) 1 rad; (

**b**) 4 rad).

**Figure 8.**Artificial neural network (ANN) classification. BP, back propagation; RBF, radial basis function; DNN, deep neural network; DBN, deep belief network; CNN, convolution neural network.

**Figure 10.**Experimental results using MRAS. (

**a**) Measured and estimated rotor position and rotor position at 20% of full load. (

**b**) Measured and estimated rotor position and rotor position at 1 rad/s. (Scale: ω

_{e}, ω

_{e(est)}: 3 rad/div; ω

_{e(error)}: 5 rad/div; i

_{q}: 2.5 A/div; θ

_{e}, θ

_{e(est)}: 150°/div; θ

_{e(}

_{error)}: 30°/div; i

_{d}: 1 A/div).

Range | Approach | Reference | Description |
---|---|---|---|

Initial and low speed | Inductance | [18,19,20,21,22,23,24,25,26,27,28,29] | The detection voltage is applied to the motor during startup to judge the change of its inductance. This method is difficult and can only be used in interior permanent magnet synchronous motor (IPMSM) with salient pole. |

Rotating high frequency (HF) Injection | [30,31,32,33,34,35,36,37,38] | 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. Rotating HF injection method is suitable for IPMSM, pulse HF injection method is suitable for surface-mounted PMSM (SPMSM) without salient pole. | |

sine-wave HF injection | [39,40,41,42,43,44,45] | ||

square-wave HF injection | [46,47,48,49,50] | ||

Carrier Frequency Component | [51,52,53] | By using the carrier frequency component signal of the PWM inverter itself, less additional hardware circuits are required. Not applicable to SPMSM. | |

Rotor Fretting | [54] | The detection error of this method is large and the research is less. This method does not depend on the rotor structure and can also be used under heavy load. SPMSM and IPMSM are applicable. | |

Compound Method | [55,56,57,58] | The combined method of multiple position estimation methods proves effective in improving the accuracy and reliability of detection. | |

Medium-high speed | Back-electromotive force (EMF) zero-crossing | [25,59,60,61] | The realization is simple, the zero-crossing point of back EMF is independent of motor speed, 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. It is applicable to brushless DC motor (BLDCM). |

Back EMF integration | [62,63,64,65] | This method does not depend on the speed of the motor, but it needs to increase the integral circuit, increase the hardware complexity, and may bring additional integral error. It is applicable to both BLDCM and PMSM. | |

Extended EMF (EEMF) | [66,67,68] | The main purpose of this method is to package all the quantities related to the rotor position (inductors) under the stator alpha-beta system. It is applicable to IPMSM. | |

Third harmonic | [65,69,70,71,72] | It has a wider operating range than the back EMF zero-crossing detection method. However, its amplitude is smaller than the back EMF amplitude and is not easy to detect, especially at low speed. It is applicable to both BLDCM and PMSM. | |

Flux estimation | [73,74,75] | 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. It is only suitable for SPMSM. | |

Extended Kalman Filter(EKF) | [76,77,78,79,80,81,82,83] | The emphasis is on the linearization of nonlinear equations. Kalman filter is a kind of observation method defined in stochastic framework, with adaptive ability and anti-interference ability, and wide speed range. However, many statistical parameters of random errors are needed, which depend on motor parameters and model accuracy. Both SPMSM and IPMSM are applicable. | |

Slide model observer (SMO) | [84,85,86,87,88,89,90,91,92,93,94,95,96,97,98] | The main feature is to establish observer model with stator current as state variable in stationary coordinate system. The main defects are that the discontinuous switching characteristics will cause buffering problems, and the low-pass filter to filter out the HF harmonics will cause the phase lag and amplitude attenuation. It is more suitable for SPMSM, though BLDCM is applicable as well. | |

Other observers | [99,100,101,102,103,104,105,106,107] | 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. | |

Artificial Neural network (NN) | [108,109,110,111,112,113] | The advantage is that it has the characteristics of adaptive and self-learning, but it cannot ensure the accuracy of identification results. It’s applicable to both BLDCM and PMSM. | |

Model reference adaptive system (MRAS) | [114,115,116,117,118,119] | The position observation is based on the accuracy of the reference model, and the accuracy of the parameters of the reference model itself directly affects the effectiveness of the identification. This method is robust to the change of motor parameters and external interference, so it is suitable for situations with variable load and working conditions. Both SPMSM and IPMSM are applicable. |

Signal Type | Rotating Signal Injection | Pulsating Signal Injection | |
---|---|---|---|

Square Wave | Sinusoidal Wave | ||

Injection Frame | α-β Frame | d-q Frame | d-q Frame |

Injection signal | $\left[\begin{array}{c}{v}_{\alpha i}\\ {v}_{\beta i}\end{array}\right]={v}_{i}\left[\begin{array}{c}\mathrm{cos}{\omega}_{i}t\\ \mathrm{sin}{\omega}_{i}t\end{array}\right]$ | ${v}_{di}=\left[\begin{array}{c}{v}_{i}{\left(-1\right)}^{k}\\ 0\end{array}\right]$ | $\left[\begin{array}{c}{v}_{di}\\ {v}_{qi}\end{array}\right]=\left[\begin{array}{c}{v}_{i}\mathrm{cos}{\omega}_{i}t\\ 0\end{array}\right]$ |

Description | Compared to the other two methods: it is phase modulation, and the other two are magnitude modulation. No need to obtain initial rotor position first but based on Nonlinear Effect of Inverter. | Simple waveform, high injection frequency. The initial rotor position need be obtained first. | The injection waveform needs to be modulated, so the signal frequency is low. The initial rotor position need be obtained first. |

Hybrid Techniques | Sample Articles |
---|---|

voltage pulse vector + equal width voltage pulse | [55] |

pulse HF signal injection + carrier frequency component method | [56,57,58] |

Back EMF Methods | Description |
---|---|

zero-crossing detection method | In order to reduce voltage and filter the terminal voltage signal, the phase delay will occur, and the commutation error may be caused by the change of motor speed. |

integration method | The integral results are not affected by the velocity fluctuation, and the sensitivity to the zero-crossing detection error is small. Additional integration circuits are needed, hardware complexity and additional integration errors are added. |

Third harmonic method | The implementation is simple and does not require depth filtering. However, the amplitude of the third harmonic is small and difficult to detect, so it is necessary to carry out complex Fourier decomposition. |

Phase | Algorithm |
---|---|

Forecasting phase | $\begin{array}{l}x{e}_{k|k-1}=x{e}_{k-1|k-1}+\left[f\left(x{e}_{k-1|k-1}\right)+B\langle {u}_{k-1}\rangle \right]{T}_{s}\\ {P}_{k|k-1}={P}_{k-1|k-1}+\left({F}_{k-1}{P}_{k-1|k-1}+{P}_{k-1|k-1}{F}_{k-1}^{T}\right){T}_{s}+{Q}_{d}\end{array}$ |

Revision phase | $\begin{array}{l}x{e}_{k|k}=x{e}_{k|k-1}+{F}_{k}\left[{y}_{k}-h\left(x{e}_{k|k-1}\right)\right]\\ {P}_{k|k}={P}_{k|k-1}-{K}_{k}{H}_{k}{P}_{k|k-1}\end{array}$ |

Kalman gain | ${K}_{k}={P}_{k|k-1}{H}_{k}^{T}{\left(H{P}_{k|k-1}{H}_{k}^{T}+R\right)}^{-1}$ |

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## Share and Cite

**MDPI and ACS Style**

Li, Y.; Wu, H.; Xu, X.; Sun, X.; Zhao, J.
Rotor Position Estimation Approaches for Sensorless Control of Permanent Magnet Traction Motor in Electric Vehicles: A Review. *World Electr. Veh. J.* **2021**, *12*, 9.
https://doi.org/10.3390/wevj12010009

**AMA Style**

Li Y, Wu H, Xu X, Sun X, Zhao J.
Rotor Position Estimation Approaches for Sensorless Control of Permanent Magnet Traction Motor in Electric Vehicles: A Review. *World Electric Vehicle Journal*. 2021; 12(1):9.
https://doi.org/10.3390/wevj12010009

**Chicago/Turabian Style**

Li, Yong, Hao Wu, Xing Xu, Xiaodong Sun, and Jindong Zhao.
2021. "Rotor Position Estimation Approaches for Sensorless Control of Permanent Magnet Traction Motor in Electric Vehicles: A Review" *World Electric Vehicle Journal* 12, no. 1: 9.
https://doi.org/10.3390/wevj12010009