Guoqiang Zhang, Gaolin Wang, and Dianguo Xu

(College of Electrical Engineering, Harbin Institute of Technology, Harbin, China)

Saliency-Based Position Sensorless Control Methods for PMSM Drives – a Review

Guoqiang Zhang, Gaolin Wang*, and Dianguo Xu

(College of Electrical Engineering, Harbin Institute of Technology, Harbin, China)

Permanent magnet synchronous motor (PMSM) drives are finding expanded use for industrial and domestic drive applications. With the distinguished characteristics such as reduced cost and increased reliability and robustness, position sensorless (self-sensing) control techniques have been good candidates for reliable and costless PMSM drives. The saliency-tracking based techniques further bring the expansion of applications with the extended controllable sensorless operating speed range.This paper presents a review on state of the art techniques for position sensorless drives using the saliency-tracking based methods. The signal injection methods and the future scope of research including the dynamic bandwidth improvement and the acoustic noise reduction are discussed.

Permanent magnet synchronous motor (PMSM), sensorlesss, saliency-tracking,high-frequency (HF) signal injection.

1 Introduction

Permanent magnet synchronous motors (PMSMs)have received increasing attentions for industrial and domestic drive applications due to their high efficiency,high power density, and wide speed range operations[1-13].Drives without machine-mounted position sensors not only reduce the system cost, but also increase the reliability and robustness. Therefore, position sensorless(self-sensing) control that utilizes a machine itself for sensing and requires no additional position sensors has been a research focus in the last few decades[14-86].Operation of model-based sensorless control relying on the back electromotive force (EMF) voltage associated with fundamental excitation of the machine is unreliable and can fail at low- and zero-speeds since the back-EMF decreases to an extent that noise, inaccuracies in sampled variables and inexact knowledge of the machine parameters yield relatively large estimation errors.To overcome the limitations of sensorless control at low speeds, several alternative techniques independent of machine parameters aimed at estimating the rotor or airgas-flux position have been developed[14-86]. By tracking some form of the inductance- or resistancebased spatial saliency in the machine, the flux or rotor position can be estimated at zero and low speeds[35-36].The inductance-based spatial saliencies can result from the geometry of the machine, e.g., reluctance rotor or PMSM with embedded magnets, differences of the d-q-axis inductances in the surface-mounted PMSM,from the slots, as well as from the saturation of the leakage paths through the fundamental magnetic field.Besides the inductance-based saliency, a high-frequency(HF) eddy-current-loss-reflected resistance-based saliency can occur in surface-mounted PMSM even for the stators without sufficient saturation. Therefore, the saliency-tracking based techniques are available to extend the controllable sensorless operating speed range.Low- and zero-speed sensorless control is challenging because the machine has to provide a resistive or inductance saliency in the desired current operating range.

As shown in Fig.1, for saliency-tracking based method a sufficient excitation, either by test signal injection or by using pulsewidth-modulated (PWM)inverter switching, is mandatory; otherwise, the rotor position is not observable[14-86]. Basically, test voltage or test current injection can be used. Techniques using HF voltage injection and evaluation of the related HF current response are state of the art. The voltage injection techniques can be categorized as to the shape of the test signal: sinusoidal or square-wave injection techniques. Moreover, one can distinguish between rotating and pulsating test signal injection. For the HF rotating signal injection scheme, a balanced voltage signal is injected into the stationary reference frame to form a rotating excitation that is superimposed on the fundamental excitation[46-54]. By applying a synchronous reference frame filter (SRFF), the negative-sequence carrier current that contains the position information can be derived and used to estimate the rotor position. Since it uses the HF rotating signal, the dynamic characteristics are restricted within a narrow limit. For the pulsating signal injection methods, a HF pulsating carrier signal is injected into the d-axis or the q-axis in the estimated synchronous reference frame[55-68]. The position can be estimated through the minimization of the amplitudemodulated carrier current response that is measured along the axis orthogonal to the injection axis. The commercial general purpose inverter with sensorless control employing the pulsating signal injection has been launched since 2008[27].

Fig.1 Saliency-tracking based position estimation[26]

However, the performance of the sensorless control with the conventional HF rotating or pulsating sinusoidal signal is still insufficient for some applications since the filtering process limits the dynamic bandwidths. To overcome the limitations of the sensorless control with conventional sinusoidal signal injection, an alternative technique using the square-wave injection in the stationary reference frame or in the estimated rotor reference frame has been developed[69-78]. The injection frequency can be increased to PWM switching frequency,and hence the filtering process can be eliminated and the dynamic performance could be enhanced.

Besides the dynamic bandwidth of the sensorless control with HF signal injection, another aspect that limits its applications is the acoustic noise resulting from the injected HF signal with the fixed frequency. Many efforts have been made to reduce the acoustic noise. The methods to select a suitable signal amplitude were proposed in [41]. Although decreasing the injected signal amplitude can attenuate the acoustic noise, the signal-to-noise ratio (SNR) would also be decreased,which makes it harder to extract the effective position information. Furthermore, the whole control performance will be deteriorated, especially for the machine whose saliency is not prominent. Adjusting the frequency of injected signal is also an alternative solution to reduce the audible noise. In [79-80], the pseudo-random HF square-wave injection method was developed for audible noise reduction. And the comparison of power spectra density (PSD) between the fix-frequency and pseudorandom frequency injection is carried out both theoretically and experimentally.

This paper presents a comparative review on HF signal injection based position sensorless control for PMSM drives. First, the theoretical backgrounds related to the HF PMSM models and the rotor position estimation schemes are presented for each HF signal injection technique. Next, the dynamic bandwidth improvement and the audible noise reduction are discussed.

2 Implementation of sensorless control using HF signal injection

2.1 PMSM Modeling

If the HF injection carrier frequency is much higher than the fundamental frequency and the low-speed sensorless operation is being evaluated, the HF model in the synchronous reference frame of PMSM can be expressed as

Transforming (1) into the stationary coordinates,yielding

2.2 Rotating signal injection

Fig.2 shows the block diagram of the rotating signal injection. In this method, a rotating signal (3) is injected in the α-β stationary frame.

where Vinj, and ωinjare the amplitude and angular speed of the injected HF rotating carrier voltage signal,respectively.

The resultant position-dependent carrier current response in the α-β stationary frame can be expressed as

where Iinj,p=(Vinj/ωinj)(ΣL/LdLq), and Iinj,n=(Vinj/ωinj)(ΔL/LdLq). It can be seen from (4) that the negative-sequence current contains the rotor position information, and the carrier-current response for rotating signal injection is phase modulated.

Fig.2 Rotating signal injection

In the demodulation process of position error signal,a band pass filter (BPF) to extract the HF current induced by injecting the HF voltage to an IPMSM and a low pass filter (LPF) to obtain a rotor position error are required. However, these filters inevitably have drawbacks, such as a time delay of the rotor position or speed estimation, and a limitation of a current control bandwidth. In [46], the rotor position information was extracted from voltage and current difference equations by using the rotating matrix in the stationary reference frame. Then, the current envelope through the all-pass filter was utilized to prevent the noise of the estimated rotor position. By using two voltage references and three sampled currents without the BPF and LPF, this proposed method solved the drawbacks about the performance deterioration and time delay by the BPF and LPF, and the bandwidth of the speed controller and current controller can be extended up to 30Hz and 300Hz, respectively.

Besides, since the rotating signal is injected in the α-β stationary frame, the HF current ripple occurs inevitably.

2.3 Pulsating signal injection

A pulsating signal is injected in the d-axis or q-axis,and the induced current (both in the estimated rotor reference frame) can be used to estimate the rotor position. If an estimated d-axis voltage signal is used to inject, the voltage signal is expressed as

As can be seen, the injection voltage can be seen as the combination of two rotating vectors. If a position difference between the actual machine rotor frame position and injection position is defined as

the resultant position-dependent carrier current response in the estimated d-q synchronous frame can be expressed as

From (7), it can be seen that the carrier-current response for pulsating signal injection is magnitude modulated by the rotor position information. The real rotor reference frame can be found by manipulating sin2θerrinto zero. For the position estimation, the saliency reflected current Isalin (8) can be extracted by multiplying sin(ωinjt) intoand using a LPF. Fig.3 shows the pulsating signal injection.

Fig.3 Pulsating signal injection

The advantage of the pulsating-vector injection is that, since the carrier current in d-axis does not affect torque production, significantly higher amplitudes can be used for magnet polarity estimation in a two-step process[53,68].

2.4 Square-wave signal injection

As can be seen from Fig.2 and Fig.3, each saliencytracking based sensorless control method has unique characteristics according to the injection signal type and the demodulation process. In every sensorless method using sinusoidal signal injection, the filtering process is necessary to demodulate the position error signal and to separate the current ripples by the intentionally injected voltage signal and the extra one by the fundamental current control. Unfortunately, the filtering process due to the limited injection frequency aggravates the dynamic bandwidth of the sensorless control system.Since the injection frequency is getting higher, the dynamics of the sensorless control can be enhanced, and the interference between the injected signal and the fundamental components of the current control can be diminished. The square-wave voltage developed in [78]demonstrates the widest frequency range for the voltage injection.

As shown in Fig.4, a square-wave pulsating signal(9) was injected in the estimated frame d-axis, and the resultant position-dependent carrier current response is obtained as (10), which is also magnitude modulated.And then the HF current response envelope curves (11)after the convergence can be used to track the position information.

Fig.4 Square-wave signal injection

In [72], the effects of the inverter nonlinearity were analyzed on injection voltage, on induced current ripple,and on the position estimation performance in sequence and a voltage injection method to minimize the impact of the inverter nonlinearity by the regulation of the HF current ripple was proposed. By the proposed method,the position estimation performance under sensorless operation was improved by 19.7% in no-load condition.

2.5 Indirect flux detection by on–line reactance measurement (INFORM)

The control diagram of INFORM is shown in Fig.5.In the INFORM method, the sequential voltage vector referencesandare assigned in three PWM cycles respectively, and updated in the next PWM cycles because of the update delay[44]. The corresponding current differentiations are calculated in another PWM cycles, which can be written in the α-β stationary frame as

where n represents the PWM cycles as shown in (13),n = 0, 1, and 2. In Fig.5(a), where single sampling mode is adopted, the circle on the edge of PWM carrier waveform refers to current samplings, and the current differentiation can be only obtained in the next sampling period.

Fig.5 Injection sequence diagram of INFORM considering the update delay

Then the rotor position can be estimated from the sum of the three current vectors as

In [45], pulsating signal injection and the INFORM methods are implemented and compared using a commercial PMSM prototype. It is claimed that both methods show similar position estimation errors and speed response, but the pulsating signal injection method has less variations in the position estimation error. The reason for average position estimation error during sensorless control of PMSM is also investigated in the view of magnetic field, and mathematical equations are derived, showing that the estimation error between estimated and encoder positions increases with load.

2.6 Zero voltage injection

When the zero voltage injection[29-31]is applied, the voltage equation of PMSM can be rewritten as

Considering the difference between the actual machine rotor frame position and estimated position, the resultant position-dependent carrier current differential response in estimation d-q axis frame can be expressed as

After omitting small terms, as can be seen, if manipulate θerrin q-axis to zero, and approximate sin2θerr=2θerr, cosθerr=1, the equation can be simplified to

From (16), it can be seen, to ensure the method functioning successfully, the coefficient of θerr, should be maintained at a certain amplitude, namely, d-axis should be injected a certain value of current. Fig.6 shows the block diagram of position and speed estimation. A Park transform type PLL (phase-locked loop) is used to calculate rotor position and speed.

Fig.6 Block diagram of position estimation

From Fig.6, it can be seen that a precise calculation of current derivatives is crucial in process of position estimation. Usually, current derivatives are sampled through a Rogowski coil or additional sensors such as voltage or current derivative sensors. However, when the motor functioning in low speed region, the period of zero vector will augment considerably as the back EMF introduced by permanent magnet decreases, this enable to calculate current derivatives during zero voltage period[34]. Fig.7 shows the current sampling scheme.During zero vector period, three phase current are sampled twice or more used to calculate current derivatives.

2.7 Position tracking observer

After demodulating the position error signal, the position tracking observer is used to track the position and speed information. The position tracking observer could be a form of a proportional-integral (PI) controller,a proportional-integral-derivative (PID) controller, or a proportional-integral-integra-derivative (PIID) controller with torque feedforward[78,81]. Commonly, the position tracking observer gets stronger robustness with the increase of the observer order[81]. Fig.8 shows the block diagram of the position tracking observer, it can be seen that two branch points for the estimated speed can be used, and the transfer functions from the actual speed to the estimated one for the two branch points are identical.However, for the branch point ①, since the LPF is necessary to filter the speed ripples, the dynamic performance is degraded.

Fig.7 Current derivatives calculation

Fig.8 Position tracking observer

Fig.9 shows the speed step response using the PIID-type position tracking observer with the pulsating square-wave injection on a 25kW prototype IPMSM.177% rated load was applied to the test IPMSM. As can be seen, the pulsating square-wave injection combining the PIID-type position tracking observer shows strong robustness against speed step disturbance.

2.8 Hybrid seamless operation

The saliency tracking based method has been shown to operate successfully at low- and zero-speed ranges with signal injection. However, there are disadvantages attributed to the signal injection, such as increased torque ripple, losses and acoustic noise.Besides, the additional voltage required to inject the signal could possibly limit the maximum output voltage of the inverter during higher operating speeds.Therefore, in sensorless control, it is recommended to use saliency tracking based methods with signal injection only at low- and zero-speed ranges, and seamless switch to a model-based method above a certain threshold speed[82-85].

Fig.9 Speed step response with the PIID-type position tracking observer under 177% rated load

Fig.10 Hybrid seamless position tracking observer

In Fig.10, the hybrid seamless position tracking observer is illustrated, where the saliency-tracking based method is used only when the model-based position estimation fails. The contribution of the injection method is gradually phased out, usually by means of speed dependent weighting, until a speed is reached which ensures correct operation of the model-based position estimation[26]. Commonly, the position combination based hybrid seamless control method shown in Fig.10(a) is adopted in the existing works[84]. As can be seen, dual position tracking observers are used to obtain the position and speed information. Besides, to simplify the implementation of the transition algorithm, as shown in Fig.10(b), a single-position tracking observer is proposed using the normalized position error combination. Fig.10(c) shows the transition algorithm using the speed weighting function.

In [84], the hybrid seamless control method with dual-position tracking observer combining the pulsating signal injection and the sliding mode observer was presented and evaluated. Fig.11 shows the switch-over area of the hybrid position observer. From the dotted line area, the transient of the estimation errors during the switch-over area is obvious. According to the actual speed, it can be seen that the switching of the two different estimation methods is smooth.

Fig.12 shows the rated load step response with the dual-tracking position observer for the hybrid control in the switch-over area on a 2.2kW prototype IPMSM.The pulsating square-wave injection for low/zero speed range and the state observer for middle/high speed range are utilized respectively. As can be seen, the position estimation error was limited in 0.04π, and this hybrid control method shows strong robustness against load step disturbance.

Fig.11 Position and speed estimation error during the switch-over area[84]

Fig.12 Load step response with the dual-tracking position observer based hybrid control method

3 Future scope of research

The saliency-tracking based position estimation method has been verified to operate successfully at low- and zero-speed ranges. However, as aforementioned,there are disadvantages attributed to the signal injection, such as increased torque ripple, losses and acoustic noise, should be further considered. Besides,the dynamic bandwidth could be degraded due to the filtering process used to carrier signal separation and demodulation. All the disadvantages limit the further applications with saliency-tracking based methods.

3.1 Dynamic bandwidth improvement

In [78], a square-wave-type voltage injection incorporated with the associated signal processing method is proposed, instead of the conventional sinusoidal-type voltage injection. Through this scheme,the error signal can be calculated without LPF and time delays, and the position estimation performance can be enhanced. Using the proposed method, the performance of the sensorless control can be enhanced; the bandwidth of the current controller was enhanced up to 250Hz,and that of the speed controller was up to 50Hz with the PWM carrier frequency 10kHz. The current and speed regulation performance was carried out as shown in Fig.13 and Fig.14.

In [86], an improved method for the estimation of position, velocity, and disturbance torque for surfacemounted PMSM position sensorless drive using HF voltage injection was proposed. From the block diagram of the proposed scheme as shown in Fig.15, it can be seen that a separate disturbance observer and a saliency-tracking observer with speed-varying bandwidth tuning are used together to improve the disturbance rejection performance while maintaining the accuracy of self-sensing position and velocity estimation.According to the experimental comparison as show in Fig.16, the proposed estimation method can achieve higher bandwidth for the disturbance estimation and decoupling which can increase the stiffness of surfacemounted PMSM closed-loop self-sensing control.

Fig.13 Current regulation performance[78]

Fig.14 Speed regulation performance[78]

Fig.15 Improved observer: a saliency-tacking observer and a separate disturbance observer[86]

Although some great achievements have been promoted on the dynamic performance for signal injection based position estimation, there is a long way to go to further feature a dynamic behavior comparable or similar to the drives with mechanical sensor on the shaft.

Fig.16 Dynamic stiffness of different closed-loop structures[86]

3.2 Acoustic noise reduction

The acoustic noise resulting from the injected HF signal is often very shrill and harsh to hear since the frequency of the signal concentrates on a narrow audible region. For this reason, the widespread application of HF signal injection based sensorless control scheme is restricted, especially in household appliances. Decreasing the amplitude of the injected signal is a feasible way to reduce the acoustic noise. To extract the position information from low signal-tonoise ratio signals effectively, a FPGA-based strategy using Delta-Sigma A/D converter and oversampling technique was introduced[85]. Through suitable design of low-pass decimation filters, a high-performance HF injection sensorless control with lower acoustic noises can be realized.

In [79] and [80], the pseudo-random HF squarewave injection method was developed for audible noise reduction. Fig.17 illustrates the implementation of the pseudo-random HF square-wave injection based position estimation. As can be seen, the random signal generator produces two square-wave signals, making a contribution to noise reduction through extending the power spectra of the induced current. Fig.18 compares the phase currents and their PSD in three cases. As can be seen, the random frequency injection can reduce the audible noise. At the same time, the SNR can be guaranteed.

Fig.17 Pseudo-random HF square-wave injection

Fig.18 Comparison of the phase currents and their PSD[80]

4 Conclusion

Speed and position estimation for sensorless control for PMSM drives can be carried out using either model based methods or injection based methods or a combination of the two for switchover. For operation at low- and zero- speed ranges, saliencytracking based techniques have to be applied since model based estimation is unreliable. In this paper, the injection based methods have been reviewed with different injection methods and the corresponding demodulation process, as well as the position tracking observer. The future scope of the saliency-tracking based methods has been discussed, the move towards techniques injecting lower strength signals or even no additional test signals with higher dynamic bandwidth and less acoustic noise, whose implementation of these sensorless methods will facilitate their widespread use in industry.

[1] M. H. Vafaie, B. M. Dehkordi, P. Moallem, and A. Kiyoumarsi,“Improving the steady-state and transient-state performances of PMSM through an advanced deadbeat direct torque and flux control system,” IEEE Trans. Power Electron., vol. 32, no. 4, pp.2964-2975, 2017.

[2] G. Wang, Y. Wang, J. Xu, N. Zhao, and D. Xu, “Weighttransducerless rollback mitigation adopting enhanced MPC with extended state observer for direct-drive elevators,” IEEE Trans.Power Electron., vol. 31, no. 6, pp. 4440-4451, 2016.

[3] A. Shinohara, Y. Inoue, S. Morimoto, and M. Sanada, “Direct calculation method of reference flux linkage for maximum torque per ampere control in DTC-based IPMSM drives,” IEEE Trans.Power Electron., vol. 32, no. 3, pp. 2114-2122, 2017.

[4] R. Ni, D. Xu, G. Wang, G. Zhang, and C. Li, “Synchronous switching of non-line-start permanent magnet synchronous machines from inverter to grid drives,” IEEE Trans. Power Electron., vol. 31, no. 5, pp. 3717-3727, 2016.

[5] G. Schoonhoven, and M. N. Uddin, “Harmonic Injection-based adaptive control of IPMSM motor drive for reduced motor current THD,” IEEE Trans. Ind. Appl., vol. 53, no. 1, pp.483-491, 2017.

[6] G. Wang, J. Xu, T. Li, G. Zhang, H. Zhan, L. Ding, and D. Xu,“Weight-transducerless starting torque compensation of gearless permanent-magnet traction machine for direct-drive elevators,”IEEE Trans. Ind. Electron., vol. 61, no. 9, pp. 4594-4604, 2014.

[7] J. S. Lee, and R. D. Lorenz, “Robustness analysis of deadbeatdirect torque and flux control for IPMSM drives,” IEEE Trans.Ind. Electron., vol. 63, no. 5, pp. 2775-2784, 2016.

[8] R. Ni, D. Xu, G. Wang, X. Gui, G. Zhang, H. Zhan, and C. Li,“Efficiency enhancement of general ac drive system by remanufacturing induction motor with interior permanent-magnet rotor,” IEEE Trans. Ind. Electron., vol. 63, no. 2, pp. 808-820,2016.

[9] C. Calleja, A. Lopez-de-Heredia, H. Gaztanaga, T. Nieva, and L.Aldasoro, “Validation of a modified direct-self control strategy for PMSM in railway-traction applications,” IEEE Trans. Ind.Electron., vol. 63, no. 8, pp. 5143-5155, 2016.

[10] R. Ni, D. Xu, G. Wang, L. Ding, G. Zhang, and L. Qu, “Maximum efficiency per ampere control of permanent-magnet synchronous machines,” IEEE Trans. Ind. Electron., vol. 62, no. 4, pp. 2135-2143, 2015.

[11] G. Wang, L. Qu, H. Zhan, J. Xu, L. Ding, G. Zhang, and D. Xu,“Self-commissioning of permanent magnet synchronous machine drives at standstill considering inverter nonlinearities,” IEEE Trans. Power Electron., vol. 29, no. 12, pp. 6615-6627, 2014.

[12] G. Wang, J. Qi, J. Xu, X. Zhang, and D. Xu, “Antirollback control for gearless elevator traction machines adopting offsetfree model predictive control strategy,” IEEE Trans. Ind.Electron., vol. 62, no. 10, pp. 6194-6203, 2015.

[13] F. Betin, G. A. Capolino, D. Casadei, B. Kawkabani, R. I. Bojoi,L. Harnefors, E. Levi, L. Parsa, and B. Fahimi, “Trends in electrical machines control samples for classical, sensorless, and fault-tolerant techniques,” IEEE Ind. Electron. Mag., vol. 8, no. 2,pp. 43-55, Jun, 2014.

[14] M. Pacas, “Sensorless drives in industrial applications,” IEEE Ind. Electron. Mag., vol. 5, no. 2, pp. 16-23, 2011.

[15] S. Bolognani, S. Calligaro, and R. Petrella, “Design issues and estimation errors analysis of back-EMF-based position and speed observer for SPM synchronous motors,” IEEE J. Emerg. Sel.Topics Power Electron., vol. 2, no. 2, pp. 159-170, 2014.

[16] I. Boldea, M. C. Paicu, G. Andreescu, and F. Blaabjerg, “"Active flux" DTFC-SVM sensorless control of IPMSM,” IEEE Trans.Energy Convers., vol. 24, no. 2, pp. 314-322, 2009.

[17] C. Zhiqian, M. Tomita, S. Doki, and S. Okuma, “An extended electromotive force model for sensorless control of interior permanent-magnet synchronous motors,” IEEE Trans. Ind.Electron., vol. 50, no. 2, pp. 288-295, 2003.

[18] T. Tuovinen, M. Hinkkanen, L. Harnefors, and J. Luomi,“Comparison of a reduced-order observer and a full-order observer for sensorless synchronous motor drives,” IEEE Trans.Ind. Appl., vol. 48, no. 6, pp. 1959-1967, 2012.

[19] Y. Park, and S. Sul, “Sensorless control method for PMSM based on frequency-adaptive disturbance observer,” IEEE J. Emerg. Sel.Topics Power Electron., vol. 2, no. 2, pp. 143-151, 2014.

[20] J. Kim, I. Jeong, K. Nam, J. Yang, and T. Hwang, “Sensorless control of PMSM in a high-speed region considering iron loss,”IEEE Trans. Ind. Electron., vol. 62, no. 10, pp. 6151-6159, 2015.

[21] G. Q. Zhang, G. L. Wang, D. G. Xu, R. G. Ni, and C. H. Jia,“Multiple-AVF cross-feedback-network-based position error harmonic fluctuation elimination for sensorless IPMSM drives,”IEEE Trans. Ind. Electron., vol. 63, no. 2, pp. 821-831, Feb,2016.

[22] G. Wang, H. Zhan, G. Zhang, X. Gui, and D. Xu, “Adaptive compensation method of position estimation harmonic error for EMF-based observer in sensorless IPMSM drives,” IEEE Trans.Power Electron., vol. 29, no. 6, pp. 3055-3064, 2014.

[23] G. Wang, T. Li, G. Zhang, X. Gui, and D. Xu, “Position estimation error reduction using recursive-least-square adaptive filter for model-based sensorless interior permanent-magnet synchronous motor drives,” IEEE Trans. Ind. Electron., vol. 61,no. 9, pp. 5115-5125, 2014.

[24] G. Wang, L. Ding, Z. Li, J. Xu, G. Zhang, H. Zhan, R. Ni, and D.Xu, “Enhanced position observer using second-order generalized integrator for sensorless interior permanent magnet synchronous motor drives,” IEEE Trans. Energy Convers., vol. 29, no. 2, pp.486-495, 2014.

[25] G. Zhang, G. Wang, D. Xu, and N. Zhao, “ADALINE-networkbased PLL for position sensorless interior permanent magnet synchronous motor drives,” IEEE Trans. Power Electron., vol.31, no. 2, pp. 1450-1460, 2016.

[26] C. S. Staines, C. Caruana, and R. Raute, “A review of saliencybased sensorless control methods for alternating current machines,”IEEJ Journal of Industry Applications, vol. 3, no. 2, pp. 86-96,2014.

[27] S. Sato, H. Iura, K. Ide, and S. Seung-Ki, "Three years of industrial experience with sensorless IPMSM drive based on high frequency injection method." pp. 74-79.

[28] M. Seilmeier, S. Ebersberger, and B. Piepenbreier, “HF test current injection-based self-sensing control of PMSM for lowand zero-speed range using two-degree-of-freedom current control,” IEEE Trans. Ind. Appl., vol. 51, no. 3, pp. 2268-2278,2015.

[29] S. Zaim, B. Nahid-Mobarakeh, and F. Meibody-Tabar, “Robust position sensorless control of nonsalient PMSM at standstill and low speeds,” IEEE J. Emerg. Sel. Topics Power Electron., vol. 2,no. 3, pp. 640-650, 2014.

[30] P. Garcia, F. Briz, M. W. Degner, and D. Diaz-Reigosa, “Accuracy,bandwidth, and stability limits of carrier-signal-injection-based sensorless control methods,” IEEE Trans. Ind. Appl., vol. 43, no.4, pp. 990-1000, 2007.

[31] C. Caruana, G. M. Asher, and M. Sumner, “Performance of HF signal injection techniques for zero-low-frequency vector control of induction machines under sensorless conditions,” IEEE Trans.Ind. Electron., vol. 53, no. 1, pp. 225-238, 2006.

[32] Y. Shibano, and H. Kubota, "Pole position estimation method of IPMSM at low speed without high frequency components injection," IEEE Applied Power Electronics Conference &Exposition, pp. 233-239.

[33] Y. Hosogaya, and H. Kubota, "Flux position estimating method of IPMSM at low speed region using current derivative without high frequency component injection," International Conference on Electrical Machines & Systems, pp. 1-5,2013.

[34] D. Hind, M. Sumner, and C. Gerada, "Estimating current derivatives for sensorless motor drive applications," European Conference on Power Electronics & Applications, pp. 1-10,2015.

[35] Y. Shih-Chin, and R. D. Lorenz, “Surface permanent magnet synchronous machine position estimation at low speed using eddy-current-reflected asymmetric resistance,” IEEE Trans.Power Electron., vol. 27, no. 5, pp. 2595-2604, 2012.

[36] Y. Shih-Chin, and R. D. Lorenz, “Comparison of resistancebased and inductance-based self-sensing controls for surface permanent-magnet machines using high-frequency signal injection,” IEEE Trans. Ind. Appl., vol. 48, no. 3, pp. 977-986,2012.

[37] H. Zhan, Z. Q. Zhu, M. Odavic, and Y. Li, “A novel zero-sequence model-based sensorless method for open-winding PMSM with common DC bus,” IEEE Trans. Ind. Electron., vol.63, no. 11, pp. 6777-6789, 2016.

[38] G. Xie, K. Lu, S. K. Dwivedi, J. R. Rosholm, and F. Blaabjerg,“Minimum-voltage vector injection method for sensorless control of PMSM for low-speed operations,” IEEE Trans. Power Electron., vol. 31, no. 2, pp. 1785-1794, 2016.

[39] C. Wu, Z. Chen, R. Qi, and R. Kennel, “Decoupling of the Secondary Saliencies in Sensorless PMSM Drives using Repetitive Control in the Angle Domain,” Journal of Power Electronics, vol. 16, no. 4, pp. 1375-1386, 2016.

[40] Z. Chen, F. Wang, G. Luo, Z. Zhang, and R. Kennel, “Secondary saliency tracking-based sensorless control for concentrated winding SPMSM,” IEEE Trans. Ind. Informat., vol. 12, no. 1, pp.201-210, 2016.

[41] S. Medjmadj, D. Diallo, M. Mostefai, C. Delpha, and A. Arias,“PMSM drive position estimation: contribution to the highfrequency injection voltage selection issue,” IEEE Trans. Energy Convers., vol. 30, no. 1, pp. 349-358, 2015.

[42] X. Wang, W. Xie, G. Dajaku, R. M. Kennel, D. Gerling, and R.D. Lorenz, “Position self-sensing evaluation of novel CWIPMSMs with an HF injection method,” IEEE Trans. Ind. Appl.,vol. 50, no. 5, pp. 3325-3334, 2014.

[43] J. M. Liu, and Z. Q. Zhu, “Sensorless control strategy by square-waveform high-frequency pulsating signal injection into stationary reference frame,” IEEE J. Emerg. Sel. Topics Power Electron., vol. 2, no. 2, pp. 171-180, 2014.

[44] E. Robeischl, and M. Schroedl, “Optimized inform measurement sequence for sensorless PM synchronous motor drives with respect to minimum current distortion,” IEEE Trans. Ind. Appl.,vol. 40, no. 2, pp. 591-598, 2004.

[45] N. Ronggang, L. Kaiyuan, F. Blaabjerg, and X. Dianguo, "A comparative study on pulse sinusoidal high frequency voltage injection and INFORM methods for PMSM position sensorless control," Conference of the IEEE Industrial Electronics Society,pp. 2600-2605, 2016.

[46] S. I. Kim, J. H. Im, E. Y. Song, and R. Y. Kim, “A new rotor position estimation method of IPMSM using all-pass filter on high-frequency rotating voltage signal injection,” IEEE Trans.Ind. Electron., vol. 63, no. 10, pp. 6499-6509, 2016.

[47] C.Y. Yu, J. Tamura, D. D. Reigosa, and R. D. Lorenz, “Position self-sensing evaluation of a FI-IPMSM based on high-frequency signal injection methods,” IEEE Trans. Ind. Appl., vol. 49, no. 2,pp. 880-888, 2013.

[48] F. Gabriel, F. De Belie, X. Neyt, and P. Lataire, “High-frequency issues using rotating voltage injections intended for position self-sensing,” IEEE Trans. Ind. Electron., vol. 60, no. 12, pp.5447-5457, 2013.

[49] N. Bianchi, E. Fornasiero, and S. Bolognani, “Effect of stator and rotor saturation on sensorless rotor position detection,” IEEE Trans. Ind. Appl., vol. 49, no. 3, pp. 1333-1342, 2013.

[50] Z. Q. Zhu, and L. M. Gong, “Investigation of effectiveness of sensorless operation in carrier-signal-injection-based sensorlesscontrol methods,” IEEE Trans. Ind. Electron., vol. 58, no. 8, pp.3431-3439, 2011.

[51] L. M. Gong, and Z. Q. Zhu, “A novel method for compensating inverter nonlinearity effects in carrier signal injection-based sensorless control from positive-sequence carrier current distortion,” IEEE Trans. Ind. Appl., vol. 47, no. 3, pp. 1283-1292,2011.

[52] D. D. Reigosa, P. Garcia, F. Briz, D. Raca, and R. D. Lorenz,“Modeling and adaptive decoupling of high-frequency resistance and temperature effects in carrier-based sensorless control of PM synchronous machines,” IEEE Trans. Ind. Appl., vol. 46, no. 1,pp. 139-149, 2010.

[53] D. Raca, P. Garcia, D. D. Reigosa, F. Briz, and R. D. Lorenz,“Carrier-signal selection for sensorless control of PM synchronous machines at zero and very low speeds,” IEEE Trans.Ind. Appl., vol. 46, no. 1, pp. 167-178, 2010.

[54] F. Briz, A. Diez, and M. W. Degner, “Dynamic operation of carrier-signal-injection-based sensorless direct field-oriented ac drives,” IEEE Trans. Ind. Appl., vol. 36, no. 5, pp. 1360-1368,2000.

[55] P. L. Xu, and Z. Q. Zhu, “Carrier signal injection-based sensorless control for permanent-magnet synchronous machine drives considering machine parameter asymmetry,” IEEE Trans.Ind. Electron., vol. 63, no. 5, pp. 2813-2824, 2016.

[56] T. C. Lin, Z. Q. Zhu, K. Liu, and J. M. Liu, “Improved sensorless control of switched-flux permanent-magnet synchronous machines based on different winding configurations,” IEEE Trans. Ind.Electron., vol. 63, no. 1, pp. 123-132, 2016.

[57] T. C. Lin, and Z. Q. Zhu, “Sensorless operation capability of surface-mounted permanent-magnet machine based on highfrequency signal injection methods,” IEEE Trans. Ind. Appl., vol.51, no. 3, pp. 2161-2171, 2015.

[58] S. Jung, and J. Ha, “Analog filtering method for sensorless ac machine control with carrier-frequency signal injection,” IEEE Trans. Ind. Electron., vol. 62, no. 9, pp. 5348-5358, 2015.

[59] S. Zhao, O. Wallmark, and M. Leksell, “Low-speed sensorless control with reduced copper losses for saturated pmsynrel machines,” IEEE Trans. Energy Convers., vol. 28, no. 4, pp.841-848, 2013.

[60] L. M. Gong, and Z. Q. Zhu, “Robust initial rotor position estimation of permanent-magnet brushless AC machines with carrier-signal-injection-based sensorless control,” IEEE Trans.Ind. Appl., vol. 49, no. 6, pp. 2602-2609, 2013.

[61] M. A. Ghazi Moghadam, and F. Tahami, “Sensorless control of PMSMs with tolerance for delays and stator resistance uncertainties,” IEEE Trans. Power Electron., vol. 28, no. 3, pp.1391-1399, 2013.

[62] S. C. Yang, and R. D. Lorenz, “Analysis of iron and magnet losses in surface-permanent-magnet machines resulting from injection-based self-sensing position estimation,” IEEE Trans.Ind. Appl., vol. 48, no. 6, pp. 1901-1910, 2012.

[63] O. A. Mohammed, A. A. Khan, A. M. El-Tallawy, A. Nejadpak,and M. J. Roberts, “A wavelet filtering scheme for noise and vibration reduction in high-frequency signal injection-based sensorless control of PMSM at low speed,” IEEE Trans. Energy Convers., vol. 27, no. 2, pp. 250-260, 2012.

[64] A. Accetta, M. Cirrincione, M. Pucci, and G. Vitale, “Sensorless control of PMSM fractional horsepower drives by signal injection and neural adaptive-band filtering,” IEEE Trans. Ind.Electron., vol. 59, no. 3, pp. 1355-1366, 2012.

[65] S. C. Yang, T. Suzuki, R. D. Lorenz, and T. M. Jahns, “Surfacepermanent-magnet synchronous machine design for saliency-tracking self-sensing position estimation at zero and low speeds,”IEEE Trans. Ind. Appl., vol. 47, no. 5, pp. 2103-2116, 2011.

[66] F. Cupertino, G. Pellegrino, P. Giangrande, and L. Salvatore,“Sensorless position control of permanent-magnet motors with pulsating current injection and compensation of motor end effects,” IEEE Trans. Ind. Appl., vol. 47, no. 3, pp. 1371-1379,2011.

[67] C. H. Choi, and J. K. Seok, “Pulsating signal injection-based axis switching sensorless control of surface-mounted permanentmagnet motors for minimal zero-current clamping effects,” IEEE Trans. Ind. Appl., vol. 44, no. 6, pp. 1741-1748, 2008.

[68] H. Jung-Ik, I. Kozo, T. Sawa, and S. Seung-Ki, “Sensorless rotor position estimation of an interior permanent-magnet motor from initial states,” IEEE Trans. Ind. Appl., vol. 39, no. 3, pp. 761-767,2003.

[69] S. C. Yang, S. M. Yang, and J. H. Hu, “Design consideration on the square-wave voltage injection for sensorless drive of interior permanent-magnet machines,” IEEE Trans. Ind. Electron., vol.64, no. 1, pp. 159-168, 2017.

[70] R. Ni, D. Xu, F. Blaabjerg, K. Lu, G. Wang, and G. Zhang,“Square-wave voltage injection algorithm for PMSM position sensorless control with high robustness to voltage errors,” IEEE Trans. Power Electron., vol. 32, no. 7, pp. 5425-5437, 2017.

[71] P. L. Xu, and Z. Q. Zhu, “Novel square-wave signal injection method using zero-sequence voltage for sensorless control of PMSM drives,” IEEE Trans. Ind. Electron., vol. 63, no. 12, pp.7444-7454, 2016.

[72] D. Kim, Y. Kwon, S. Sul, J. Kim, and R. Yu, “Suppression of injection voltage disturbance for high-frequency square-wave injection sensorless drive with regulation of induced highfrequency current ripple,” IEEE Trans. Ind. Appl., vol. 52, no. 1,pp. 302-312, 2016.

[73] S. Yang, “Saliency-based position estimation of permanentmagnet synchronous machines using square-wave voltage injection with a single current sensor,” IEEE Trans. Ind. Appl.,vol. 51, no. 2, pp. 1561-1571, 2015.

[74] Y. D. Yoon, and S. K. Sul, “Sensorless control for induction machines based on square-wave voltage injection,” IEEE Trans.Power Electron., vol. 29, no. 7, pp. 3637-3645, 2014.

[75] N. C. Park, and S. H. Kim, “Simple sensorless algorithm for interior permanent magnet synchronous motors based on highfrequency voltage injection method,” IET Electr. Power Appl.,vol. 8, no. 2, pp. 68-75, 2014.

[76] S. Murakami, T. Shiota, M. Ohto, K. Ide, and M. Hisatsune,“Encoderless servo drive with adequately designed IPMSM for pulse-voltage-injection-based position detection,” IEEE Trans.Ind. Appl., vol. 48, no. 6, pp. 1922-1930, 2012.

[77] S. Kim, J. I. Ha, and S. K. Sul, “PWM switching frequency signal injection sensorless method in IPMSM,” IEEE Trans. Ind.Appl., vol. 48, no. 5, pp. 1576-1587, 2012.

[78] Y. Young-Doo, S. Seung-Ki, S. Morimoto, and K. Ide, “Highbandwidth sensorless algorithm for ac machines based on square-wave-type voltage injection,” IEEE Trans. Ind. Appl., vol.47, no. 3, pp. 1361-1370, 2011.

[79] G. Wang, L. Yang, G. Zhang, X. Zhang, and D. Xu, “Comparative investigation of pseudorandom high-frequency signal injection schemes for sensorless IPMSM drives,” IEEE Trans. Power Electron., vol. 32, no. 3, pp. 2123-2132, 2017.

[80] G. Wang, L. Yang, B. Yuan, B. Wang, G. Zhang, and D. Xu,“Pseudo-random high-frequency square-wave voltage injection based sensorless control of IPMSM drives for audible noise reduction,” IEEE Trans. Ind. Electron., vol. 63, no. 12, pp. 7423-7433, 2016.

[81] K. Lee, S. Park, and S. Jeong, “A seamless transition control of sensorless PMSM compressor drives for improving efficiency based on a dual-mode operation,” IEEE Trans. Power Electron.,vol. 30, no. 3, pp. 1446-1456, 2015.

[82] F. J. W. Barnard, W. T. Villet, and M. J. Kamper, “Hybrid active-flux and arbitrary injection position sensorless control of reluctance synchronous machines,” IEEE Trans. Ind. Appl., vol.51, no. 5, pp. 3899-3906, 2015.

[83] G. Wang, R. Yang, and D. Xu, “DSP-based control of sensorless IPMSM drives for wide-speed-range operation,” IEEE Trans. Ind.Electron., vol. 60, no.2, pp.720-727, 2013.

[84] S. C. Yang, and R. D. Lorenz, “Surface permanent-magnet machine self-sensing at zero and low speeds using improved observer for position, velocity, and disturbance torque estimation,”IEEE Trans. Ind. Appl., vol. 48, no. 1, pp.151-160, 2012.

* Corresponding Author, E-mail: wgl818@hit.edu.cn

Supported by the Research Fund for National Science Foundation of China (51522701), grants from Power Electronics Science and Education Development Program of Delta Environmental & Educational Foundation (DREK2015002), National Key Research and Development Program (2016YFE0102800).

the B.S. degree in Electrical Engineering from Harbin Engineering University, Harbin, China, in 2011, and the M.S. degree in Electrical Engineering from Harbin Institute of Technology, Harbin, China,in 2013, where he is currently working toward Ph.D. degree in Power Electronics and Electrical Drives.

His current research interests include parameter identification technique, and control of electrical drives, with main focus on sensorless field-oriented control of interior permanent magnet synchronous machines.

Gaolin Wang(M’13) received the B.S., M.S.and Ph.D.degrees in Electrical Engineering from Harbin Institute of Technology, Harbin,China, in 2002, 2004 and 2008, respectively.In 2009, he joined the Department of Electrical Engineering, Harbin Institute of Technology as a Lecturer, where he has been a Professor of Electrical Engineering since 2014.From 2009 to 2012, he was a Postdoctoral Fellow in Shanghai STEP Electric Corporation.He has authored more than 80 technical papers published in journals and conference proceedings. He is the holder of ten Chinese patents.His current major research interests include permanent magnet synchronous motor drives, high performance direct-drive for traction system, position sensor-less control of AC motors and efficiency optimization control of interior PMSM.

Dr. Wang serves as an Associate Editor of IET Electric Power Applications, Journal of Power Electronics, and CES Transactions on Electrical Machines and System. He received the Outstanding Research Award and the Delta Young Scholar Award from the Delta Environmental and Educational Foundation in 2012 and 2014,respectively. He is currently supported by the National Natural Science of China for Excellent Young Scholars.

DianguoXu(M’97-SM’12-F’16) received the B.S. degree in Control Engineering from Harbin Engineering University, Harbin, China,in 1982, and the M.S. and Ph.D.degrees in Electrical Engineering from Harbin Institute of Technology (HIT), Harbin, China, in 1984 and 1989, respectively.

In 1984, he joined the Department of Electrical Engineering, HIT as an assistant professor. Since 1994, he has been a professor in the Department of Electrical Engineering, HIT. He was the Dean of School of Electrical Engineering and Automation, HIT from 2000 to 2010. He is now the vice president of HIT. His research interests include renewable energy generation technology, power quality mitigation, sensor-less vector controlled motor drives, high performance servo system. He published over 600 technical papers.

Dr. Xu is a senior member of IEEE, a Deputy Editors-in-Chief of the CES Transactions on Electrical Machines and System, an Associate Editor of the IEEE Transactions on Industrial Electronics, and the IEEE Journal of Emerging and Selected Topics in Power Electronics.He serves as Chairman of IEEE Harbin Section.