Received June 12, 2019, accepted June 23, 2019, date of publication June 26, 2019, date of current

version July 17, 2019.

Digital Object Identifier 10.1109/ACCESS.2019.2925214

An Improved Position-Sensorless Control

Method at Low Speed for PMSM Based
on High-Frequency Signal Injection
into a Rotating Reference Frame
SHUANG WANG, (Member, IEEE), KANG YANG , AND KANG CHEN
School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200240, China
Corresponding author: Shuang Wang (wang-shuang@shu.edu.cn)
This work was supported in part by the National Key Research & Development Program of China under Grant 2018YFB0104801.

ABSTRACT In this paper, a novel sensorless control strategy with the injection of a high-frequency pulsating
sinusoidal voltage into a rotating reference frame for a surface-mounted permanent magnet synchronous
motor (SPMSM) is proposed. Conventional schemes may face the problems of applying to the motor with
no obvious salient pole effect, and the effect of filter on the bandwidth of the system. Different from the
conventional schemes, the new proposed strategy injects a high-frequency pulsating sinusoidal voltage signal
is injected into the estimate d-q rotating reference frame, and the rotor position information is obtained from
the response of injected high-frequency current signal in the α-β stationary reference frame other than the
d-q rotating reference frame,which can avoid failure of applying to the SPMSM with no obvious salient
pole effect. With this approach, band-pass filter, which is necessary in the conventional sensorless control,
is removed to simplify the control structure and improve the system dynamic control performance. Therefore,
this paper proposes a simple structure, which modulates the high-frequency current signal directly and only
passes through the low-pass filter to obtain the estimated rotor position angle. Finally, the feasibility of the
improved high-frequency pulsating sinusoidal voltage injection control method is verified by simulation and
experiment.

INDEX TERMS Sensorless control, high-frequency pulsating sinusoidal voltage, surface-mounted

permanent magnet synchronous motor (SPMSM), salient pole effect.

NOMENCLATURE d-q Two-phase rotating reference frame

PMSM Permanent magnet synchronous motor d̂ − q̂ Estimated two-phase rotating reference frame
FOC Field-oriented control θ The actual rotor position angle
EMF Electromotive force θ̂ Estimated rotor position angle
HF High-frequency θp The phase deviation of the fundamental current
SPMSM Surface-mounted permanent magnet 1θ The difference between the actual rotor position
synchronous motor angle and the estimated rotor position angle
SNR Signal-to-noise ratio
EKF Extended Kalman filter
I. INTRODUCTION
LPF Low-pass filter
Permanent magnet synchronous motor (PMSM) has become
BPF Band-pass filter
the best choice for many industrial applications because of
MRAS Model reference adaptive system
its high efficiency and high torque density compared with
α-β Two-phase stationary reference frame
induction machines, especially in the field of advanced man-
ufacturing and electric drive [1]–[5]. As important infor-
The associate editor coordinating the review of this manuscript and mation of the machine, the rotor position is not only used
approving it for publication was Xiaodong Sun. when the field-oriented control (FOC) scheme is adopted
2169-3536
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S. Wang et al.: Improved Position-Sensorless Control Method at Low Speed for PMSM

[6], [7], but also used during calculating the rotor speed for high-frequency signals, the signal injections can be mainly
closed loop control. Hence, a mechanical sensor, such as divided into rotating sinusoidal voltage injection [17], [18],
photoelectric encoder and resolver, is usually mounted on pulsating sinusoidal voltage injection [19], and square-wave
the rotor shaft of a PMSM to obtain an accurate rotor posi- voltage injection [20]–[22],and according to the reference
tion information. However, mechanical position sensors have frame of the injected high-frequency signals, the injec-
some problems, such as difficult installation, complex wiring, tion methods can be mainly divided into two groups:
increasing hardware cost, increasing volume and weight, and 1) HF voltage injection methods in the stationary α-β ref-
easy to fail in special environment such as damp and violent erence frame [23]–[25], 2) HF voltage injection methods in
vibration. Hence, in the PMSM control system where the the rotary d − q reference frame [26]–[28].
position accuracy is relatively low, such as fans and pumps, First of all, this paper studies the conventional high-
the position-sensorless control method is adopted. The advan- frequency pulsating sinusoidal voltage injection method. The
tage of position-sensorless control not only consists in replac- principle of this conventional method is to inject the high-
ing mechanical sensors, but also in providing redundancy frequency pulsating sinusoidal voltage signal into an axis of
protection for the system when the mechanical sensor fails. the estimated synchronous rotating reference frame, which
Therefore, various kinds of sensorless control methods that will interact with rotor-position-dependent saliencies into the
help to remove mechanical sensor in PMSMs drive systems machine and modulate the response currents to estimate the
have been proposed in past decades. rotor position. The information containing the rotor position
The sensorless control scheme was first proposed by angle of the motor is extracted from the high-frequency cur-
Abbondanti in 1975, since then, it has entered a stage of rent component. However, in view of the conventional high-
rapid development [8]–[10]. The sensorless vector control frequency pulsating sinusoidal voltage injection method,
method of PMSM can be divided according to whether the which relies on the salient pole effect of the motor [29], [30],
motor is running at middle and high-speed or low speed. an improved high-frequency pulsating sinusoidal voltage
The high-speed sensorless method based on the electromo- injection method is proposed, in which, the rotor position
tive force (EMF)model to estimate the rotor position works angle information is extracted from the high-frequency cur-
well. In [10], a parallel reduced-order extended Kalman fil- rent response signal in α-β two-phase stationary reference
ter (EKF) for rotor position estimation is proposed for the frame, which is independent of the salient polarity of the
reduction of computation resources. Sliding mode current motor, so it can also be applied to the surface-mounted
observer and the adaptive EMF observer designed to estimate permanent magnet synchronous motor (SPMSM) with no
the rotor speed and position of PMSM are analyzed in [11]. obvious salient polarity effect. Compared with the conven-
In [12], the rotor position estimation scheme is achieved tional method, this method also reduces bandpass filters,
by designing a model reference adaptive system (MRAS) which omits the process of extracting high-frequency sig-
observer on the basis of the control winding stator current. nals from bandpass filters, demodulates iαh and iβh directly,
In the field of combining artificial intelligence algorithms where iαh and iβh are the high-frequency current on the α-β
with motor control, Sun et al. [13], [14] proposed the appli- two-phase stationary reference frame, respectively, and then
cation of neural network algorithm in the field of motor filters through low-pass filters to obtain signals containing
sensorless control. Lin et al. [15] proposed a fuzzy control only the position information of the rotor. This measure sim-
algorithm to compensate the ideal computed torque controller plifies the system structure and eliminates the influence of
designed for the tracking of the rotor position reference phase and amplitude of the system caused by bandpass filters,
command. At present, such methods are often combined which is one of the main problems to be solved.
with other control methods, which is still in the theoretical This paper is organized as follows: In Section II, the
research stage in the field of motor control because of the conventional high-frequency pulsating sinusoidal voltage
complexity of calculation, and there is still a long way to injection method is analyzed. Section III describes the anal-
go before practical applications. At very low speed range, ysis of improved high-frequency pulsating sinusoidal volt-
however, these position-sensorless control methods couldn’t age injection method. Experimental results of high-frequency
work very well because of the small amplitude of back- pulsating sinusoidal voltage injection method are presented
EMF signal. To overcome the drawback that the back-EMF in Section IV to verify the effectiveness of the proposed
is not obvious in the low speed region, usually under 5% sensorless control strategy. Section V summarizes this paper.
of the rated speed, various methods for observing the rotor
position based on the salient pole effect or the saturated II. ANALYSIS OF CONVENTIONAL HIGH-FREQUENCY
salient pole effect of the motor have been presented [16],in PULSATING SINUSOIDAL VOLTAGE INJECTION
In the d and q reference frames, the voltage equation of a
which, the most popular methods are high-frequency (HF)
PMSM can be written as below:
signal injection methods. The salient-pole tracking method
based on high-frequency injection does not depend on d

ud = Rid + Ld id − ωr Lq iq

the back EMF and motor parameter information, and can dt (1)
achieve better estimation results in the low speed or even uq = Riq + Lq d iq + ωr Ld id + ωr ψf

zero speed range. According to the types of the injected dt
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where ud , uq , id , iq , Ld , Lq are the d-q axis stator voltages, d-q Substituting (3) into (4), the following can be obtained as:
axis stator currents, d-q axis inductances, respectively, where  1 
R, ωr , λmpm are the stator resistances, the rotational speed of   0  
îdh −1  Ldh  udh
the motor, the permanent magnet flux linkage, respectively. p = T (1θ)  1  uqh (6)
îqh 0
This formula represents the actual d-q reference frame and
Lqh
cannot be directly used for position estimation, so it needs to
be converted to the estimated position reference frame, or the According to the coordinate axis of the injected high-
α-β stationary reference frame. When the PMSM runs at frequency signal, the injection mode can be divided into two
zero or low speed range, the product related to ωr in formula groups: 1) Uh cos (ωh t) is injected from the d̂-axis, and then
(1) can be omitted. Therefore, formula (1) can be simplified îq is extracted from the q̂ -axis for detection. 2) Uh cos (ωh t)
as below: is injected from the q̂ -axis, and then îq is extracted from the

d d̂ -axis for detection. Where ωh is the angular frequency of
ud = Rid + Ld id

the high-frequency injection signal.
dt (2)
uq = Riq + Lq d iq
 Substituting (5) into (6), the relationship between current
dt and voltage in the estimated d̂ − q̂ two-phase rotating ref-
When the frequency of the injected signal is much larger erence frame can be obtained. If the high-frequency voltage
than the rotational frequency of the motor itself, in this case, injection axis is chosen on the d̂ -axis, the high-frequency
the PMSM is equivalent to the pure inductance model [29], current response is:
so the formula (2) can be written as below:  
Uh sin (ωn t)  Lqh cos 1θ + Ldh sin 1θ 
  2 2
      îdh
udh Ldh 0 i = sin(21θ) (7)
P dh ωn Ldh Lqi


= (3) îqh Lqh − Ldh
uqh 0 Lqh iqh 2
where udh , uqh , idh , iqh , Ldh , Lqh , P are d-q axis high- If the high-frequency voltage injection axis is chosen on the
frequency voltage, d-q axis high-frequency current, d-q axis q̂ -axis, the high-frequency current response is:
high-frequency inductances, derivative operator, respectively.  
sin(21θ)
Uh sin (ωh t) 
 

îdh Lqh − Ldh  (8)
= 2
îqh ωh Ldh Lqh L cos 1θ + L sin 1θ
2 2
qh dh

Formula 9 can be obtained from Formula 8 as follows:

Uh Lqh − Ldh
îqh = sin (ωh t) sin(21θ) (9)
2ωh Ldh Lqh
Ideally, when the PMSM rotor position estimation system
enters the steady state, the estimated value of the position
is consistent with the actual value. At this time, the position
FIGURE 1. Schematic diagram of the angular relationship between the estimation error 1θ = 0. It can be seen from formula (7)
actual reference frame and the estimated reference frame. and formula (8) that the high-frequency current response îqh
produced by injecting high-frequency voltage into d̂ -axis
The relationship between the estimated d̂ − q̂ two-phase is equal to 0 in the steady state of the system, which has
rotating reference frame and the actual d-q two-phase rotating no effect on the system torque; while the high-frequency
reference frame is shown in Fig.1. Where θ, θ̂, 1θ, are the current response îqh produced by injecting high-frequency
actual rotor position angle, the estimated rotor position angle, voltage into q̂ -axis is not equal to 0 in the steady state of
the difference between the actual rotor position angle and the system, and a large torque ripple is generated to cause the
the estimated rotor position angle, respectively. As can be motor to shake, thereby affecting the estimation accuracy of
seen from Fig.1, the estimated differential response of the the rotor position. Therefore, d̂ -axis signal injection is used
current response under the estimated d-q two-phase rotating in this chapter. The rotor position estimation error 1θ can
reference frame can be calculated as below: be obtained by detecting the q̂ -axis current and performing
   
îdh i appropriate processing on the current signal. After the multi-
p = T (1θ)p dh
−1
(4)
îqh iqh plier and low pass filter (LPF), the output current containing
the error of rotor position estimation can be obtained as:
cos 1θ sin 1θ
 
In the formula, T (1θ) = is the
− sin 1θ cos 1θ
 
LPF îqh × sin (ωh t) = k sin(21θ) (10)
rotation change matrix. The estimated voltage in the d-q two-
phase rotating reference frame can be written as: where
   

ûdh u Uh Lqh − Ldh
= T −1 (1θ) dh (5) k= (11)
ûqh uqh 4ωh Ldh Lqh
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FIGURE 2. Structural block diagram of conventional high-frequency

pulsating sinusoidal voltage injection method. FIGURE 3. Structural block diagram of improved high-frequency pulsating
sinusoidal voltage injection method.

It can be seen that the estimated rotor position can be equal to

the actual rotor position by adjusting the formula (9) to zero the angle signal is extracted from the high-frequency current
through appropriate control method. The specific implemen- response of the α-β two-phase stationary reference frame.
tation block diagram is shown in Figure 2. The specific control block diagram is shown in Figure 3.
Formula (3) is the high-frequency voltage equation of the
III. ANALYSIS OF IMPROVRD HIGH-FREQUENCY d-q reference frame of the PMSM under high-frequency sig-
PULSATING SINUSOIDAL VOLTAGE INJECTION nal injection. The current of d-q axis in formula (3) can be
Although the conventional high-frequency pulsating sinu- converted to the current of α-β axis, which can be equivalent
soidal voltage injection method can effectively extract the to the following formula:
rotor position information and get the estimated rotor posi-      
udh Ldh 0 i
tion, the method depends on the saliency of the motor struc- = T (θ)P αh (12)
ture or saturation saliency. Once the saliency is not obvious, uqh 0 Lqh iβh
the signal-to-noise ratio (SNR) of position-related signals is
very small, which is one of the main problems to be solved. where
It is difficult to extract the angle signal, which results in the
cos θ sin θ
 
failure of rotor position estimation [31]. T (θ ) = (13)
It can be seen from formula (9) that when the salient pole − sin θ cos θ
effect of SPMSM is not obvious, Ldh and Lqh are approx-
imately equal. At this time, Lqh minus Ldh is equal to 0, The high-frequency current response of PMSM in α-β
and formula (8) is equal to 0. The position estimation error two-phase stationary reference frame can be derived from
information will be small, and it is difficult to extract the angle formula (12):
signal, which will cause the angle estimation to fail. At the  1 
same time, the use of the bandpass filter in Figure 2 affects   0  
iαh  udh
the phase and amplitude of the system signal. To solve these P = T −1 (θ)  Ldi (14)

iβh 1  uqh
problems, an improved high-frequency pulsating sinusoidal 0
voltage injection method is proposed in this paper. This Lqh
method does not depend on the salient polarity of the motor,
and the effect of the bandpass filter on the signal is reduced, Substituting (5) into (14), the formula (15) can be obtained
which can better observe the rotor position of PMSM. The as shown in bottom of this page. Inject a high-frequency
detailed analysis is as follows. pulsating sinusoidal voltage signal into the d̂ -axis of the
estimated rotating reference frame:
A. ROTOR POSITION EXTRACTION
Uh cos ωh t
   
The high-frequency pulsating sinusoidal voltage is injected ûdh
= (16)
into the d̂ -axis of the estimated rotating reference frame, and ûqh 0

 1 1 1 1 
  cos θ cos 1θ + sin θ sin 1θ cos θ sin 1θ − sin θ cos 1θ  
iαh  Ldh Lqh Ldh Lqh  ûdh
P =
  (15)
iβh 1 1 1 1  ûqh
sin θ cos 1θ − cos θ sin 1θ sin θ sin 1θ + cos θ cos 1θ
Ldh Lqh Ldh Lqh

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Substituting (16) into (15), the formula (17) can be From the phase-frequency characteristic curve, it can be
obtained as: seen that a high-frequency signal passing through the band-
 1 1  pass filter produces a phase shift of 0.21 rad at 900 Hz. This
  cos θ cos 1θ + sin θ sin 1θ phase shift also changes as the order of the filter, the cut-off
iah Uh  L Lqh
 di

=  frequency, the passband bandwidth, and the frequency of the
iβh ωh  1 1 
injected high frequency signal change. Therefore, the use of
sin θ cos 1θ − cos θ sin 1θ
Ldi Lqi a bandpass filter causes a phase shift in the signal and a bias
sin ωh t (17) in the estimated angle, which is one of the main problems to
be solved below.
It can be seen from formula (17) that the high-frequency Document [33], [34] analyses the angle estimation error
current response in α-β two-phase stationary reference frame caused by bandpass filter, and proposes a phase compensation
contains rotor position information. If the angular error 1θ is algorithm, which improves the angle error effectively. How-
small enough, the estimated rotor position converges to the ever, additional compensation algorithm needs to add a large
actual rotor position. Ldh is equal to Lqh for a SPMSM, so the number of calculation modules, which further increases the
stationary α-β two-phase high-frequency current response complexity of the system.
can be simplified as follows: In order to solve the signal phase shift problem caused by

iαh

Uh

cos θ
 the band-pass filter, this paper adopts the method that the
= sin ωh t (18) static two-phase current iαh and iβh have modulated directly.
iβh ωh Ldh sin θ
Only the low-pass filter is required to obtain the signal con-
In position-sensorless control using high-frequency pul- taining the rotor position information, and the band-pass filter
sating sinusoidal voltage injection method, the current vec- is omitted, which simplifies the system structure and elimi-
tor iαβ in two-phase stationary reference frame includes the nates the effects of bandpass filters on signal amplitude and
fundamental current vector iαβb , the high-frequency current phase. The structure diagrams before and after simplification
component iαβh , and the high order harmonic current vector are shown in Figure 5.
iαβx caused by the PWM switching signal.

iαβ = iαβb + iαβh + iαβx (19)

In the formula (19), iαβh contains the position information

of the rotor. Generally, it is necessary to extract the high-
frequency current component iαβh with a band-pass filter.
However, the use of the band-pass filter will increase the com-
plexity of the system. More seriously, it will cause the shift of
the amplitude and phase of the signal [32], which affects the
accuracy of the estimation. For example, the high-frequency
signal with 900Hz frequency is extracted by bandpass filter.
The type of bandpass filter is Butterworth, the order is 4,
the low-pass cut-off frequency is 600 Hz, and the high-pass
cut-off frequency is 1200 Hz. The phase-frequency character-
istic curve of the band-pass filter designed according to the
above requirements is shown in Figure 4.
FIGURE 5. Structural chart of rotor position estimation. (a) Before
simplification. (b) After simplification.

During the operation of PMSM at low speed, the funda-

mental current iαβb is multiplied by the modulation signal
2 sinωh t, and the following formula can be obtained as:

iαβb × 2 sin ωh t
 
i
= αb 2 sin ωh t
iβb
cos ωr t − θp
 
= 2k sin ωh t
sin ωr t − θp
sin (ωr + ωh ) t + sin (ωh − ωr ) t − 2θp sin ωh t
 
=k
cos (ωr + ωh ) t − cos (ωh − ωr ) t − 2θp sin ωh t
FIGURE 4. Phase-frequency characteristic curve of bandpass filter. (20)

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S. Wang et al.: Improved Position-Sensorless Control Method at Low Speed for PMSM

where k is the amplitude of the fundamental current, ωr is the

rotational angular frequency of the motor, and θ p is the phase
deviation of the fundamental current.
Since the rotational frequency of the fundamental current
ωr at low speed is very low and much smaller than ωh ,
it can be seen from formula (20) that the signal obtained
by multiplying iαβb and 2sinωh t is composed of three high-
frequency signals, so the signal can be filtered by low-pass
filter. Similarly, the frequency of high-order harmonic current
iαβx is much higher than the frequency of injection signal,
and the signal multiplied by 2sinωh t is still high-frequency
harmonic signal, which can also be filtered by low-pass filter.
Hence, it can be concluded that:
     FIGURE 7. Current waveform in two-phase stationary reference frame.
iαl iα
= LPF 2 sin ωh t
iβl iβ
  
iαh
= LPF 2 sin ωh t
iβh
cos θ
 
Uh
= (21)
ωh Ldh sin θ
It can be seen from formula (21) that the improved high-
frequency pulse voltage injection method is only related to
the inductance value and does not depend on the salient
polarity of PMSM, so it is suitable for SPMSM with very
small salient polarity. The actual rotor position information
can be obtained by processing the high-frequency current
signal. The results obtained by using iαβ directly multiplied
by 2sinωh t and filtering by low-pass filter are consistent with
those obtained by using iαβh modulation and filtering by
low-pass filter. In the process of processing, the band-pass
filter is omitted, the amplitude attenuation and phase shift
caused by the band-pass filter are eliminated, and the system
structure is simplified. Therefore, the improved method pro-
posed in this paper solves the two drawbacks of the conven-
tional high-frequency pulsating sinusoidal voltage injection
method.

B. ROTOR POSITION OBSERVER

In this paper, the two-phase phase-locked loop observer is
used to observe the rotor position and rotational speed. The
specific structure is shown in Figure 6.
FIGURE 8. Dynamic performance of conventional high-frequency
pulsating sinusoidal voltage injection method. (a) Estimated angle
waveform at sudden change of speed. (b) Estimated angle waveform for
steering abrupt change.

From Fig.6, the rotor position error signal for observation

can be obtained as follows:
ε = iβl cos θ̂ − iαl sin θ̂ = kh sin(θ − θ̂) (22)
where
Uh
kh =
ωh Ldh
When the angle error between estimated angle and actual
FIGURE 6. Two-phase phase-locked loop structure block diagram. angle θ − θ̂ is very small, formula (22) can be simplified

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FIGURE 9. Dynamic performance of improved high-frequency pulsating

sinusoidal voltage injection method (a) Estimated angle waveform at FIGURE 11. Current signal processing (a)Waveform after modulation of
sudden change of speed. (b) Estimated angle waveform for steering high-frequency current signal(b)Output waveform of low-pass filter.
abrupt change.

kh ki are both positive numbers. Therefore, PLL can lock the

angle well and the estimated rotor position can converge to
the actual rotor position.

C. SIMULATION RESULTS
The feasibility of the improved high-frequency pulsating
sinusoidal voltage injection method has been verified by
theoretical analysis. Due to the complexity of the con-
trol system, simple theoretical analysis is difficult to func-
tion in system analysis and design, so it is necessary to
carry out auxiliary verification through computer simulation
research. In this paper, the conventional high-frequency pul-
sating sinusoidal voltage injection method and the improved
FIGURE 10. Test bench description. high-frequency pulsating sinusoidal voltage injection method
for PMSM rotor position estimation model are built on
as follows: MATLAB/Simulink simulation platform to verify the correct-
ness of theoretical derivation. The simulation parameters of
ε = kh sin(θ − θ̂) ≈ kh (θ − θ̂) (23)
the motor body in this paper are derived from a SPMSM used
Therefore, the closed-loop transfer function of the two-phase in the experiment. The rated voltage and the rated current are
phase-locked loop can be expressed as: set to 24V, and 4.6A, respectively, in the simulations. The
rated power of the motor, the pole pair, the stator resistance
θ̂ kh kp s + kh ki
= 2 (24) and the cross-axis inductance are set to 70W, 2 pairs, 0.27,
θ s + kh kp s + kh ki and 0.9mH, respectively.
Since kh is a positive number, it can be judged from Rolls- The vector control strategy of id = 0 is adopted in the
Holwitz theorem that the system is stable when kh kp and simulation to realize the position sensorless control of the

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FIGURE 12. Conventional high-frequency pulsating sinusoidal voltage FIGURE 13. Improved high-frequency pulsating sinusoidal voltage
injection method for rotor position observation at 100rpm. (a) Angle injection method for rotor position observation at 100rpm. (a) Angle
comparison. (b) Angle contrast magnification. comparison. (b) Angle contrast magnification.

two-phase current has good sinusoidal characteristics when

low speed range of the PMSM. A high-frequency pulsating the load is suddenly applied for 0.5 seconds.
sinusoidal voltage signal having a frequency of 900 Hz and an Figure 8 shows the simulation waveform of the dynamic
amplitude of 5 V is injected on the estimated d-axis, and rotor performance of the conventional high-frequency pulsating
position information is extracted from the high-frequency sinusoidal voltage injection method. Fig.8(a) is the contrast
current response of the two-phase stationary reference frame. waveform between the actual angle and the estimated angle
In the conventional high-frequency pulsating sinusoidal volt- when the motor speed changes suddenly. The motor suddenly
age injection method, the high-pass cut-off frequency of the accelerates from 50 rpm to 100 rpm in 1 second, and the
band-pass filter for extracting the high-frequency current sig- angular error is about 0.3 rad. In the steady state, the estimated
nal is set to 1200 Hz, and the low-pass cut-off frequency is error of 100 rpm is about 0.04 rad, and the estimated error
set to 600 Hz, which ensures efficient extraction of the high- of 50 rpm is about 0.02 rad less than 100 rpm. It can be seen
frequency current response signal. that the estimation accuracy of high-frequency pulsating sinu-
The amplitude of the high-frequency sinusoidal signal used soidal voltage injection method is related to the speed, and the
for modulation is 2V and the frequency is 900 Hz. The cut-off smaller the speed, the higher the estimation accuracy. Fig.8(b)
frequency of the low-pass filter for extracting the modulated shows that the PMSM suddenly changes from 50 rpm to
signal is set to 300 Hz. Finally, the angular and velocity −50 rpm in 1 second. It can be seen from the figure that
signals are solved by using a two-phase phase phase-locked when the motor is switched from forward to reverse, the angle
loop. The position estimator of the improved high-frequency estimation will fluctuate slightly. The angle error is less than
pulsating sinusoidal voltage injection method omits the band- 0.4 rad, and the estimated angle basically follows the actual
pass filter on the basis of the original model and directly angle.
modulates the current signal. Figure 7 is the current waveform Figure 8. Dynamic performance of conventional high-
in two-phase stationary reference frame and the current har- frequency pulsating sinusoidal voltage injection method
monic content in Figure 7 is mainly caused by high-frequency (a) Estimated angle waveform at sudden change of speed.
injection voltage. It can be seen from Figure 7 that the (b) Estimated angle waveform for steering abrupt change.

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FIGURE 15. Conventional high-frequency pulsating sinusoidal voltage

injection method for rotor position observation during steering abrupt
change. (a) Steering of motor from forward to reverse. (b) Steering of
FIGURE 14. Rotor position observation at sudden change of speed. motor from reverse to forward.
(a) Conventional high-frequency pulsating sinusoidal voltage injection
method. (b) Improved high-frequency pulsating sinusoidal voltage TABLE 1. Motor parameters.
injection method.

Figure 9 shows the simulation waveform of the dynamic

performance of the improved high-frequency pulsating sinu-
soidal voltage injection method. Fig.9(a) shows the simula-
tion waveform of the motor speed from 50 rpm to 100 rpm
in 1 second. It can be seen that the estimated angle can
converge to the actual angle faster than previous one, and
the estimation accuracy is higher. Fig.9(b) is a simulation
waveform of the sudden change of the motor speed from
50 rpm to −50 rpm in 1 second. It can be seen that the
the command and monitors the system status, the SPMSM
angle estimation will produce small fluctuations when the
tow platform, the oscilloscope and the control system and the
motor is switched from forward to reverse. Compared with
drive system of DSP. The controlled motor and the magnetic
the conventional high-frequency pulsating sinusoidal voltage
powder brake are connected by a coupling. The main electri-
injection method, the estimated angle can follow the actual
cal parameters of the SPMSM are shown in Table 1.
angle faster and the phase delay is smaller. It can be seen
that the improved high-frequency pulsating sinusoidal volt-
A. IMPROVED HIGH-FREQUENCY PULSATING
age injection method can effectively eliminate the phase shift
SINUSOIDAL VOLTAGE INJECTION METHOD
problem caused by the band-pass filter, and the injection
FOR CURRENT SIGNAL PROCESSING
method has higher estimation accuracy and better dynamic
performance. In the improved experimental method, the interruption fre-
quency of the system is set as 10 kHz. In the cases of rotor
IV. EXPERERIMENTAL RESULTS position estimation, the magnitude of the injection sinusoidal
The proposed sensorless control scheme was verified on the signal voltage is 10 V, and its frequency is 1000 Hz. The given
platform with a 70W SPMSM, as shown in Fig. 10. motor speed instruction is 100 rpm, and the motor runs from
The system mainly involves the upper computer PC that sends start-up to stable state under no-load condition. Fig.11(a) is

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S. Wang et al.: Improved Position-Sensorless Control Method at Low Speed for PMSM

FIGURE 16. Improved high-frequency pulsating sinusoidal voltage FIGURE 17. Phase current waveform of high-frequency pulsating
injection method for rotor position observation during steering abrupt sinusoidal voltage injection method. (a)Phase current waveform of motor
change. (a) Steering of motor from forward to reverse. (b) Steering of under no load. (b) Phase current waveform of motor loading.
motor from reverse to forward.

a waveform obtained by modulating the current iαβh . The improved high-frequency pulsating sinusoidal voltage injec-
waveform in Fig.11(a) passes through a digital low-pass filter tion method is about 0.08 rad, and the phase delay is about
and outputs the waveform in Fig.11(b). The rotor angle signal 0.03 rad. The improved method eliminates the influence of
of the motor can be observed after the waveform of Fig.11(b) band-pass filter on angle estimation performance, improves
passes through the observer. the estimation accuracy and reduces the phase delay of angle
From the experimental waveforms, it can be seen that estimation, so it has better steady-state performance.
the digital low-pass filter designed in the experiment can
effectively obtain the sinusoidal wave signal containing the C. OBSERVATION EXPERIMENT OF ROTOR POSITION
position information of the rotor. OF MOTOR IN SUDDEN CHANGE OF SPEED
Fig.14 is the experimental waveform of rotor position obser-
B. OBSERVATION EXPERIMENT OF MOTOR ROTOR vation in case of sudden change of speed. Among them,
POSITION AT 100RPM OPERATION Fig.14(a) is the rotor position observation waveforms
Given the motor speed of 100 rpm, Fig.12 is the exper- obtained by using the conventional high-frequency pulsat-
imental waveform of rotor position observation based on ing sinusoidal voltage injection method. Fig.14(b) is the
conventional high-frequency pulsating sinusoidal voltage rotor position observation waveforms obtained by using the
injection method and Fig.13 is the experimental waveform of improved high frequency pulse voltage injection method.
rotor position observation based on improved high-frequency From the experimental waveforms, it can be seen that the
pulsating sinusoidal voltage injection method. two high-frequency injection position estimation methods
The experimental waveforms show that the two high- can effectively observe the rotor position information in case
frequency injection methods can effectively observe the rotor of sudden change of rotational speed. The phase delay of
position. The steady-state error between the estimated angle the improved high-frequency pulse voltage injection method
and the actual angle of the conventional high-frequency pul- is about 0.05 rad, which is obviously reduced compared
sating sinusoidal voltage injection method is about 0.12 rad, with the angle phase delay of 0.1 rad before improvement.
and the phase delay is about 0.06 rad. The steady-state error The observation effect is better than the previous angle
between the estimated angle and the actual angle of the observation.

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 S. Wang et al.: Improved Position-Sensorless Control Method at Low Speed for PMSM

It can be seen that the phase current of the motor using

high-frequency pulsating sinusoidal voltage injection method
contains high-frequency current response and has good sinu-
soidal degree under load.
Given the speed of 100 rpm, Fig.18 shows the experi-
mental waveforms of rotor position observation with two
high-frequency injection methods under abrupt load change.
Among them, Fig.18(a) is the rotor position observation
waveform for the conventional high-frequency pulsating
sinusoidal voltage injection method, Fig.18(b) is the rotor
position observation waveform for the improved high-
frequency pulsating sinusoidal voltage injection method.
It can be seen from the experimental waveform that both
high-frequency pulsating sinusoidal voltage injection meth-
ods have good resistance to load disturbance. In the case of
a sudden load change, the motor will experience some jitter
and will soon return to a steady state. The estimated error of
the conventional high-frequency pulsating sinusoidal voltage
injection method is about 0.15 rad, and the improved high-
frequency pulsating sinusoidal voltage injection method has
an estimation error of about 0.12 rad. The improved high-
frequency pulse injection method has a smaller estimation
error than the pre-improvement angle.

V. CONCLUSION
In this paper, an improved position-sensorless control method
for PMSM based on high-frequency signal injection into a
FIGURE 18. Rotor position observation under sudden load.
(a) Conventional high-frequency pulsating sinusoidal voltage injection rotary reference frame is proposed. Firstly, in order to solve
method. (b) Improved high-frequency pulsating sinusoidal voltage the problem that the conventional high-frequency voltage
injection method.
injection method is not suitable for motor with no obvious
D. OBSERVATION EXPERIMENT OF ROTOR POSITION
salient pole effect, a method of extracting high-frequency
OF MOTOR IN SUDDEN CHANGE OF STEERING
current response signal in α-β two-phase stationary refer-
Fig.15 and Fig.16 respectively show the experimental wave- ence frame is proposed. Then, based on the improved high-
forms of the rotor position when the motor steering abruptly frequency pulsating sinusoidal voltage injection method, this
changes with the conventional high-frequency pulsating sinu- paper adopts the method that the static two-phase current
soidal voltage injection method and the improved high- lαh and iβh have modulated directly. Only the low-pass filter
frequency pulsating sinusoidal voltage injection method at is required to obtain the signal containing the rotor posi-
the speed of 100rpm. tion information, and the band-pass filter is omitted, which
It can be seen from the experimental waveform that the simplifies the system structure and eliminates the effects
two high-frequency injection methods can effectively observe of bandpass filters on signal amplitude and phase. Finally,
the rotor position information under the condition of sud- experiments show that the dynamic steady state performance
den change of the steering. The conventional high-frequency of this method is better than the previous method.
pulsating sinusoidal voltage injection method has an angular
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