IEEJ Journal of Industry Applications

Vol.1 No.1 pp.15–23 DOI: 10.1541/ieejjia.1.15

Paper

Sensorless Control of IPMSM: Past, Present, and Future

Seung-Ki Sul∗a) Member, Sungmin Kim∗ Non-member

(Manuscript received Jan. 5, 2012, revised Feb. 24, 2012)

This paper presents the history of techniques used for sensorless control of the Interior Permanent Magnet Syn-
chronous Machine (IPMSM) over the last 20 years. The techniques used in the first stage were based on the equivalent
circuit of the IPMSM. They extracted rotor position information from the back EMF estimated through simple arith-
metic. In the last 10 years, model reference adaptive control or observer-based control techniques have evolved and
they have been used for the sensorless control of the IPMSM; however, the rotor position continues to be obtained from
the back EMF. Simultaneously, sensorless control based on the magnetic saliency of the IPMSM has been achieved
and commercialized. In this paper, an evaluation of the major techniques used for the sensorless control of the IPMSM
has been presented, and their limitations have been clarified. Finally, the direction of future development of sensorless
control is indicated.

Keywords: IPMSM, sensorless control

a simple operating principle, the torque density of IPMSM

1. Introduction is considerably higher than that of the general-purpose in-
Since the early 1980s, with the development of high- duction motor. The torque density per unit volume is 30%
performance rare-earth permanent magnets, the Interior Per- higher and the torque density per unit weight is 25% higher
manent Magnet Synchronous Motor (IPMSM) has evolved. in the power range of several tens of kilowatt, for operation
It was first used in high-performance servo drive and has re- in near 1800 r/min. Further, the efficiency of the IPMSM is
cently been used in general-purpose industrial drives (1) . From 7% higher than that of the high-efficiency premium induc-
the 1990s, because of the soaring of cost of electricity, the tion motor and 10% higher than that of the standard general-
IPMSM has been considered as a candidate that could re- purpose induction motor. Hence, recently, IPMSMs with rat-
place the induction motor. The induction machine has many ings exceeding 500 hp have been used to replace the induc-
merits, for example, it is mechanically robust, has low cost, tion machine in general industrial applications such as hoist
is technically mature, and can be designed to have differ- operation. However, in making the replacement, the position
ent speeds, torques, and shapes. However, because of the sensor of the IPMSM has been of concern (4) . Even though
magnetizing current, its efficiency is poorer than that of a the IPMSM is mechanically robust and has a small size, the
permanent-magnet-based motor, especially at a low load fac- position sensor increases the axial length of the IPMSM and
tor (2) . At the early stage of development of permanent mag- results in reduced torque density per unit volume. Further-
net motor, Surface mounted Permanent Magnet Synchronous more, the sensor can adversely affect the robustness of the
Motor (SPMSM) has been designed and applied to high per- IPMSM, both electrically and mechanically. To overcome
formance servo application, where the control performance these problems, position sensorless drive techniques for the
is the first concern. However, IPMSM has several merits IPMSM have been studied over the last two decades, and
compared to SPMSM, namely smaller size of magnet, eas- some of them have been commercialized and used for indus-
ier detention of magnet, less eddy current in magnet, and trial purposes (5) (6) . Still, the performance of the sensorless
possibility of flux weakening control (3) . Even though the drive of the IPMSM is limited. Some commercialized tech-
control of the IPMSM is complex because of the reluctance niques had shown reasonable performances in overall oper-
torque associated with the saliency of the magnetic struc- ating conditions except low speed/low frequency region. For
ture of the rotor, the IPMSM has been used in many indus- last ten years, sensorless drive techniques based on high fre-
trial applications. In some applications, a general-purpose quency signal injection methods have been evolved. Those
IPMSM has been used as the Surface-Mounted Permanent techniques can guarantee the reasonable torque control per-
Magnet Synchronous Machine, where the d-axis current is formance even at zero speed/zero frequency. An overview of
set to be zero, for easier implementation of the control algo- the sensorless control techniques of the IPMSM developed
rithm at the cost of the reluctance torque. Even under such for last two decades are described in this paper, and the merit
and the demerit of typical technique are discussed. Based on
a) Correspondence to: Seung-Ki Sul. E-mail: sulsk@plaza.snu. the discussion, the direction of future development of sensor-
ac.kr less control technique for the IPMSM could be enlightened.
∗
Seoul National University Power Electronics Center (SPEC),
Department of Electrical Engineering and Computer Science, 2. Past
Seoul National Univeristy
599, Gwanangno, Gwanak-gu, Seoul 151-744, Korea The sensorless control of the IPMSM had been studied for


c 2012 The Institute of Electrical Engineers of Japan. 15
 Sensorless Control of IPMSM: Past, Present, and Future（Seung-Ki Sul et al.）

Fig. 2. Voltage plane in stationary frame, rotor refer-

ence frame, and estimated rotor reference frame

Fig. 1. Analytical model of Interior Permanent Magnet

Synchronous Machine

several decades but the major publications have been reported Fig. 3. Angle error correction controller based on PI
regulator
from early of 1990’s (7) (8) . The information of the rotor posi-
tion is included in the back EMF as shown in Fig. 1.
The back EMF can be calculated in the stationary frame the position error can be directly derived as (4).
model of the IPMSM or in the estimated rotor reference  
frame. The technique based on back EMF presents good −1 ω̂r λ f sin θ̃r
θ̃r = tan · · · · · · · · · · · · · · · · · · · · · · · · · (4)
performance in the middle and high speed operating region ω̂r λ f cos θ̃r
of the IPMSM. And it is commercialized by many compa-
nies. The performance above 10% of the rated speed with Because of the assumption of the steady state ignoring the
rated load in motoring and generating operation is quite sat- variation of current, this direct calculation is not suitable to
isfactory and acceptable for the most of low end drive ap- estimate the position error when the current varies rapidly
plication. The bandwidth of the speed regulation loop can according to the load torque disturbance or torque reference
be extended more than several Hz. However, at standstill change. Hence, the control bandwidth is limited. This short-
or very low rotating speed, because the magnitude of the coming can be lessened by employing the closed loop state
back EMF is proportional to the rotating speed, the signal observer (13) . From (1), under the assumption of slow enough
is too weak to be used as the position information and the variation of back EMF at the estimated rotor reference frame,
signal is easily contaminated by the measurement noises or a state equation augmenting back EMF voltage, êr̂ds , êr̂qs can
the nonlinear effects of PWM inverter. To enhance the per- be formulated as (5) and (6). And the angle error can be ob-
formance of the sensorless control at lower operating speed, tained as like (4).
Model Reference Adaptive Control (MRAC) and/or closed x̂˙ = A x̂ + Bu + L (y − c x̂)
observer has been applied (9) (10) . And simultaneously, several ⎡ R ω̂r Lqs ⎤
⎢⎢⎢ − s 1 ⎥⎥⎥ ⎡ r̂ ⎤
careful dead time compensation methods had been incorpo- ⎢⎢⎢⎢ Lds L L
0 ⎥⎥⎥ ⎢⎢⎢ îds ⎥⎥⎥
⎥⎥ ⎢⎢ ⎥⎥
⎢⎢⎢ ds ds
1 ⎥⎥⎥⎥⎥ ⎢⎢⎢⎢⎢ îr̂qs ⎥⎥⎥⎥⎥
rated (11) (12) . With these refinements the controllable speed can
⎢⎢⎢ −ω̂r Lds Rs
be down to a few percent of the rated speed and the control = ⎢⎢⎢ − ⎥⎢ ⎥
Lqs ⎥⎥⎥⎥⎥ ⎢⎢⎢⎢⎢êr̂ ⎥⎥⎥⎥⎥
0
bandwidth can be extended up to 10 Hz. ⎢⎢⎢ Lqs Lqs
⎢⎢⎢ ⎥ ⎢ ds ⎥
All back EMF based sensorless control techniques are ⎢⎢⎣ 0 0 0 0 ⎥⎥⎥⎥⎦ ⎢⎣êr̂ ⎥⎦
qs
based on the following voltage equation of the IPMSM. 0 0 0 0
⎡ 1 ⎤
⎫
dir̂ds ⎪
⎪
⎢⎢⎢
⎢⎢⎢ L 0 ⎥⎥⎥⎥
vds = R s ids + Lds
r̂ r̂
− ω̂r Lqs iqs − ω̂r λ f sin θ̃r ⎪
r̂ ⎪
⎪ ⎢⎢⎢ ds ⎥⎥⎥
dt ⎪
⎪
⎬ ⎢⎢⎢ ⎥⎥⎥⎥ ⎡⎢vr̂ ⎤⎥
⎪
⎪ + ⎢⎢⎢ 0 ⎢ 1 ⎥⎥⎥ ⎢⎢⎢⎢ ds ⎥⎥⎥⎥ + L (y − ŷ) · · · · · · · · · · · · · (5)
r̂
diqs ⎪
⎪
⎪
⎪ ⎢⎢⎢ Lqs ⎥⎥⎥⎥⎥ ⎣vr̂qs ⎦
vqs = R s iqs + Lqs
r̂ r̂
+ ω̂r Lds ids + ω̂r λ f cos θ̃r ⎪
r̂ ⎭ ⎢⎢⎢
0 ⎥⎥⎥⎥⎦
⎥
dt ⎢⎢⎣ 0
· · · · · · · · · · · · · · · · · · · · (1) 0 0
⎡ r̂ ⎤  
⎢⎢îds ⎥⎥
ŷ = ⎢⎢⎢⎣ r̂ ⎥⎥⎥⎦ =
where the voltages and currents are measured in the estimated 1 0 0 0
x̂ = C x̂ · · · · · · · · · · · · · · · (6)
rotor reference frame. And the error between the real rotor îqs 0 1 0 0
position and the estimated rotor position is defined by (2) as
shown in Fig. 2. Also, the direct update of angle error is vulnerable to mea-
surement noise and parameter errors. And the estimated ro-
θ̃r = θr − θ̂r · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (2) tor angle can be updated through angle error correction con-
troller based on PI regulator as shown in Fig. 3, where the ro-
êr̂ds = −ω̂r λ f sin θ̃r ≈ vr̂ds − R s ir̂ds + ω̂r Lqs ir̂qs tational speed can be obtained as a byproduct. The controller
· · · · · · · (3)
êr̂qs = ω̂r λ f cos θ̃r ≈ vr̂qs − R s ir̂qs − ω̂r Lds ir̂ds is a kind of the state filter.
These back EMF based sensorless methods estimate the
Under the assumption of the steady-state operation, the rotor position and speed from the stator voltage and cur-
back EMF voltage can be estimated simply by (3). Then, rents. With these basic ideas, many different implementation

16 IEEJ Journal IA, Vol.1, No.1, 2012

 Sensorless Control of IPMSM: Past, Present, and Future（Seung-Ki Sul et al.）

techniques have been reported. Some are based on the esti-

mation of the back EMF voltage from the permanent magnet
flux linkage using a state observer or a Kalman filter (14) (15) .
Others use the voltage or current error between the measured
values and the calculated values in the estimated rotor po- (a) voltage model
sition (16)–(18). In Ref. (16), the concept of an Extended EMF
is proposed to simplify the estimation of the back EMF. By
applying the Extended EMF concept, many approximations
to estimate the back EMF are eliminated. Because of the
difference of d-axis inductance and q-axis inductance of the
(b) current model
IPMSM, the voltage equation in the estimated rotor reference
Fig. 4. Block diagram of voltage and current model
frame is complex. While, with Extended EMF, all inductance based sensorless control
saliency related terms are moved to the Extended EMF terms
in voltage equations. Then the modified voltage equation in
the estimated rotor reference frame can be simple and the sen-
sorless algorithm can be applied easily. The modified voltage
equation can be described as (7) with Extended EMF such as
(8) at real rotor position:
dirds Fig. 5. Representative block diagram of sensorless con-
vrds = R s irds + Lds − ωr Lqs irqs trol technique based on Back EMF
dt
· · · · · · · · · · · (7)
dirqs
vrqs = R s irqs + Lds + ωr Lqs irds + Eex
dt But, theoretically, all techniques would not work at zero fre-
     dirqs quency, where back EMF does not exist. Practically, in the
Eex = ωr Lds − Lqs irds + λ f − Lds − Lqs case of a few kW or above rated power of the IPMSM, be-
dt
· · · · · · · · · · · · · · · · · · · · (8) cause back EMF is always estimated from the terminal volt-
age and current information, the technique would not work
In a different approach, the estimated voltage/current dif- at lower than 1% of the rated speed even with careful param-
ference with the actual voltage/current can be used for ex- eter adaptation and dead time compensation. In the most of
tracting the position error (17) . If the model is exact with the applications of drive where the induction motor was replaced
actual motor, the voltage and/or current can be calculated ex- by the IPMSM, torque and speed control range down to a few
actly. However, if there are differences between the actual percents of the rated speed would be enough. However, some
voltage and/or current and the calculated ones based on the application where speed and/or torque should be controlled
model, it can be understood that there is the position error be- absolutely from standstill, that is, zero speed, the back EMF
tween the actual position and the estimated position. There- based techniques cannot be used.
fore, from the voltage and/or current difference, the position
3. Present
error can be estimated. This method can be implemented
based on the machine voltage model and the machine cur- The rotor position of the IPMSM can be estimated from
rent model, respectively. In the voltage model, the calculated the characteristics of the IPMSM: the spatial inductance dis-
voltage based on the voltage model is compared with the volt- tribution is determined by the rotor position because of the
age reference of the current control loop. The difference be- saliency of the magnetic path of d and q axis as shown in
tween the calculated voltage and the voltage reference can be Fig. 6. The saliency comes from the difference of magnetic
used as a position correction value as Fig. 4(a). In the current permeability of the core and permanent magnet.
model, the calculated current and the measured current are To extract the spatial inductance variation, the relationship
compared to get the position error values as Fig. 4(b). These between current and voltage can be employed. To examine
error values can be used as correction value to the state filter the current-voltage relationship, PWM current ripple can be
or observer. used (19)–(22). By measuring current variation according to the
Unlike the back EMF estimation or model based meth- voltage vector variation in a PWM period, inductance can be
ods, the voltage reference of current controller can be di- calculated directly (19)–(21) or estimated with a non-linear esti-
rectly used as the position error related values (18) . In these mator (22) . However, these techniques require the modifica-
machine model based sensorless techniques, the machine pa- tion of PWM switching pattern, because the current varia-
rameters such as resistance, inductance, and the permanent tion in the conventional SVPWM is too small to be used for
magnet flux linkage have critical effects on the position esti- the calculation of the inductance. And additional devices to
mation performance. measure the phase currents in arbitrary time should be de-
Even though there are so many variations of sensor- signed in control hardware, which might not be acceptable to
less control techniques based on back EMF voltage for the many industry applications. Similarly, the intended discon-
IPMSM, the techniques can be represented as a block dia- tinuous voltage signal injected method has been proposed (23) .
gram in Fig. 5. The design of each block might be differ- In Ref. (23), large voltage signal is injected for very short
ent according to the specific sensorless control technique. time interval and the current variation by the injected volt-
And, the performance of each technique may be different. age signal is measured. From measured current variation, the

17 IEEJ Journal IA, Vol.1, No.1, 2012

 Sensorless Control of IPMSM: Past, Present, and Future（Seung-Ki Sul et al.）

Fig. 8. Block diagram of the heterodyning demodula-

tion process
Fig. 6. Typical lay-out of the IPMSM and d-q axis of
rotor reference frame actually differs from the ideal injection voltage. The injection
voltage in the estimated rotor reference frame can be rewrit-
ten with consideration of the estimated rotor position error as
(9).
 
cos ωh t
vr̂∗
dqsh = Vin j · · · · · · · · · · · · · · · · · · · · · · · · · · · · (9)
0
Considering the position error, the actual injection voltage
signal into the real rotor reference frame can be described as
(10).
⎡ ⎤
  ⎢⎢⎢ cos θ̃r cos ωh t ⎥⎥⎥
Fig. 7. Magnitude of current ripple according to the in- vrdqsh = T θ̃r vr̂∗ dqsh = Vin j ⎣ ⎢ ⎥⎦ · · · · · · · (10)
jected continuous high frequency pulsating sinusoidal − sin θ̃r cos ωh t
voltage signal at different rotor position to the stator  
where T θ̃r stands for the transformation from estimated ro-
tor reference frame to real rotor reference frame. Then, the
inductance and rotor position can be estimated. From this corresponding current response in the estimated rotor refer-
method, however, the rotor position information can be dis- ence frame can be deduced as (11).
continuously obtained, and the rotor position estimation and ⎡ r̂ ⎤ ⎡ ⎤
⎢⎢⎢idsh ⎥⎥⎥  −1 ⎢⎢irdsh ⎥⎥
the overall control performance could be degraded. ⎢⎢⎣ r̂ ⎥⎥⎦ = T θ̃r ⎢⎢⎢⎣ r ⎥⎥⎥⎦
From the late of 1990’s, the continuous signal injection iqsh iqsh
methods without PWM modification have been proposed, ⎡ 2  ⎤
⎢⎢⎢ cos θ̃r sin2 θ̃r ⎥
and the signal can be easily augmented into the conventional ⎢⎢⎢ + sin ωh t⎥⎥⎥⎥
Vin j ⎢⎢⎢ Lds Lqs ⎥⎥⎥⎥
current control loop (24)–(31). The continuous voltage signals = ⎢⎢⎢⎢   ⎥⎥⎥⎥ · · · · · · · (11)
into the IPMSM causes the current ripple, which reflects rotor ωh ⎢⎢ 1 −ΔL ⎥⎥
⎢⎣ sin 2θ̃r sin ωh t ⎥⎦
position as shown in Fig. 7. 2 Lds Lqs
From the corresponding current ripple, the rotor position
information can be extracted with a properly designed ob- As it can be seen from (11), the rotor position error is
server and/or a state filter. For each signal injection sensor- placed in the estimated q-axis current response. To sepa-
less method, demodulation process should be incorporated to rate the position error from the estimated q-axis current re-
extract the rotor position related value from current ripple. sponse, demodulation processes have been employed gener-
These continuous signal injection sensorless methods can be ally. Among the various demodulation processes, the het-
further classified into two categories according to where the erodyning demodulation process is the most well known
signal is injected: the rotating voltage signal injection in the method (24) . Fig. 8 shows the simple heterodyning demodu-
stationary reference frame (24)–(30) and the pulsating voltage sig- lation process. Using this process, the position error can be
nal injection in the estimated rotor reference frame (24)–(29). The extracted from the q-axis current response. The final result
rotating voltage signal technique injects the continuous volt- of the demodulation process from the method in Fig. 8, ε f ,
age signal spatially regardless of the rotor position, and the can be derived as (12) under the assumption that the error be-
pulsating voltage signal technique injects the continuous pul- tween the real rotor position and the estimated one is small.
 
sating voltage signal on the estimated rotor position. The 1 Vin j −ΔL  
pulsating signal injection technique is more robust to local εf ≈ θr − θ̂r · · · · · · · · · · · · · · · · · · · (12)
2 ωh Lds Lqs
saliency, which may occur from the design of the IPMSM,
especially in the case of concentrated winding. Moreover, the And, the demodulation process result, ε f , can be used as a
loss of the pulsating signal injection due to the injected sig- corrective error input to observer or state filter in Fig. 9. One
nal is a half of that of the rotating voltage signal method, and of the typical implementations of the block diagram in Fig. 9,
the temperature of the magnet of the motor would be lower which had been commercialized, is shown in Fig. 10 (26) . In
in pulsating signal injection (32)–(34) . this implementation, the measurement axis was introduced
If the pulsating voltage signal is injected into the exact d- and the current at this axis was used for the demodulation. A
axis rotor reference frame, q-axis current ripple due to the simple PI type state filter was used instead of observer as an
injected voltage does not happen. However, because the ex- angle correction controller.
act rotor position is not available, the injection voltage signal In this technique, because of number of filters, namely low

18 IEEJ Journal IA, Vol.1, No.1, 2012

 Sensorless Control of IPMSM: Past, Present, and Future（Seung-Ki Sul et al.）

Fig. 12. Demodulation process with the square wave

signal injection
Fig. 9. Control block diagram of general pulsating
signal injection techniques

(a) Speed control (b) Position control

Fig. 13. Speed and position control performance with
the square signal injection to estimated d axis (11 kW 6
pole general purpose IPMSM)

With the injection signal in Fig. 11, the demodulation pro-

cess can be simplified as shown in Fig. 12 and there is no low
Fig. 10. Control block diagram of pulsating signal pass filter. On the top of easy tuning of the controller, the
injection technique speed control bandwidth with this technique can be extended
up to 25 Hz as shown in Fig. 13(a) with an off-the-shelf
11 kW general purpose IPMSM thanks to no signal delay of
low pass filters. The estimated speed (Wrpm est) through the
injected signal tracks the reference speed (Wrpm ref) better
than the speed from encoder (Wrpm enc) at near zero speed.
The speed from encoder has bumps at near zero speed due
to the limited number of pulse per revolution (1024 pulses in
here) and the sampling time (1 ms in here). From Fig. 13(b),
the position control bandwidth can be understood as 5 Hz.
The signal injection technique is effective for position and
speed estimation in ultra-low speed region including zero sta-
Fig. 11. Triangular carrier wave and square wave tor frequency. However, due to the signal injection, the torque
injected signal at estimated d axis ripple and the acoustic noise at the injected signal frequency
are inevitable. Furthermore, the additional voltage to inject
pass filters, and band pass filter, the tuning of the filters are the signal, which may be several tens of percent of the rated
difficult and the control bandwidth is limited due to the sig- voltage of the IPMSM, would be prohibitive in the medium
nal delays of the filters. With this implementation, the speed or higher speed operation region of the IPMSM where the
control bandwidth has been limited to less than 10 Hz in the voltage from PWM inverter is already near rated value. As
case of general purpose IPMSM drive. mentioned in chapter 2 of this paper, because the back EMF
To improve the speed control bandwidth, a different imple- based technique is able to estimate position and speed with-
mentation method has been reported (27)–(29) . A square wave out acoustic and additional torque ripple above 10% of the
signal was injected synchronously to the triangular carrier rated speed, a hybrid method can be employed as shown in
wave of PWM of inverter as shown in Fig. 11, and the in- Fig. 14, where the high frequency signal injection (HFSI)
jection frequency was increased up to a half of switching fre- technique is used at lower speed and back EMF technique
quency. With the injected signal, the current in the stationary at higher speed (35) . The key idea in here is the changeover
d and q axis reference frame can be represented as (13). which is done only based on the internal speed ω̂cmb . The
internal speed ω̂cmb consists of the estimated speed of both
⎡ ⎤
⎡ s ⎤ ⎢⎢⎢ 1 cos(θr ) sin ωh t⎥⎥⎥ techniques. The internal estimated speed is set as (14).
⎢
⎢⎢⎢⎢idsh ⎥⎥⎥⎥ ⎢⎢⎢ Lds ωh ⎥⎥⎥  
⎢⎣ s ⎥⎦ ≈ ⎢⎢⎢ ⎥⎥⎥ ∵ θ̃ ≈ 0 ω̂cmb = ω̂0 + G1 · ω̂BE MF + G2 · ω̂HFS I · · · · · · · · · · (14)
⎢⎣⎢ 1 ⎥⎥ r
sin(θr ) sin ωh t ⎦⎥
iqsh
Lds ωh where ω̂0 is given by direct calculation from estimated back
· · · · · · · · · · · · · · · · · · · (13) EMF voltage, ω̂BE MF is a kind of the correction control term

19 IEEJ Journal IA, Vol.1, No.1, 2012

 Sensorless Control of IPMSM: Past, Present, and Future（Seung-Ki Sul et al.）

Fig. 15. Injected signal and second other harmonic

signal for initial position identification

Fig. 14. Position and speed estimator with a hybrid

method

to make the angle error ε̂ null, and G1 and G2 are weight-

ing factors. The weighting factors are regulated along with
the command and/or the estimated speed. The internal esti-
mated speed ω̂cmd is only employed in the machine model of Fig. 16. Block diagram of signal processing for initial
pole position identification
the back EMF based method, and not employed to estimate
the position of the magnet flux. The position is estimated by
integration of the estimated speed ω̂r .
To get the rated torque with rated current at starting, the ini-
tial position should be identified. The variation of the magni-
tude of the ripple current due to inductance variation shown
in Fig. 7 reveals symmetry to the d axis in a half period of
rotor position. So, d axis (north pole of magnet) and −d axis
(south pole of magnet) in rotor reference frame of the IPMSM
cannot be differentiated from the variation of the magnitude
of the current ripple. So, another technique is needed for the
starting of the IPMSM with rated torque at rated current. The Fig. 17. Pulsating injection voltage signal in the esti-
north pole and south pole can be identified with the charac- mated rotor reference frame. In a PWM period, three
teristic of the magnetic saturation of the core due to the flux successively measured currents are used to estimate the
rotor position
linkage from the permanent magnet (36) (37) .
The d-axis second harmonic component of injected fre-
quency has polarity information as (15). eliminated. To reduce the acoustic noise, a signal injection
  technique whose frequency is PWM switching frequency has
ε pol ≡ LPF ir̂dsh cos 2ωh t · · · · · · · · · · · · · · · · · · · · · · (15) been proposed (31) . The injected voltage is shown in Fig. 17.
In this technique, the sampling of the current and updating
where LPF stands for Low Pass Filtering process and the cut
PWM is done twice in a PWM switching period. And, the
off frequency of the filter is one order less than injected sig-
sampling period, ΔT , is a half of PWM switching period. The
nal frequency. The injected signal is shown in Fig. 15 and a
difference between successively sampled currents at the esti-
block diagram of the signal processing for initial pole posi-
mated rotor reference frame has rotor position information as
tion identification is shown in Fig. 16. With this technique
seen from (16).
the initial pole position can be identified within 100 ms (28) .
⎡ r̂ ⎤ ⎡ ⎤
Generally, the frequency of injected voltage signal is deter- ⎢⎢⎢Δidsh ⎥⎥⎥  −1 ⎢Δir ⎥
mined between the current control bandwidth and the PWM ⎢⎢⎣ ⎥⎥⎦ = T θ̃r ⎢⎢⎢⎢⎣ dsh ⎥⎥⎥⎥⎦
Δir̂qsh Δirqsh
switching frequency. As the frequency of the injected sig-
⎡ ⎤
nal is getting higher, the dynamics of the sensorless control ⎢⎢⎢ cos2 θ̃r sin2 θ̃r ⎥⎥⎥
can be enhanced and the interference between the injected ⎢⎢⎢ + ⎥⎥⎥
⎢ L L ⎥⎥⎥
= ±ΔT · Vin j ⎢⎢⎢⎢  ds  qs ⎥⎥⎥ · · · · · (16)
signal and the fundamental components of the current con- ⎢⎢⎢ 1 1 1 ⎥
trol can be diminished (30) . If the PWM switching frequency ⎣ − sin 2θ̃r ⎥⎦
2 Lds Lqs
is near or above the audible frequency range, the acoustic
noise by injected signal can be remarkably reduced or totally Especially, q axis current can be used as the input of the

20 IEEJ Journal IA, Vol.1, No.1, 2012

 Sensorless Control of IPMSM: Past, Present, and Future（Seung-Ki Sul et al.）

demodulation process, ε f , as shown in Fig. 18. Thanks to Refs. (39) (40), the inherent or inserted stator or rotor bridges
the development of IGBT and DSP technology, the switch- in structurally symmetric machines generate saliency and can
ing frequency of recently announced PWM inverter can be be also used for sensorless control. In Ref. (41), machine
over 16 kHz, which is near the limit of human audible range. spatial saliency is analyzed with zigzag leakage flux concept
With this injection frequency, the audible noise can be vir- and the machine design rules for generating the inductance
tually eliminated at the cost of larger magnitude of injection saliency in the SPMSM was proposed.
voltage and a little increased loss due to the higher frequency With the introduction of commercial sensorless drive en-
injected signal. As shown in Fig. 19, with this signal injection abling zero speed operation, many IPMSM drives with posi-
technique, the electric rotor position error is less than 0.3 rad, tion sensor have been replaced with the sensorless drive. One
which means less than 0.1 rad error in mechanical angle with- of the typical examples is lift application, where the torque
out any position compensation in the case of 11 kW, 6 pole, control at zero speed to prevent roll back and shock at the
general purpose IPMSM. With careful compensation accord- starting of the cage of the lift is prerequisite. And in other ap-
ing to the torque and speed, the position error can be reduced plications where higher starting torque and less acceleration
further. time are key requirements, namely oil injected screw com-
With specially designed IPMSM for sensorless control, the pressor and injection molding machine, the sensorless drives
speed and position control bandwidth can be extended more increase reliability and reduce cost (42) .
than 50 Hz and 10 Hz, respectively as shown in Fig. 20. The
4. Future
flux density of the specially designed IPMSM is reduced and
it reveals better sinusoidal inductance variation according to Though the sensorless control techniques has been evolved
the rotor position at the cost of reduced torque density (38) . remarkably for last decades and the performance of the sen-
As the machine design technology developed, the SPMSM sorless drive is comparable to low end servo where the res-
which has inherently the isotropic inductance characteristics olution of encoder is less than a few hundreds per revolu-
can be also used for signal injection sensorless control. In tion, there are still number of problems to be solved. In some
IPMSMs, especially the machine with higher torque density
and wide flux weakening range, the variation of the induc-
tance according to the rotor position is not sinusoidal and the
position where minimum inductance occurs are moving ac-
cording to the stator current as shown in Fig. 21. This phe-
nomenon comes in many different forms. The position error
Fig. 18. Demodulation process with PWM switching
frequency signal injection

(a) no load condition

(a) Position control (25% load) (b) Position control (70% load)
Fig. 19. Electric rotor position control with 11 kW, 6
pole general purpose IPMSM. Electric rotor position ref-
erence varies from −2 rad to 2 rad. (a) 25% load condition
(b) 70% load condition

(b) 100% load condition

Fig. 21. Magnitude of current ripple according to the
(a) Speed control (b) Position control injected continuous high frequency pulsating sinusoidal
Fig. 20. Speed and position control performance with voltage signal at different rotor position to the stator
specially designed IPMSM for sensorless control (80 W (25 kW, concentrated winding, IPMSM for electric vehi-
6 pole IPMSM) cle traction application)

21 IEEJ Journal IA, Vol.1, No.1, 2012

 Sensorless Control of IPMSM: Past, Present, and Future（Seung-Ki Sul et al.）

between the real position and the estimated position has 2nd, induction motor using extended Kalman filter”, IEEE Trans. Ind. Applicat.,
6th, etc harmonics by this flux saturation (43) (44) . The flux den- Vol.30, No.5, pp.1225–1233 (1994-9/10)
( 15 ) S. Bolognani, L. Tubiana, and M. Zigliotto: “Extended Kalman filter tun-
sity of the IPMSM in the figure is increased to get higher ing in sensorless PMSM drives”, IEEE Trans. Ind. Applicat., Vol.39, No.6,
torque density and the stator employs concentrated winding pp.1741–1747 (2003-11/12)
to reduce axial length of the motor. The sensorless drive with ( 16 ) S. Morimoto, K. Kawamoto, M. Sanada, and Y. Takeda: “Sensorless control
strategy for salient-pole PMSM based on extended EMF in rotating reference
this type of the IPMSM is formidable target to achieve.
frame”, IEEE Trans. Ind. Appl., Vol.38, No.4, pp.1054–1061 (2002-7/8)
Though the control bandwidth has been improved several ( 17 ) N. Matsui: “Sensorless operation of brushless DC motor drives”, in Proc.
fold in the last decade, to apply the sensorless drive to high IEEE IECON’93, pp.739–744 (1993)
grade control purpose, the bandwidth should be improved at ( 18 ) B.-H. Bae, S.-K. Sul, J.-H. Kwon, and J.-S. Byeon: “Implementation of
sensorless vector control for super-high-speed PMSM of turbo-compressor”,
least a few times more. To achieve this control bandwidth, IEEE Trans. Ind. Applicat., Vol.39, No.3, pp.811–818 (2003-5/6)
the design of the IPMSM itself and all signal processing tech- ( 19 ) A.B. Kulkarni and M. Ehsani: “A novel position sensor elimination technique
niques especially careful compensation of all nonlinearity of for the interior permanent-magnet synchronous motor drive”, IEEE Trans.
PWM inverter and measurement system should be incorpo- Ind. Applicat., Vol.28, No.1, pp.144–170 (1992-1/2)
( 20 ) S. Ogasawara and H. Akagi: “Implementationand position control perfor-
rated simultaneously (45) . mance of a position-sensorless IPM motor drive system based on magnetic
With the high frequency signal injection, the rotor position saliency”, IEEE Trans. Ind. Applicat., Vol.34, pp.806–812 (1998-7/8)
can be identified from standstill. However, because the iden- ( 21 ) M. Mamo, K. Ide, M. Sawamura, and J. Oyama: “Novel rotor position ex-
traction based on carrier frequency component method (CFCM) using two
tified position is in electrical angle, the absolute position of
reference frames for IPM drives”, IEEE Trans. Ind. Electron., Vol.52, No.5,
the rotor is not yet identified except 2 poles IPMSM, which pp.508–514 (2005-4)
is rarely used in the field. For some application such as tool ( 22 ) V. Petrovic, A.M. Stankovic, and V. Blasko: “Position estimation in salient
changer or robot manipulator, absolute position information PM synchronous motors based on PWM excitation transients”, IEEE Trans.
Ind. Applicat., Vol.39, No.3, pp.835–843 (2003-5/6)
of the rotor is prerequisite. In this case, still the identifica- ( 23 ) M. Schroedl: “Sensorless control of AC machine at low speed and standstill
tion and control of the absolute position of the rotor is an based on the ‘INFORM’ method”, in Conf. Rec. IEEE-IAS Annu. Meeting,
open question. The special design of the rotor and stator of pp.270–277 (1996)
the IPMSM together with novel signal processing technol- ( 24 ) P.L. Jansen and R.D. Lorenz: “Transducerless position and velocity esti-
mation in induction and salient AC machines”, IEEE Trans. Ind. Applicat.,
ogy might open new horizon of the sensorless control of the Vol.31, No.2, pp.240–247 (1995-3/4)
IPMSM in absolute positioning. ( 25 ) M.J. Corley and R.D. Lorenz: “Rotor position and velocity estimation for a
salient-pole permanent magnet synchronous machine at standstill and high
speeds”, IEEE Trans. Ind. Applicat., Vol.34, No.4, pp.784–789 (1998-7/8)
References ( 26 ) J.-I. Ha and S.-K. Sul: “Sensorless field-orientation control of an induction
machine by high-frequency signal injection”, IEEE Trans. Ind. Applicat.,
Vol.35, No.1, pp.45–51 (1999-1/2)
(1) D.W. Novotny and T.A. Lipo: “Vector control and dynamics of AC drives”, ( 27 ) R. Leidhold and P. Mutschler: “Improved method for higher dynamics in sen-
Clarendon Press, Oxford (1996) sorless position detection”, in Proc. IEEE IECON2008, pp.1240–1245 (2008)
(2) H. Murakami, Y. Honda, H. Kiriyama, S. Morimoto, and Y. Taketa: “The ( 28 ) Y.-D. Yoon, S.-K. Sul, S. Morimoto, and K. Ide: “High bandwidth sensorless
performance comparison of SPMSM, IPMSM and SynRM in use as air- algorithm for AC machines based on square-wave-type voltage injection”,
conditioning compressor”, in Proc. IEEE IAS Annual Meeting, pp.840–845 IEEE Trans. Ind. Applicat., Vol.47, No.3, pp.1361–1370 (2011-5/6)
(1999) ( 29 ) R. Masaki, S. Kaneko, M. Hombu, T. Sawada, and S. Yoshihara: “Develop-
(3) K. Akatsu, K. Narita, Y. Sakashita, and T. Yamada: “Characteristics compar- ment of a position sensorless control system on an electric vehicle driven by
ison between SPMSM and IPMSM under high flux density condition by both a permanent magnet synchronous motor”, in Proc. IEEE PCC Osaka 2002,
experimental and analysis results”, in Proc. ICEMS, pp.2848–2853 (2008) Vol.2, pp.571–576 (2002)
(4) P. Vas: “Sensorless vector and direct torque control”, Oxford (1998) ( 30 ) S. Kim, Y.-C. Kwon, S.-K. Sul, J. Park, and S.-M. Kim: “Position sensorless
(5) G. Lee, W.-J. Lee, J. Ahn, and D. Cheong: “A simple sensorelss algorithm for operation of IPMSM with near PWM switching frequency signal injection”,
an interior permanent magnet synchronous motor using a flux observer.pdf”, in Proc. of ICPE2011-ECCE Asia (2011)
in Proc. of ICPE2011-ECCE Asia (2011) ( 31 ) S. Kim, J.-I. Ha, and S.-K. Sul: “PWM switching frequency signal injection
(6) P.P. Acarnley and J.F. Watson: “Review of position-sensorless operation of sensorless method in IPMSM”, in Proc. of ECCE, pp.3021–3028 (2011)
brushless permanent-magnet machines”, IEEE Trans. Ind. Electron., Vol.53, ( 32 ) F. Briz, M.W. Degner, P. Garcia, and R.D. Lorenz: “Comparison of saliency-
No.2, pp.352–362 (2006-4) based sensorless control techniques for AC machines”, IEEE Trans. Ind. Ap-
(7) M. Schroedl: “Operation of the permanent magnet synchronous machine plicat., Vol.40, No.4, pp.1107–1115 (2004-7/8)
without a mechanical sensor”, in Proc. Power Electronics and Variable-Speed ( 33 ) F. Briz, M.W. Degner, A. Diez, and R.D. Lorenz: “Static and dynamic behav-
Drives, pp.51–56 (1990) ior of saturation-induced saliencies and their effect on carrier-signal-based
(8) N. Matsui, T. Takeshita, and K. Yasuda: “A new sensorless drive of brushless sensorless AC drives”, IEEE Trans. Ind. Applicat., Vol.38, No.3, pp.670–678
DC motor”, in Proc. IEEE IECON’92, pp.430–435 (1992) (2002-5/6)
(9) R.B. Sepe and J.H. Lang: “Real-time observer-based (adaptive) control of ( 34 ) D.D. Reigosa, F. Briz, M.W. Degner, P. Garcia, and J.M. Guerrero: “Tem-
a permanent-magnet synchronous motor without mechanical sensors”, IEEE perature issues in saliency-tracking-based sensorless methods for PM syn-
Trans. Ind. Applicat., Vol.28, No.6, pp.1345–1352 (1992-11/12) chronous machines”, IEEE Trans. Ind. Applicat., Vol.47, No.3, pp.1352–
( 10 ) A. Piippo, M. Hinkkanen, and J. Luomi: “Analysis of an adaptive observer 1360 (2011-5/6)
for sensorless control of interior permanent magnet synchronous motors”, ( 35 ) K. Ide, H. Iura, and M Inazumi: “Hybrid sensorless control of IPMSM Com-
IEEE Trans. Ind. Electron., Vol.55, No.2, pp.570–576 (2008-2) bining high frequency injection method and back EMF method”, in Proc. of
( 11 ) N. Hur, K. Hong, and K. Nam: “Sensorless vector control in the presence of IECON, pp.2236–2241 (2010)
voltage and current measurement errors by dead-time”, in Proc. IEEE IAS ( 36 ) Y. Jeong, R.D. Lorenz, T.M. Jahns, and S.-K. Sul: “Initial rotor position esti-
Annual Meeting, pp.433–438 (1997) mation of an interior permanent-magnet synchronous machine using carrier-
( 12 ) Y. Inoue, K. Yamada, S. Morimoto, and M. Sanada: “Effectiveness of voltage frequency injection methods”, IEEE Trans. Ind. Applicat. (2005-1/2)
error compensation and parameter identification for model-based sensorless ( 37 ) J.-I. Ha, K. Ide, T. Sawa, and S.-K. Sul “Sensorless rotor position estimation
control of IPMSM”, IEEE Trans. Ind. Applicat., Vol.45, No.1, pp.213–221 of an interior permanent-magnet motor from initialstates”, IEEE Trans. Ind.
(2009-1/2) Applicat., Vol.39, No.3, pp.761–767 (2003-5/6)
( 13 ) Y.-C. Son, B.-H Bae, and S.-K Sul: “Sensorless operation of permanent mag- ( 38 ) S. Murakami, M. Hisatsune, T. Shiota, M. Ohto, and K. Ide: “Encoderless
net motor using direct voltage sensing circuit”, in Proc. IEEE IAS, pp.1674– servo drive with adequately designed IPMSM for pulse voltage injection
1678 (2002) based position detection”, in Proc. of ECCE, pp.3013–3020 (2011)
( 14 ) Y.-R. Kim, S.-K. Sul, and M.-H. Park: “Speed sensorless vector control of ( 39 ) J.-I. Ha: “Analysis of inherent magnetic position sensors in symmetric AC

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 Sensorless Control of IPMSM: Past, Present, and Future（Seung-Ki Sul et al.）

machines for zero or low speed sensorless drives”, IEEE Trans. Magn., Sungmin Kim (Non-member) was born in Seoul, Korea in 1980. He
Vol.44, No.12, pp.4689–4696 (2008-12) received the B.S. and M.S. degrees in electrical engi-
( 40 ) J.-H. Jang, S.-K. Sul, J.-I. Ha, K. Ide, and M. Sawamura: “Sensorless drive neering from Seoul National University, Seoul, Ko-
of surface-mounted permanent-magnet motor by high-frequency signal injec- rea, in 2002, 2008, respectively, where he is currently
tion based on magnetic saliency”, IEEE Trans. Ind. Applicat., Vol.39, No.4, pursuing the Ph.D. degree. His current research in-
pp.1031–1039 (2003-7/8)
terests are power electronics control of electric ma-
( 41 ) S.-C. Yang, T. Suzuki, R.D. Lorenz, and T.M. Jahns “Surface-permanent-
chines, sensorless drives, matrix converter drive, and
magnet synchronous machine design for saliency-tracking self-sensing posi-
power conversion circuits.
tion estimation at zero and low speeds”, IEEE Trans. Ind. Applicat., Vol.47,
No.5, pp.2103–2116 (2011-9/10)
( 42 ) S. Sato, H. Iura, K. Ide, and S.-K. Sul: “Three years of industrial experience
with sensorless IPMSM drive based on high frequency injection method”, in
Proc. of Sensorless Control for Electrical Drives (SLED), pp.74–79 (2011)
( 43 ) D.D. Reigosa, P. Garcia, D. Raca, F. Briz, and R.D. Lorenz: “Measure-
ment and adaptive decoupling of cross-saturation effect and secondary salien-
cies in sensorless controlled IPM synchronous machines”, IEEE Trans. Ind.
Applicat., Vol.44, No.6, pp.1758–1767 (2008-11/12)
( 44 ) M.W. Degner, and R.D. Lorenz: “Using multiple saliencies for the estimation
of flux, position, and velocity in AC machines”, IEEE Trans. Ind. Applicat.,
Vol.34, No.5, pp.1097–1104 (1998-9/10)
( 45 ) P. Garcia, F. Briz, M.W. Degner, and D.D. Reigosa: “Accuracy, bandwidth,
and stability limits of carrier-signal-injection-based sensorless control meth-
ods”, IEEE Trans. Ind. Applicat., Vol.43, No.4, pp.990–1000 (2007-7/8)

Seung-Ki Sul (Member) was born in Korea in 1958. He received

the B.S., M.S., and Ph.D. degrees in electrical engi-
neering from Seoul National University, Seoul, Ko-
rea, in 1980, 1983, and 1986, respectively. From
1986 to 1988, he was an Associate Researcher with
the Department of Electrical and Computer Engineer-
ing, University of Wisconsin, Madison. From 1988
to 1990, he was a Principal Research Engineer with
Gold-Star Industrial Systems Company. Since 1991,
he has been a member of the faculty of the Depart-
ment of Electrical Engineering and Computer Science, Seoul National Uni-
versity, where he is currently a Professor. From 2005 to 2007, he was the
Vice Dean of College of Engineering, Seoul National University. From 2008
to 2011, he was the President of Korea Electrical Engineering & Science
Research Institute (KESRI). He is IEEE Fellow. His current research inter-
ests are power-electronic control of electric machines, electric/hybrid vehicle
drives, and power-converter circuits.

23 IEEJ Journal IA, Vol.1, No.1, 2012