IEEJ Journal of Industry Applications
Vol.11 No.2 pp.317–326
DOI: 10.1541/ieejjia.21005712

Paper

Eﬀect of Harmonic Current Suppression on Iron Loss of IPMSM
Using Repetitive Perfect Tracking Control
Yuhiro Inagaki∗
Osamu Shimizu∗
Hiroshi Fujimoto∗
Yoshiki Yasuda∗∗

Student Member,
Member,Senior Member,
Member,Masahiro Mae∗
Sakahisa Nagai∗
Takayuki Miyajima∗∗
Akio Yamagiwa∗∗

Student Member
MemberMemberMember(Manuscript received May 20, 2021, revised Sep. 30, 2021)
J-STAGE Advance published date : Nov. 26, 2021

Permanent magnet synchronous motors (PMSMs) have wide applicability owing to their many advantages. For efficient driving of PMSMs, a number of high-eﬃciency control methods have been developed. However, few studies
have discussed the relationship between the tracking characteristics to the current command and driving loss. Here,
we propose using the RPTC, which is a digital controller with high tracking performance, as the current controller
for reducing the iron loss. The RPTC can suppress the periodic disturbances; therefore, the iron loss caused by the
harmonic current in the input current is reduced. Simulations confirmed that the presence or absence of the harmonic
current aﬀects the iron loss reduction. Experiments also showed that RPTC reduced the extent of the iron loss ininterior permanent magnet synchronous motors (IPMSMs).
Keywords: IPMSM, iron loss, harmonic current suppression, repetitive perfect tracking control

1.

issues such as the shape and placement of the magnets (5) ;these harmonics deteriorate the tracking performance withrespect to the current command. In addition, the tracking
error caused by the harmonic current increases iron loss andreduces the overall motor’s driving eﬃciency. Therefore, it
is important to suppress the harmonic current for an eﬃcient
IPMSM drive. Because the harmonic current can be regarded
as a periodic disturbance, control methods such as repetitive
control are eﬀective in suppressing it. In particular, RPTC,
corresponding to a repetitive control based on perfect tracking control (PTC) (6)–(8) can be expected to strongly suppress
the harmonic current and achieve high tracking performancewith respect to the current command, by applying it as thecurrent controller.
In this study, the eﬀect of suppressing the harmonic current
on the motor’s iron loss was validated by comparing the ironloss results for the dq-axis current control of an IPMSM withthose for a PI controller only and for an RPTC. The validation
was based on simulations and experiments.

Introduction

Permanent magnet synchronous motors (PMSMs) have
many advantages, such as high output power and controllability, and are widely used in industrial applications. In
particular, interior permanent magnet synchronous motors(IPMSMs) are often used in electric vehicles, owing to theirlarge torque. For further eﬀective utilization of energy, it isnecessary to drive PMSMs with high eﬃciency through control.
Analyzing the causes of driving loss and taking relevantmeasures to alleviate it is important for achieving highly eﬃcient motor driving. For PMSMs, the loss is mainly classified
into copper loss and iron loss. Copper loss occurs in the motor windings, while iron loss occurs in the electromagnetic
steel sheet. Typical examples of highly eﬃcient current control are the id = 0 control and maximum torque per ampere(MTPA) control (1) . These methodologies reduce copper loss.
However, these are not necessarily the most eﬃcient control methods, because they do not consider iron loss. Somemethods that determine the dq-axis current command, minimizing the sum of copper loss and iron loss, have also been
proposed (2)–(4) . However, the tracking performance of current
command often depends on the general current PI controller,
and only a few studies examined the eﬀect of changing thecurrent controller on the motor eﬃciency.
IPMSMs exhibit large harmonics, owing to their structural2.

2.1 Causes of Iron Loss
Iron loss occurs in the ironcore of a PMSM and is broadly classified into hysteresis loss
and eddy current loss (9) . The IPMSM core contains harmonicmagnetic flux density components owing to various factors,
such as harmonic currents. Several iron loss model equations
and experimental phenomena, such as minor loops of hysteresis, show that iron loss is aﬀected by an increase in thepresence of higher-frequency components (10)–(12).
Electromagnetic simulations were conducted to confirm
the eﬀect of the harmonic current on iron loss. In addition,∗

The University of Tokyo
5-1-5, Kashiwanoha, Kashiwa, Chiba 227-8561, Japan∗∗DAIKIN INDUSTRIES, Ltd.
1-1-1, Nishi-Hitotsuya, Settsu, Osaka 566-8585, Japanc 2022 The Institute of Electrical Engineers of Japan.
⃝

Iron Loss of PMSM

317

Eﬀect of Harmonic Current Suppression on Iron Loss of IPMSM Using Repetitive Perfect Tracking Control（Yuhiro Inagaki et al.）Fig. 1. Simulated IPMSM model (1/6 model (60◦ ))Table 1. Parameters of the simulated IPMSM
ParameterValued-axis inductance Ld
q-axis inductance Lq
Resistance R
Permanent magnet flux linkage Ke
Number of pole pairs P

1.03 mH
1.31 mH
85 mΩ
31.2 mWb
6

Fig. 2. Amplitude of the simulated motor phase current
Table 2. Simulation results

experiments were conducted to confirm the possibility thatiron loss could be suppressed by improving the current controller. In the simulations, suppressed and non-suppressed
motor harmonic currents are set, and the eﬀect of harmonics
on iron loss was confirmed, based on the extents of hysteresisand eddy current losses.
2.2 Initial Simulation-based Study
The change in
the iron loss caused by the harmonic current presence wasverified in simulations. JMAG-Designer (JSOL) was used forthe electromagnetic field analysis and for the iron loss analysis, while the direct linkage function of the JMAG-Designer
and MATLAB & Simulink (MathWorks) was used for simulating the PI current control. The simulated model, which
had the same stator and rotor dimensions as the experimental IPMSM, is shown in Fig. 1. This is a 1/6 partial model for
simulating the motor size, and the analysis was performed forthe setup at 60◦ . The result was converted into a full model,using periodicity for reducing the calculation scale. 35A360(JSOL) was used as a material for the electromagnetic steel
sheet, while N39UH (Shin-Etsu Chemical) was used as a material for the magnet.
The parameters of this model are listed in Table 1. The values of the residual flux density and coercivity of the magnets
in the simulation were adjusted, so that the permanent magnet
flux linkage Ke matched that of the experimental motor.
First, the dq-axis current of the simulated motor model wascontrolled by the PI controller, including the PWM inverter
model of the Simulink model. The phase current and typical order harmonics (n = 5, 7, 11, 13) in the steady state
were recorded. As simulation conditions, the q-axis current
was set to 10 A and the d-axis current was set to −0.892 A
according to MTPA, as follows (13) :!
Ke2
Ke
id ref =−+ i2q ref .· · · · · · · (1)2(Lq − Ld )4(Lq − Ld )2

Loss

with harmonics

without harmonics

Hysteresis loss
Eddy current loss
Total iron loss

3.764 W
1.289 W
5.053 W

3.746 W
1.271 W
5.017 Wthe loss in the transient state. The algorithm for calculatingiron loss in the JMAG-Designer included the hysteresis loss
calculation algorithm using the play hysteron model, and theeddy current loss calculation algorithm using the homogenization method.
The rotation speed was set to 1000 rpm. The amplitudesof the diﬀerent components of the phase current, including
the harmonics set under this condition, are shown in Fig. 2.
The trend of the iron loss caused by the presence of harmonics was investigated by comparing the motor current and an
ideal current source.
Table 2 shows the results for iron loss, with and without
harmonics. The iron loss values were averaged over a periodof the electric angle. These results confirm that removing
the harmonic current reduces the hysteresis loss and the eddy
current loss, and the overall iron loss is reduced by approximately 0.71%, compared with the case in which the harmonic
current is included. Therefore, RPTC, which suppresses the
harmonic current, is expected to be eﬀective in reducing iron
loss.
3.

Overview of the RPTC (7) (8)3.1 Plant Model of the IPMSM
The IPMSM modelfor the dq-coordinate system is shown in Fig. 3. The diﬀerent
parameters are explained in Table 3. In this study, a perfect
tracking controller and a PI controller were designed on thedq-coordinate. The dq axis voltage equation is expressed asfollows:" # "#" # "#
vd
R + sLd −ωe Lq id
0=+.· · · · · · · · (2)
ωe Ke
vq
ωe Ld
R + sLq iq

Because the dq-axis current has coupling terms, decoupling control is widely used. To eliminate the coupling terms,
the dq-voltages are calculated as follows:
vd = v′d − ωe Lq iq , · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(3)vq = v′q + ωe (Ld id + Ke ). · · · · · · · · · · · · · · · · · · · · · · · · ·(4)Iron loss was simulated using the JMAG-Designer. To
make the simulation time realistic, the inverter model was notconsidered in the simulations of iron loss, and the phase current values in the steady state were used to avoid calculating

State variables are defined as the dq-axis current, and inputs are defined as the decoupled dq-axis voltage. The
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Eﬀect of Harmonic Current Suppression on Iron Loss of IPMSM Using Repetitive Perfect Tracking Control（Yuhiro Inagaki et al.）Fig. 3. Block diagram of the IPMSM model
Table 3. Parameters of the IPMSM and their interpretation
Parameter

Meaning

vd , vq
id , iq
Ld , Lq
R
Ke
P
JM
BM
ωm
ωe

dq-axis voltage
dq-axis current
dq-axis inductanceResistance
Permanent-magnet flux linkage
Number of pole pairs
Inertia
Viscous friction coeﬃcient
Mechanical angular velocity
Electric angular velocity

Fig. 5. Sensitivity function of the PI controller and feedback RPTC

Fig. 4. General current PI control

Fig. 6. Block diagram of the PTC (dq-axis current)id, qcontinuous-time state equation and the output equation of the
IPMSM are expressed as follows:id, q ref1.· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (10)τs + 1

Fig. 5 shows the sensitivity function from the output end
disturbance (d(t) in Fig. 4) to the output. This figure suggeststhat the PI controller is not able to suppress disturbances suchas harmonics, which have higher frequency components thanthe bandwidth of the controller; thus, the tracking error remains. Since there is a limit to extending the bandwidth of
the PI controller, harmonics suppression by the RPTC focusing on the periodicity of disturbance was investigated.
3.3 PTC
The block diagram of the PTC on the dqaxis is shown in Fig. 6. Subscripts d and q indicate that eachcoeﬃcient and variable are calculated on its axis. The PTC
system has a feedforward controller and a feedback controller(C2 [z]). The feedforward controller is a stable inverse systemthat achieves zero error to the target value at the sampling
points (6) . For the n-th order plant model, it is necessary toswitch the control input n times. In the case of this IPMSM
model, the plant is a first-order model and is controlled by asingle-rate controller.
To design the feedforward controller, the state and output equations in Eq. (5) and Eq. (6) are discretized using the
PWM hold (14) . In contrast to other holders based on the averaging approximation that assumes that the inverter can output arbitrary voltages, PWM hold is a discretization based on
a PWM pulse consisting of the inverter voltage ±E [V] and0 [V]. The control input u[k] is the inverter’s ON time. Therefore, the PWM hold is more appropriate than the zero-orderẋ(t) = Ac x(t) + Bc u(t), · · · · · · · · · · · · · · · · · · · · · · · · · (5)y(t) = Cc x(t) + Dc u(t),· · · · · · · · · · · · · · · · · · · · · · · · · · (6)
where
"
#
"′ #
v (t)
id (t), u(t) = d′
, · · · · · · · · · · · · · · · · · · (7)vq (t)
iq (t)
⎤
⎤
⎡ R
⎡1
⎧
0 ⎥⎥⎥
⎢⎢⎢− Ld⎢⎢⎢ Ld 0 ⎥⎥⎥⎪⎪⎪⎥⎥⎥ , Bc = ⎢⎢⎢⎥⎥ ,⎪⎪A = ⎢⎢⎪⎦⎣01 ⎥⎪⎨ c ⎣⎢ 0− LRq ⎦
L
· · · · · · · · · · · · (8)
q
⎪
"
#
⎪
⎪
⎪
1
0
⎪
⎪
⎪
⎩Cc = 0 1 , Dc = O.
x(t) =

3.2 Design of the Feedback Controller
In general,a PI controller is used for current control. The control systemthat was used in the present study is illustrated in Fig. 4. The
current PI controller C PI (s) was designed using the pole zerocancellation method and is given as follows:

C PI (s) ==Ls + R.· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (9)τsτ is often set to approximately 10 times the control period. C PI [z] is the discretized C PI (s). Considering Eq. (5),and Eq. (6), the transfer function from the reference current
id, q ref to the PMSM dq-current id, q is derived as follows:
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IEEJ Journal IA, Vol.11, No.2, 2022

Eﬀect of Harmonic Current Suppression on Iron Loss of IPMSM Using Repetitive Perfect Tracking Control（Yuhiro Inagaki et al.）hold for instantaneous value control (15) (16) . The discrete timestate and output equation of the IPMSM based on the PWM
hold are expressed as follows:

period of the transformation wass T s . The RPTC has PSG
and C2 [z]. In the experiment, the conventional method only
had this feedback controller.
The RPTC has a PSG that adds the compensation signal
for the periodic tracking error to the current command andthe feedforward controller of the PTC that achieves zero error
to the target value one sample ahead at each sampling point.
Therefore, the RPTC can suppress harmonics that cannot be
suppressed in the bandwidth of the PI controller. The sensitivity function from the output end disturbance d(t) to the output for the basic configuration of the FB RPTC without thelow-pass filter is shown in Fig. 5. In Fig. 5, the fundamental frequency of the harmonic disturbance to be suppressed
was set to 100 Hz. This result shows that the RPTC strongly
suppresses the harmonics. However, the FB RPTC based on
the internal model principle exhibits some problems, suchas a deterioration of the suppression characteristics of otherorder harmonics and disturbance relearning when the speed
changes. To solve these problems, a feedforward RPTC wasalso considered in this study.
3.4.2 Feedforward RPTC (FF RPTC)
RPTC canrealize a feedforward controller by switching the compensation signal of the PSG (7) . A block diagram of the RPTC
with switches is shown in Fig. 8. By turning ON or OFF
two switches, feedforward type error compensation is performed. Switch 1 is turned on to record errors in the memory during one period of the periodic disturbance after reaching the steady state. After recording, switch 1 is turned oﬀ

x[k + 1] = Ax[k] + Bu[k], · · · · · · · · · · · · · · · · · · · · · · (11)y[k] = Cx[k] + Du[k]. · · · · · · · · · · · · · · · · · · · · · · · · · (12)A, B, C, and D are calculated using Eq. (13). T u is thecontrol input period. E is the DC power supply voltage of a3-phase inverter.
A = eAc Tu , B = eAc Tu /2 Bc E, C = Cc , D = Dc .· · · · (13)
From Eq. (11), and Eq. (12), the stable inverse model, andthe nominal output are expressed as Eq. (14), and Eq. (15).
u0 [k] = B−1 (1 − z−1 A)xd [k + 1], · · · · · · · · · · · · · · · (14)y0 [k] = z−1Cxd [k + 1] + Du0 [k]. · · · · · · · · · · · · · · · (15)In reality, disturbances and modeling errors occur. However, these can be suppressed by a feedback controller C2 [z],and the tracking performance is improved by the feedforward
controller. C2 [z] denotes the discretized PI controller.
3.4 RPTC
3.4.1 Feedback RPTC (FB RPTC)In this section,
feedback type RPTC based on the internal model principle
is described. The block diagram of the FB RPTC on the
dq-axis is shown in Fig. 7. The decoupling control and coupling terms are the same as those in Fig. 6. The RPTC system
has a periodic signal generator (PSG). The PSG records theperiodic disturbance in memory and uses it for compensation (8) (17) .
The memory size is defined as Nd . The memory size Nd isexpressed by Eq. (16) using a tracking error period T d and acontrol period T s .
Nd =Td.· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (16)Ts

For the implementation, a low-pass filter Q with no phasedelay is applied to the compensation signal, for removing thesensor noise. The low-pass filter is expressed as follows:r f [k] = Qr[k] =Fig. 8. Block diagram of the RPTC with switchesz + γ + z−1
r[k],· · · · · · · · · · · · · · · · (17)γ+2where r f [k] is the filter output, r[k] is the PSG output, and γ
is the design parameter of the filter. In this experiment, γ was
set to 2, and the cutoﬀ frequency of the filter was 1.8 kHz (8) (18) .
In this study, T s was set to 0.1 ms, and τ of the PI controller
mentioned in Section 3.2 was set to 10T s = 1 ms. C2 [z] was
obtained from C PI (s), using the Tustin transformation. The

Fig. 9. Block diagram of the PSG

Fig. 7. Block diagram of the feedback RPTC (dq-axis
current)

Fig. 10. PSG for handling speed variations
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Eﬀect of Harmonic Current Suppression on Iron Loss of IPMSM Using Repetitive Perfect Tracking Control（Yuhiro Inagaki et al.）(a) Harmonics with speed variations(b) Tracking error (feedforward RPTC)(c) Tracking error (feedback RPTC)

Fig. 11. Tracking errors, for the simulated FF and FB RPTC

and switch 2 is turned on, to compensate for the tracking error caused by the periodic disturbance as a feedforward controller. Feedforward compensation has the advantage of notexacerbating the inter-harmonics.
Theoretically, it is suﬃcient to record the tracking error for
one period. However, tracking errors were recorded for several periods and averaged to remove the asynchronous components. The compensation signal is then passed through the
low-pass filter Q. In this study, the average number of times
m was set to 10. A more detailed block diagram of the PSG
is shown in Fig. 9.
In addition, the compensation signal recorded in the memory is linked to the position information of the rotary encoder, for handling speed variations (17) . Assuming that themain cause of harmonics is the distortion of the flux linkage
caused by the motor structure, the appearance of harmonics
is considered to be highly dependent on the position of the rotor. Therefore, suppression of harmonics is possible even forspeed variations by referring to the encoder information andrecalling the compensation signal in the memory, as shownin Fig. 10.
The simulation showed the diﬀerence in disturbance suppression between the FF RPTC and FB RPTC, with respect tospeed variations. The disturbance current simulating the 6thorder harmonics was added to the output end of the control
system in Fig. 7 and Fig. 8, and the tracking errors are shownin Fig. 11. Because the speed doubled at 20 ms, the frequencyof the harmonics also doubled. At this time, the FB RPTC
had to relearn the tracking error, but the FF RPTC provided
the compensation signal generated in the first error-recording
step as the feedforward signal referring to the encoder position. This system enabled instantaneous error compensation.
4.

Fig. 12. Experimental setup
Table 4. Parameters of the experimental IPMSM
ParameterValued-axis inductance Ld
q-axis inductance Lq
Resistance R
Permanent magnet flux linkage Ke
Pole pairs P
Supply voltage Vdc
Carrier frequency F sControl period T sMemory size Nd

0.613 mH
1.21 mH
85.6 mΩ31.2 mWb
6100 V
10 kHz0.1 ms
600

angular frequency. Thus, the memory size Nd was 600 from
Eq. (16). This is because the mechanical angular velocity
component caused by the encoder eccentricity or vibration
was confirmed on the dq-axis.
In the loss measurement experiment, iron loss was calculated by subtracting the IPMSM output, copper loss, and mechanical loss from the input power, as follows:
Pir = Pin − Pout − Pco − Pme ,· · · · · · · · · · · · · · · · · · · (18)where Pin is the input power, Pout is the output power, Pco isthe copper loss, Pir is the iron loss, and Pme isthe mechanicalloss. Mechanical loss is considered to be caused by friction
and other factors.
The power meter measured the input power and the phasecurrent. Copper loss in this study was calculated from thephase current and winding resistance measured in advance,
as follows:

Experiment

4.1 Experimental Setup and Conditions
The experimental setup is shown in Fig. 12, and the parameters of the
IPMSM used in this experiment are listed in Table 4. Because this is a single-rate control, T u and T s were the samevalue and set to 0.1 ms.
As the driving conditions, the q-axis current command was
set to iq ref = 10 A, and the d-axis current command was
set to id ref = −1.86 A according to the MTPA condition in
Eq. (1). The rotation speed was maintained at 1000 rpm bya load servo motor. Thus, the electrical angular frequency
was 100 Hz. The fundamental frequency of the tracking error to be suppressed by the RPTC was set as the mechanicalPco = Iu2 rms Ru + Iv2rms Rv + Iw2 rms Rw ,· · · · · · · · · · · · · · (19)where Iu rms , Iv rms and Iw rms are the phase currents. Ru , Rv
and Rw are the resistances of the windings.
The output of the IPMSM was calculated from the torquemeasured by the torque meter and the rotation speed measured by the encoder, as follows:
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Eﬀect of Harmonic Current Suppression on Iron Loss of IPMSM Using Repetitive Perfect Tracking Control（Yuhiro Inagaki et al.）Table 5. Experimental temperature and phase resistanceParameter

Value

Initial winding temperature T S T i
U phase resistance Ru (T S T i )V phase resistance Rv (T S T i )W phase resistance Rw (T S T i )Temperature coeﬃcient α

20.3 ◦ C
86.3 mΩ
88.1 mΩ86.7 mΩ3.92 × 10−3

Table 6. Current amplitude of dq-axis harmonics (average)
Current amplitude

Fundamental

The 6th harmonic

The 12th harmonic

idPI

1.86 A
1.86 A
1.86 A
10.0 A
10.0 A
10.0 A615 mA
210 mA
45.7 mA
495 mA
150 mA
23.7 mA

101 mA
99.6 mA
37.0 mA
20.3 mA
13.2 mA
2.51 mA

idFF RPTC
idFB RPTC
iqPI
iqFF RPTC
iqFB RPTC

Pout = τm ωm ,· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (20)

Table 7. Current amplitude of dq-axis harmonics at
1200 rpm (average)

where τm denotes the motor torque. The mechanical loss Pme
was also calculated using the measured torque and rotation
speed. This mechanical loss was measured beforehand byrotating the rotor of the IPMSM without magnets. The rotation speed was maintained at 1000 rpm by the load servo
motor.
A power meter PW3390 (HIOKI), which was able to measure electric power with an accuracy of 0.01 W, was used.
The torque meter TMB307/411 (MAGTROL), which could
measure up to 10 Nm torque with an accuracy of ±0.15% wasused.
Measurements of the input power, output power, and diﬀerent losses were conducted separately using the PI control and
RPTC, for 5 s. These procedures were performed 12 times.
The results for Pir were compared for the same set, and theaverages over 10 sets, excluding the maximum and minimum
diﬀerences of Pir , are reported as loss reduction results.
Thermocouple thermometers were attached to the bearing
and windings of the IPMSM. Because the mechanical loss
was expected to vary with temperature, the bearing temperature was maintained as stable as possible, for minimizing thevariation in the mechanical loss. Therefore, the mechanicalloss measured beforehand was assumed to be constant in allsets of experiments. In addition, more accurate copper loss
results were calculated by correcting the winding resistanceof each phase, as follows (19) :Current amplitude

Fundamental

The 6th harmonic

The 12th harmonic

idPI

1.86 A
1.86 A
10.0 A
10.0 A731 mA242 mA576 mA
233 mA

77.7 mA
74.0 mA
10.5 mA
10.1 mA

idFF RPTC
iqPI
iqFF RPTC

Table 8. Eﬃciency and ratio of loss to input power (average)
Eﬃciency and LossPI

FF RPTCFB RPTC

Eﬃciency
Copper loss Pco
Iron loss Pir

95.09%
3.33%
0.37%

95.18%
3.29%
0.32%

95.19%
3.28%
0.32%

handling speed variations.
Table 8 lists the eﬃciency and loss ratios. Each value wasnormalized by the input power of the IPMSM. These values
are averages calculated over 10 sets of experimental results.
Because the amount of iron loss is small, it is aﬀected by
the measurement error of the torque meter. Therefore, themaximum and minimum values of the results are shown in
Fig. 16, and Fig. 17 as the error range. As a result, the ironloss reduction eﬀect of the RPTC was confirmed by repeating the experiment and averaging the results. In terms of theeﬃciency and the loss relative to the input power, it was confirmed that the FF RPTC improved the driving eﬃciency by
0.09% and FB RPTC improved it by 0.1%, compared with
the PI controller. The iron loss of the FF and FB RPTCs was
reduced to approximately 86.0% of the PI controller’s ironloss.
The simulation results in Section 2 confirmed that the suppressing the harmonic current reduces iron loss, and this experiment also showed that suppression of the 6th and 12th order harmonics on the dq-axis reduced the IPMSM loss. The
diﬀerences in iron loss between the PI and FF RPTC and between the PI and FB RPTC were significant. However, thediﬀerence in iron loss between the FF RPTC and FB RPTC
was slight. These results indicate that the current disturbance
suppression at high frequencies is important for reducing ironloss and for improving eﬃciency. It can be said that the FF
RPTC can handle speed variations and exhibits almost thesame eﬃciency improvement as in the case of the feedback
harmonics suppression based on the internal model principle.
4.3 Loss Simulation using Actual Phase Current Data
Because several measuring instruments were used in thisexperiment, there is variation in the loss results as shown in
Fig. 16, and Fig. 17. Therefore, the actual phase current dataof the PI control and RPTC were used for additional verification by the JMAG-Designer simulation.
The actual phase current data were recorded using the current probe TCP0020 (Tektronix). The measurement range ofR(T ST ) = R(T S T i ){1 + α(T ST − T S T i )},· · · · · · · · · · · (21)where T ST is the winding temperature, T S T i is the initial
winding temperature and α is the temperature coeﬃcient of
the copper resistance (20.3◦ C). The experimental conditions
are listed in Table 5.
4.2 Experimental Results
Fig. 13 and Fig. 14 show
the fast Fourier transform (FFT) results of current control for
the PI control, the FF RPTC, and the FB RPTC. In addition,
Table 6 lists the amplitudes of typical harmonics. The results confirm that the FF and FB RPTCs suppress the 6th
and 12th order harmonics significantly. For determining theimpact of the FF RPTC handling speed variations, the harmonic components at 1200 rpm were investigated using thecompensation signal recorded at 1000 rpm. Fig. 15 shows the
FFT results for the current PI control and for the FF RPTC, at
1200 rpm. Table 7 lists the amplitudes of typical harmonics.
According to the results, the FF RPTC does not inherently worsen the inter-order harmonics, but some parts of
the harmonics are worsened, as shown in Fig. 13, Fig. 14 andFig. 15.This error is owing to the modeling error of the feedforward controller. However, the FF RPTC strongly suppresses the typical harmonic components, such as the 6thorder, and is expected to be useful for a broader range ofconditions than the FB RPTC, owing to its performance on
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Eﬀect of Harmonic Current Suppression on Iron Loss of IPMSM Using Repetitive Perfect Tracking Control（Yuhiro Inagaki et al.）(a) Spectrum of Id (PI)(b) Spectrum of Id (FF RPTC)(c) Spectrum of Id (FB RPTC)

Fig. 13. Comparison of d-axis harmonics (left: PI, center: FF RPTC, right: FB RPTC)(a) Spectrum of Iq (PI)(b) Spectrum of Iq (FF RPTC)(c) Spectrum of Iq (FB RPTC)

Fig. 14. Comparison of q-axis harmonics (left: PI, center: FF RPTC, right: FB RPTC)(a) Spectrum of Id (PI 1200 rpm)(b) Spectrum of Id (FF RPTC 1200 rpm)(c) Spectrum of Iq (PI 1200 rpm)(d) Spectrum of Iq (FF RPTC 1200 rpm)

Fig. 15. Comparison of PI and FF RPTC dq-axis harmonics (1200 rpm with learning signal at 1000 rpm)

Pme :P′in = P′out + P′co + P′ir + Pme ,· · · · · · · · · · · · · · · · · · · (22)where P′in , P′out , P′co , and P′ir are analytical values. The ironloss calculation algorithm used in this simulation was thesame as that described in Section 2.
In terms of the eﬃciency and the loss as a ratio to the input power, the results in Table 9 confirm that the FF RPTC
improved the driving eﬃciency by 0.07% and FB RPTC improved it by 0.13%, compared with the PI controller. Considering iron loss in more detail, the FF and FB RPTC reduced 3.0 ∼ 3.2% of the iron loss caused by the PI controller. The actual phase current data were obtained from theexperiments in Section 4.2. As shown in Fig. 13, Fig. 14, andTable 6, the harmonics of the phase currents of the FF and
FB RPTC were suppressed, and the JMAG simulation using
these data also showed the trend for the iron loss reduction,owing to the RPTC. Comparing the results in Tables 8 and 9,
the trend of the diﬀerence in iron loss between the PI and the
FF RPTC, and between the PI and the FB RPTC was significant, and the diﬀerence in iron loss between the FF RPTC
and the FB RPTC was slight, which was also consistent between the experimental and simulation results. Therefore, thesimulation results also support the experimental observations

Fig. 16. Ratio of iron loss, and range of errors

the current probe was set to 20 A. These data were applied using the current source in the IPMSM simulation model shownin Fig. 1, and the rotation speed was set to 1000 rpm.
Table 9 shows the eﬃciency and the loss ratio for the simulation using current data. Owing to the slight diﬀerences in
the input power and output for each controller, each value wascalculated as a ratio to the input power. Since this simulation
did not capture the mechanical loss, the input power was calculated as follows, using the measurement mechanical loss
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Eﬀect of Harmonic Current Suppression on Iron Loss of IPMSM Using Repetitive Perfect Tracking Control（Yuhiro Inagaki et al.）while the FB RPTC improved it by 0.13%. The reduction ofiron loss and the improvement of eﬃciency owing to the suppression of harmonics were confirmed by both experimental
results and simulation results.
Regarding the diﬀerent RPTC schemes, according to ourexperimental results, the FF RPTC still exhibited the tracking
error derived from the modeling error, while the FB RPTC almost suppressed the harmonics in the steady state. However,in terms of the iron loss and drive eﬃciency, these two methods exhibited similar performances. Based on these results,
the FF RPTC performed better than the PI control in terms ofeﬃciency; in addition, it could handle speed variations.
There is a research that shows the possibility of improving eﬃciency when the harmonic current commands are set
to other than 0 A (20) . Verification of changes in the iron loss
and total loss for the PMSM when the harmonic current is
actively controlled is a topic for future work. In addition, therelationship between harmonic control and motor drive performance has conventionally been studied from the perspective of the torque ripples (21) (22) . In the future, it will be necessary to consider the three elements, namely the harmonic
control, the drive eﬃciency, and the torque ripples.

(a) Overall view.

References(b) Magnified view.

(1)Fig. 17. Ratio of copper loss, and range of errors
Table 9. Eﬃciency and ratio of loss to input power (using actual current data)
Eﬃciency and LossPI

FF RPTCFB RPTC

Eﬃciency
Copper loss P′coIron loss P′ir

94.02%
3.23%
1.61%

94.09%
3.19%
1.56%

94.15%
3.15%
1.57%

(2)

(3)

(4)

that changing the current controller from the PI to the RPTCeﬀectively reduces losses.
5.

(5)Conclusion

In this paper, the application of the RPTC to current control was proposed, for reducing the iron loss of IPMSMs. The
harmonics of an IPMSM increase the iron loss and decrease
the motor’s driving eﬃciency. Because the harmonics can be
regarded as a periodic disturbance, they can be suppressed by
the RPTC, which is a repetitive control based on the PTC. In
the RPTC, the harmonics of the fundamental frequency arerecorded as errors and compensated by the periodic signal
generator, for suppressing harmonics and reducing iron loss.
The first simulation results showed that iron loss was reduced when the harmonic current was eliminated. The experimental results also showed that the iron loss of the FF
and FB RPTC was reduced to 86.0% of the PI controller’siron loss. The FF RPTC improved the driving eﬃciency by
0.09%, while the FB RPTC improved it by 0.1%, comparedwith the PI controller. Furthermore, an additional experiment
was conducted by the simulation using actual current data.
The simulation results showed that the FF and the FB RPTC
reduced 3.0 ∼ 3.2% of iron loss caused by the PI controller,
and the FF RPTC improved the driving eﬃciency by 0.07%,

(6)

(7)

(8)

(9)

( 10 )( 11 )( 12 )

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T. Inoue, Y. Inoue, S. Morimoto, and M. Sanada: “Maximum Torque per Ampere Control of a Direct Torque-Controlled PMSM in a Stator Flux Linkage
Synchronous Frame”, IEEE Transactions on Industry Applications, Vol.52,
No.3, pp.2360–2367 (2016)
Q. Guo, C. Zhang, L. Li, J. Zhang, and M. Wang: “Maximum eﬃciency per
torque control of permanent-magnet synchronous machines”, IEEE Transactions on Industrial Electronics, Vol.62, No.4, pp.2135–2143 (2015)
H. Zhang, M. Dou, and J. Deng: “Loss-minimization strategy of nonsinusoidal back EMF PMSM in multiple synchronous reference frames”, IEEE
Transactions on Power Electronics, Vol.35, No.8, pp.8335–8346 (2020)
A. Balamurali, G. Feng, A. Kundu, H. Dhulipati, and N.C. Kar: “Noninvasive and Improved Torque and Eﬃciency Calculation Toward Current Advance Angle Determination for Maximum Eﬃciency Control of PMSM”,
IEEE Transactions on Transportation Electrification, Vol.6, No.1, pp.28–40(2020)
J. Lee, Y.C. Kwon, and S.K. Sul: “Experimental Identification of IPMSM
Flux-Linkage Considering Spatial Harmonics for High-Accuracy Simulationof IPMSM Drives”, 2018 IEEE Energy Conversion Congress and Exposition,
ECCE 2018, pp.5804–5809 (2018)
H. Fujimoto, Y. Hori, and A. Kawamura: “Perfect tracking control basedon multirate feedforward control with generalized sampling periods”, IEEE
Transactions on Industrial Electronics, Vol.48, No.3, pp.636–644 (2001)
T. Nakai and H. Fujimoto: “Harmonic Current Suppression Method of
PMSM Based on Repetitive Perfect Tracking Control”, IECON 2007 - 33rd
Annual Conference of the IEEE Industrial Electronics Society, pp.1049–1054(2007)
H. Fujimoto and T. Takemura: “High-precision control of ball-screw-driven
stage based on repetitive control using n-times learning filter”, IEEE Transactions on Industrial Electronics, Vol.61, No.7, pp.3694–3703 (2014)
K. Yamazaki and A. Abe: “Loss investigation of interior permanent-magnet
motors considering carrier harmonics and magnet eddy currents”, IEEE
Transactions on Industry Applications, Vol.45, No.2, pp.659–665 (2009)
H. Nam, K.H. Ha, J.J. Lee, J.P. Hong, and G.H. Kang: “A study on ironloss analysis method considering the harmonics of the flux density waveform using iron loss curves tested on epstein samples”, IEEE Transactions
on Magnetics, Vol.39, No.3 I, pp.1472–1475 (2003)
K. Narita, H. Sano, T. Yamada, R. Akaki, and M. Aoyama: “An Accurate
Iron Loss Analysis Method Based on Finite Element Analysis Considering
Dynamic Anomalous Loss”, 2018 IEEE Energy Conversion Congress andExposition, ECCE 2018, no. ohm m, pp.4309–4314 (2018)
G. Liu, M. Liu, Y. Zhang, H. Wang, and C. Gerada: “High-speed permanent
magnet synchronous motor iron loss calculation method considering multiphysics factors”, IEEE Transactions on Industrial Electronics, Vol.67, No.7,

IEEJ Journal IA, Vol.11, No.2, 2022

Eﬀect of Harmonic Current Suppression on Iron Loss of IPMSM Using Repetitive Perfect Tracking Control（Yuhiro Inagaki et al.）( 13 )( 14 )( 15 )( 16 )( 17 )( 18 )( 19 )( 20 )( 21 )( 22 )

Osamu Shimizu (Member) received the B.S. and M.S. degrees in Faculty of Environment and Information Studies from
Keio University, Japan in 2007 and 2009, respectively. He worked as an associate at Toyota Motor
Corporation, Sim-Drive Co., Ltd., Honda R & D Co.,
Ltd. in 2009–2017. He received the Ph.D. degree inthe Department of Media and Governance from Keio
University in Japan. He joined as assistant professor
at Nagoya University in 2017. From 2018. He joined
Graduate School of Frontier Science at University ofTokyo as a project assistant professor and became a project lecturer fromyear 2021. His interests are in design and control of electric vehicle driving
system and WPT system. He is a member of IEEE, IEE and the Society ofAutomotive Engineers of Japan.

pp.5360–5368 (2020)
S. Morimoto, M. Sanada, and Y. Takeda: “Wide-Speed Operation of Interior Permanent Magnet Synchronous Motors with High-Performance Current Regulator”, IEEE Transactions on Industry Applications, Vol.30, No.4,
pp.920–926 (1994)
A. Kawamura, H. Fujimoto, and T. Yokoyama: “Survey on the real time
digital feedback control of PWM inverter and the extension to multi-rate
sampling and FPGA based inverter control”, IECON Proceedings (Industrial
Electronics Conference), No.1, pp.2044–2051 (2007)
K. Sakata and H. Fujimoto: “Perfect tracking control of servo motor basedon precise model with PWM hold and current loop”, Fourth Power Conversion Conference-NAGOYA, PCC-NAGOYA 2007 - Conference Proceedings,
pp.1612–1617 (2007)
T. Miyajima, H. Fujimoto, and M. Fujitsuna: “Control method for IPMSM
based on PTC and PWM hold model in overmodulation range—Study on
robustness and comparison with anti-windup control—”, 2010 IEEE Energy
Conversion Congress and Exposition, ECCE 2010 - Proceedings, pp.2844–
2850 (2010)
T. Nakai and H. Fujimoto: “Harmonic current suppression method of SPM
motor based on repetitive perfect tracking control with speed variation”,
IECON Proceedings (Industrial Electronics Conference), No.2, pp.1210–
1215 (2008)
K.K. Chew and M. Tomizuka: “Digital Control of Repetitive Errors in Disk
Drive Systems”, IEEE Control Systems Magazine, Vol.10, No.1, pp.16–20(1990)
H. Iwata, K. Ohishi, Y. Yokokura, Y. Okada, Y. Ide, D. Kuraishi, and A.
Takahashi: “Robust Estimation Method for Stator Temperature Based on
Voltage Disturbance Observer Autotuning Resistance for SPMSM”, IEEJ
Journal of Industry Applications, Vol.9, No.4, pp.341–350 (2020)
K. Yoshimoto and Y. Kitajima: “A Novel Harmonic Current Control for
IPMSMs”, The 2005 International Power Electronics Conference A MultiMode Charging Circuit for Rechargeable Batteries, pp.1569–1574 (2005)
K. Nakamura, H. Fujimoto, and M. Fujitsuna: “Torque ripple suppression
control for PM motor with current control based on PTC”, 2010 International
Power Electronics Conference - ECCE Asia -, IPEC 2010, No.1, pp.1077–
1082 (2010)
N. Nakao, K. Tobari, T. Sugino, Y. Ito, M. Mishima, and D. Maeda: “Torqueripple suppression control for PMSMs using feedforward compensation andonline parameter estimation”, IEEJ Journal of Industry Applications, Vol.10,
No.4, pp.497–505 (2021)

Sakahisa Nagai (Member) received the B.E., M.E., and Ph.D. degrees
in electrical and computer engineering from Yokohama National University, Kanagawa, Japan, in 2014,2016, and 2019, respectively. He was a JSPS fellowship for Young Scientists from 2018 to 2019. In 2019,
he joined the University of Tokyo, Chiba, Japan, as aproject assistant professor. His research interests include sensorless actuation, motion control, wirelesspower transfer, and power electronics. He is a member of IEEE and IEE Japan.
Hiroshi Fujimoto (Senior Member) received the Ph.D. degree in the
Department of Electrical Engineering from the University of Tokyo in 2001. In 2001, he joined the Department of Electrical Engineering, Nagaoka University of Technology, Niigata, Japan, as a research associate. From 2002 to 2003, he was a visiting scholar in
the School of Mechanical Engineering, Purdue University, U.S.A. In 2004, he joined the Department ofElectrical and Computer Engineering, Yokohama National University, Yokohama, Japan, as a lecturer andhe became an associate professor in 2005. He had been an associate professor of the University of Tokyo from 2010 to 2020 and became a professor
from year 2021. He received the Best Paper Awards from the IEEE Transactions on Industrial Electronics in 2001 and 2013, Isao Takahashi PowerElectronics Award in 2010, Best Author Prize of SICE in 2010, The Nagamori Grand Award in 2016, and First Prize Paper Award IEEE Transactions
on Power Electronics in 2016. His interests are in control engineering, motion control, nano-scale servo systems, electric vehicle control, motor drive,
visual servoing, and wireless motors. Dr. Fujimoto is a senior member of
IEE of Japan and IEEE. He is also a member of the Society of Instrument
and Control Engineers, the Robotics Society of Japan, and the Society ofAutomotive Engineers of Japan. He is an associate editor of IEEE/ASME
Transactions on Mechatronics from 2010 to 2014, IEEE Industrial Electronics Magazine from 2006, IEE of Japan Transactions on Industrial Application from 2013, and Transactions on SICE from 2013 to 2016. He is achairperson of JSAaE vehicle electrification committee from 2014 to 2020
and a past chairperson of IEEE/IES Technical Committee on Motion Control
from 2012 to 2013.

Yuhiro Inagaki (Student Member) received the B.E. degree fromWaseda University in 2020. He is currently working toward the M.E. degree in Department of Electrical Engineering and Information Systems, Graduate
School of Engineering, the University of Tokyo. Hisinterests are in motor drive, motion control.

Masahiro Mae (Student Member) received the B.E. and M.S. degrees
from The University of Tokyo in 2018 and 2020, respectively. He is currently working towards the Ph.D.
degree in the Department of Electrical Engineering
and Information Systems, Graduate School of Engineering, The University of Tokyo. He is also a research fellow (DC2) of Japan Society for the Promotion of Science from 2021. His research interests arein control engineering, precision motion control, multirate control, and multi-input multi-output systems.
He is a student member of the Institute of Electrical and Electronics Engineers and the Society of Instrumental and Control Engineers.

Takayuki Miyajima (Member) received the B.S. and M.S. degrees inelectrical and computer engineering from Yokohama
National University, Japan, in 2009 and 2011, respectively and the Ph.D. degree from the University ofTokyo, Japan in 2014. From April 2014, he has beenwith DAIKIN INDUSTRIES, Ltd. He works on thedevelopment of motor control of air conditioner andhydraulic equipment.

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Eﬀect of Harmonic Current Suppression on Iron Loss of IPMSM Using Repetitive Perfect Tracking Control（Yuhiro Inagaki et al.）
Yoshiki Yasuda (Member) received the B.E. and M.E. degrees from
Osaka Prefecture University, Sakai, Japan, in 2002,
2004 respectively. Since 2004, he has been withDAIKIN INDUSTRIES, Ltd. He works on the development of motors for air conditioners and hydraulicequipment.

Akio Yamagiwa (Member) received the B.E. and M.E. degrees from
Toyama University, Toyama, Japan, in 1988 and1990, respectively. From 1990, he has been withDAIKIN INDUSTRIES, Ltd. He works on the development of motors for air conditioners andhydraulic equipment. He was a senior researcher from2002 to 2011 and has been a chief engineer from2012. He was general manager of the Technology Research Association of Magnetic Materials for HighEﬃciency Motors from 2012 to 2017 and has been achief researcher from 2018. He received the IEEJ Technical Development
Award in 1998. He is a member of IEE of Japan and the Japan Society of
Mechanical Engineers.

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