Analysis of Current Control Bandwidth in
Current Source Type Motor Emulator
Gensui Tanaka1, Katsuki Miura1, Keita Ohata1, Hitoki Watanabe1, Jun-ichi Itoh1, and Ikuya Sato2
1

Nagaoka University of Technology, Japan
2
FUJI ELECTRIC CO., LTD., Japan

Abstract-- This paper focus on the stability issue of an
inverter test system with a current source type motor
emulator (CSTME). The CSTME imitates various motor
operations with accuracy. However, the CSTME requires
high current control bandwidth to prevent interference
between the current controls of both the inverter under test
(IUT) and the CSTME. This paper reveals the required
current control bandwidth, which is to prevent interference
between current controls, based on root locus analysis results.
From the result of the stability analysis, the current
controller of the CSTME requires 2.2 times higher
bandwidth than IUT’s bandwidth. The stability limit of theroot locus analysis agrees with the simulation of the time
domain. In addition, the effect to the stability limit with timedelay is also investigated. Then, the CSTME’s required
current control bandwidth becomes more than 3.1 times ofthat of IUT. The validity of the analysis is verified by thesimulation on the time domain.
Index Terms-- Current control bandwidth, Motoremulator, Root locus, Stability Analysis.

I. INTRODUCTION
Recently, a Hardware-in-the-loop (HIL) simulation has
been used before experimental verification [1]-[3]. The
HIL simulation provides some advantages overconventional off-line simulation, such as reliability andshorter development time. The HIL simulation has beenmostly used to test the control system, which is called
Controller HIL (CHIL) simulation. The CHIL simulation,
which receives gate-signal from the controller under test
and sends the detected signals, is used to confirm theresponse and the performance of the system. However, theCHIL simulation tests only the controller, not the hardware
for driving motors including power converters and othercomponents.
On the other hand, a Power HIL (PHIL) simulation has
been attracted to develop the power converter and its
control without an actual load. The most significant
advantage of the PHIL simulation is that it can confirm theperformance and reliability of the main power circuit, suchas power loss, temperature rising, surge voltage, detection
circuit accuracy, and so on.
The PHIL simulation is very effective in developing a
special specifications motor drive system, such as highspeed, high power density and so on. The development ofspecial specifications motor drive system has to prepare an
inverter under test (IUT), a motor under test (MUT), a
coupling, a load machine, and load machine inverter.
Many kinds of equipment are required for the inverter test.
Moreover, the development period will be long because

there are many development items in not only the IUT but
also the MUT and load machine [4]. The PHIL simulation,
which emulates the behavior of a test motor to develop atest inverter and controller, is so-called “a motor emulator.”
The motor emulator reduces the cost, the development
time, and the space to build a test environment.
There are two types of motor emulators, the voltage
source type [5]-[8] and the current source type [9]-[14].
The voltage source type motor emulator imitates the backelectromotive force (EMF) of the target motor and thevoltage drop on the inductor and the resistor. However, thevoltage source type motor emulator does not apply to the
IUT with an open-loop control or a V/f control. In addition,
the voltage source type motor emulator does not evaluate
the current transients with accuracy even when the current
control is implemented in the IUT because it imitates theback EMF and the voltage drop in the steady state. On theother hand, the current source type motor emulator(CSTME) imitates the motor current accurately. The motor
current commands are calculated by the terminal voltageof the CSTME. Besides, the CSTME is applied regardlessof the control method of the IUT. In addition, many kindsof motors are imitated by changing the motor differential
equation implemented in the controller of the CSTME [9][11]. For these reasons, the CSTME is more suitable forthe motor emulator system in terms of general-purpose use.
However, the control of the CSTME may become
unstable because of the interference between the current
control bandwidth of both the IUT and the CSTME [13][14]. Empirically, the current control bandwidth of the
CSTME needs to be larger than that of the IUT. However,it seems that the minimum bandwidth of the CSTME was
not clearly mentioned in the past literatures.
This paper clarifies the control bandwidth required forthe current control of the CSTME. The stability limit isrevealed by the stability analysis with a root locus. The
originality of this paper is the evaluation of the bandwidth,
which is required to prevent interference between thecurrent controls based on a root locus analysis.
This paper is organized as follows; first, theconfiguration of the CSTME is introduced; second, thedesign method of the controller is described; third, astability analysis of the inverter test system using the
CSTME is discussed by a root locus, and the current
response required for the CSTME is clarified; Then thevalidity of the analysis result is confirmed by thesimulation.

II. CURRENT SOURCE TYPE MOTOR EMULATOR

IUT

Fig.1 shows the system configuration of an inverter test
system using the CSTME. The hardware configuration of
the CSTME is the same as a PWM rectifier. The controllerof the CSTME detects the phase current and the output
voltage of the IUT. The virtual motor speed and torque are
given by the equation of motion of the motor. The
calculated motor speed value is sent to the controller of the
IUT.
The state equation of an IPMSM based on the dq-axis
is expressed as

R
 −
Ld
id  P  =
iq   − Ld
re
Lq


Lq 
 vd  i   0 
Ld   d   Ld  + re m  (1), +
R  iq   vq   −
Lq 
−

  
Lq 
 Lq rewhere vd and vq are the dq-axis voltage, id and iq are the dqaxis current, Ra is the armature resistance value, Ld and Lq
are the dq-axis synchronous inductance values, re is theelectric angler frequency, P is the differential operator, andm is the flux linkage of the permanent magnet. Here, theoutput torque Te and the relationship between the electric
angular velocity and torque on the dq-axis are expressed as
Te = p{ miq + ( Ld − Lq )id iq } ................................. (2),pPre =(Te − TL ) ............................................... (3),J

id_emu *1
R+sLd

vd_inv

Ld

1
1+sTi

Current
Sensing

Drive
Controller

where TL is the load torque, p is the pairs of poles, and J is
the inertia of the motor. It is noted that the damping factor
and spring factor are in (3).
The current commands are obtained by solving thedifferential equation (1), (2), and (3) for the current using
the Euler method in a DSP.
Fig. 2 shows the whole system block diagram of the
CSTME. The CSTME controller is composed of the motor
model and the current controller. The feed-forward
compensation is applied in the CSTME controller in orderto cancel the interference between the inductor on the dqaxis. The low pass filters, which are connected in front ofadding a point, are used to cancel the zero points of theclosed-transfer function of the current control.

Coupling inductor1sLrec

reLrec×

feed-forward compensationLqq-axis current PI controller

iq_emu*

1
1+sTi

id*
speed PI controller

re×reLrec

Ld - Lq

Kp(1+sTi)
sTi

11+sTi_cd

reLrec
vq_emu *1
1+sTi_cq

1
sLrec

iq

Control block diagram of the CSTME.

motor modeld-axis current PI controller

Kp_cd(1+sTi_cd )11
sTi_cdvd_inv R+sLd id_emu * 1+sTi

q-axis current PI controller

Kp_s(1+sTi_s )sTi_smotor model

coupling inductor
Kp(1+sTi)
1 id
*
sTi
sL
rec
vd_emuq-axis current PI controller

Kp_cq(1+sTi_cq )11
sTi_cqvq_inv R+sLq iq_emu * 1+sTicontroller of CSTME

coupling inductor
1 iq
sLrec

Kp(1+sTi)
sTi
vq_emu *re 1controller of IUT

1
Js

p

reLrecd-axis current PI controller

1
1+sTi_sidFig. 2*PI
PWM
Current Control

Eq.(2)
Eq.(3)
TL
Fig. 1 The system configuration of the inverter test system withcurrent source type motor emulator.

motor model×

vq_inv

Eq.(1)

Current
Sensing
idq
idq *

re*

re

1
R+sLd

Voltage
Sensing
vdq

re
Te

vd_emu *Kp(1+sTi)
sTi

d-axis current PI controllerCurrent Source Type Motor Emulator
Lrec

Js

p



Fig. 3The control block diagram of the inverter test system with the IUT and the CSTME.

×

Ld - LqreFig. 3 shows the control block diagram of the inverter
test system with the IUT and the CSTME. Note that theField Oriented Control (FOC) is applied in the IUT. The
decoupling control, which is commonly utilized for the
IPMSM in order to cancel the cross-coupling terms
between the d-axis and the q-axis, is also applied to the
IUT. As shown in Fig. 3, the current control loop of the
CSTME is put into the current control loop of the IUT.
Thus, the system might become unstable due to theinterference between each current controller when the
bandwidth of both current controllers is dose.
Fig.4 shows the block diagram of the current controller
used in the CSTME. The transfer function of the PI current
controller used in the CSTME is expressed as
1 + sTi............................................... (5),
GPI (s) = Kp
sTi
where Kp is the proportional gain, and Ti is the integral time.
The closed-loop transfer function of the inductor current
controller is expressed as
Kp(1 + sTi )LrecTi................................... (6).
Gc ( s) =
Kp
Kp
2
s +
s+
Lrec
LrecTi
The first-order lag element is inserted into the current
command in order to cancel the zeros of the controller. The
first-order lag element F(s) is expressed as1...................................................... (4).
F ( s) =1 + sTi
The parameters of the controller Kp and Ti are designed bycomparison with the second-order standard form. The
second-order standard form is represented as2......................................... (7),G( s) = 2
s + 2 s +  2
where  is the natural angler frequency and  is thedamping factor, which is set to 0.707. The parameters of
the PI controllers are calculated by (8) and (9).
Kp = 2 Lrec ......................................................... (8).
2 ................................................................. (9).
Ti =
In this paper, the required current control bandwidth fc isclarified by stability analysis. The relationship between and fc is expressed as
 = 2 f c ............................................................. (10).

III. STABILITY ANALYSIS
In this section, the stability of the motor emulation
system is analyzed by the system’s pole arrangement.
Table 1 shows the parameters of the MUT in this paper.
Two types of motors are used to evaluate the stability of
the controller.
A. Ideal modelFig. 5 shows the simplified block diagram analyzed inthis paper. Table 2 shows the parameters used in theKp(1+sTi)
sTi

iq*

1
1+sTi

Fig. 4

Configuration of the current PI controller.

1
sLrec

iq

Table 1The parameters of the target IPMSM.
(a) Motor A.
Parameter
SymbolValue
Output powerPn
3.7 kW
Maximum speed
n7200 rpm
Output torqueTn
4.91 N・m
Pole pairsp2Winding resistanceR
116 mWd-axis inductanceLd
2.59 mH
q-axis inductanceLq
3.63 mH

flux linkage ofm 0.0905 Wb
permanent magnet
Moment of inertia
J
30×10-4 N・m(b) Motor B
Parameter
SymbolValue
Output power
Pn
5.5kW
Maximum speed
1500rpmn
Output torqueTn
35N・m
Pole pairsp3
Winding resistanceR
0.21W
d-axis inductanceLd
4.3mH
q-axis inductanceLq
10.2mH
flux linkage ofm 0.2001 Wb
permanent magnet
Moment of inertia
J
18×10-3N・m

analysis. The ideal model neglects the control delay,
parameter mismatching, out voltage error of power
converters, current detection error, and so on.
The zero-d-axis-current control is applied to the IUT.
The block diagram shown in Fig. 5 is expressed as only the
q-axis controller because the effect of the d-axis disappears
with the feed-forward compensation of the cross-couplingterms and the zero-d-axis-current control. The systemstability is analyzed based on the simplified block diagram
shown in Fig. 5.
Fig. 6 shows the root locus of the whole system when
the current control bandwidth of the CSTME which isrepresented as fc_emu is varied from 900 Hz to 1100 Hz for
analysis on motor A and motor B. The pole arrangementof the system is calculated by MATLAB/Simulink. Notethat the current control bandwidth of the IUT which isrepresented as fc_inv is set to 500 Hz at a constant. As shownin Fig. 5, the poles are shifted to the left half plane (LHP)
according to increasing the bandwidth of the current
controller in the CSTME. The poles are placed in the righthalf plane (RHP) when the current control bandwidth of
the CSTME is less than or equal to 1032 Hz in Fig. 5 (a)(Motor A) and 1055 Hz in Fig. 5 (b) (Motor B). This meansthat the stability limits of the systems with motor A andMotor B are 1033 Hz and 1055 Hz, respectively. The
stability limits of the two systems become almost the sameeven the Motor A and Motor B have different power andspeed rating. It means that the stability limit is robust forthe motor parameters.

speed PI controller

re*1
1+sTi_sq-axis current PI controller

Kp_s(1+sTi_s)sTi_s

1
1+sTi_cq

motor modelq-axis current PI controller

Kp_cq(1+sTi_cq )11
sTi_cqvq_inv R+sLq iq_emu * 1+sTi

re 1
Js

controller of CSTMEp

The simplified control block diagram of the CSTME and the IUT with FOC.

B. Including time delay element model
An actual system has a time delay, which is caused bysampling, PWM, detection, and so on. These delays havea significate influence on the system’s stability [15]-[16].
The time delay is assumed as one sampling time by the
DSP in this paper. Then, the transfer function Gd(s) of thetime delay element is expressed as1.................................................... (11),
Gd ( s) =1 + Ts swhere Ts is the sampling time, which is the inverse of theswitching frequency shown in Table 2. Note that the delay
times Ts of the IUT and the CSTME are represented as
Ts_inv and Ts_emu, respectively.
Fig. 8 shows the system block diagram considering thetime delay element. The PWM delays are added to the PI
controller of both current controllers. The first-order lag
element is connected to the output part of the IUT and the
CSTME, respectively.
Fig. 9 shows the root locus of the whole system
considering the PWM delay when the current control
bandwidth of the CSTME is varied from 1150 Hz to 1450
Hz for analysis. The current control bandwidth of the IUT
is set to 500 Hz at a constant, as well as the ideal analysis.
As shown in Fig. 9, the poles are shifted to the LHP
according to increasing the bandwidth of the CSTME, as
well as the ideal model analysis results. The poles areplaced in the RHP when the current control bandwidth of
the CSTME is less than or equal to 1277 Hz in Fig. 5 (a)(Motor A) and 1302 Hz in Fig. 5 (b) (motor B). This meansthat the stability limits of the systems are 1277 Hz and
1302 Hz, respectively. The stability limit of the includingtime delay model becomes approximately 1.24 times
higher than that of the ideal model. Besides, the systemstability limit becomes almost same regardless of the
motor parameters in this case.
Fig. 10 shows the required current control bandwidth of
the CSTME for Motor A. The vertical axis represents a

Table 2 Analysis Parameters.
Parameter
SymbolValue
Coupling inductor
Lrec
1.73mH
ASR bandwidth of IUT
fs_inv
20 Hz
ACR bandwidth of IUT
fc_inv
500 Hz
IUT switching frequency
20 kHzfsw_inv
CSTME switching frequency fsw_re c
100 kHz

Imaginary [s-1]

6000

3000

fc_emu=1100 Hz

fc_emu=900 Hz

stable0

unstable

fc_emu=1100 Hz

-3000

-6000
-400

-200

fc_emu=1033 Hz
fc_emu=900 Hz

0Real [s-1](a) Motor A.

200

400

6000
Imaginary [s-1]Fig. 7 shows the relationship between the current
control bandwidth of the IUT and the CSTME when thesystem is at the stability limit. The current control
bandwidth of the IUT is varied from 100 Hz to 1000 Hz.
As shown in Fig. 7, the current control bandwidth of the
CSTME at a stable limit is changed almost linearlyaccording to the bandwidth of the IUT. In any case, thebandwidth of the CSTME at a stable limit is approximately
2.1 times higher than the bandwidth of the IUT. Therefore,
the current controller of the CSTME requires 2.2 times
higher bandwidth than the current control bandwidth of the
IUT in order to keep the system stability.

3000

fc_emu=1100 Hz
stable0fc_emu=1100 Hz

-3000

-6000
-400

fc_emu=900 Hz
unstable

fc_emu=1055 Hz
fc_emu=900 Hz

-200

0
200
400
Real [s-1](b) Motor B
Fig. 6 Root locus of ideal model when the current control bandwidthof the CSTME is varied from 900 Hz to 1100 Hz and 1150 Hz.
Stability limit[Hz]

Fig. 5

Stability limit[Hz]

controller of IUT

coupling inductor
1 iq
sLrec

Kp(1+sTi)
sTi
vq_emu *

2500
2000
1000
0

0

200
400
600
800
1000
Current control bandwidth of IUT [Hz](a) Motor A.

2500
2000
1000
0

0

200
400
600
800
1000
Current control bandwidth of IUT [Hz](b) Motor B.
Fig. 7 Stability limit of the ideal model when the current control
bandwidth of IUT varied from 100 Hz to 1000 Hz.

ratio to the current control bandwidth for the IUT. Fig. 10(a) shows the required bandwidth of the CSTME when thesampling time delay Ts is not included. The requiredspeed PI controller

re*1
1+sTi_s

Time delay
element
Kp_cq(1+sTi_cq )1
sTi_cqvq_inv 1+sTs_inv

q-axis current PI controller

Kp_s(1+sTi_s )sTi_s1
1+sTi_cq

motor modelTime delay
element
Kp(1+sTi)1
sTi
vq_emu* 1+sTs_emu

q-axis current PI controller

1
1
R+sLq iq_emu * 1+sTi

re 1
Js

controller of CSTMEpControl block diagram of the CSTME and the IUT with the delay time element.

6000

Imaginary [s-1]bandwidth is 2.2 times of the current control bandwidth of
the IUT when the bandwidth of the IUT is set to from 400
Hz to 1000 Hz. The ratio of required bandwidth for the
CSTME is increased when the bandwidth of the IUT is set
to 400 Hz or less. The reason is to maintain the current PI
control for coupled inductor that fast for the electrical time
constant of the motor model. On the other hands, Fig. 10(b) shows the required current control bandwidth of the
CSTME with the sampling delay Ts_inv and Ts_emu. Then,the ratio of required bandwidth of the CSTME is increased.
As a result, the required bandwidth becomes more than 3.1
times of the current control bandwidth of the IUT whenthat of the CSTME is less than 1000 Hz.
Fig. 11 shows the difference of the pole placement
between with and without time delay in same bandwidth.
The current control bandwidth of the CSTME is set to1200 Hz and 1300 Hz when the IUT’s current control
bandwidth is 500 Hz. All the poles are in the LHP and thesystem is stable under both bandwidth in the model
without time delay. In contrast, poles are in the RHP when
the current control bandwidth of the CSTME is set to 1200
Hz in the model with time delay. Thus, the system is moreunstable due to the effect of the time delay, even in thesame current control bandwidth.

3000

fc_emu=1150 Hz

stableunstable

fc_emu=1450 Hz

-3000

-6000
-400

-200

fc_emu=1277 Hz
fc_emu=1150 Hz
0Real [s-1]

200

400

(a) Motor A.

6000

3000

fc_emu=1450 Hz-3000

fc_emu=1150 Hz

stable0

unstable

fc_emu=1450 Hz

-6000
-400

fc_emu=1302 Hz
fc_emu=1150 Hz

-200

0
200
400
Real [s-1](b) Motor B
Fig. 9 Root locus of model with time delay when the current control
bandwidth of the CSTME is varied from 1150 Hz to 1450 Hz.
3.5

3.0
2.5
2.0
1.5

IV. SIMULATION RESULTS

0

200
400
600
800
1000
Current control bandwidth of IUT [Hz](a) Without time delay.

fc_emu/fc_inv
[-]

3.5
3.0
2.5
2.0
1.5

0

200
400
600
800
1000
Current control bandwidth of IUT [Hz](b) With time delay.
Fig. 10 Stability limit of the model with and without time delay when
the current control bandwidth of IUT varied from 100 Hz to 1000 Hz(Motor A).

6000
Imaginary [s-1]This section verifies the validity analysis in section III
on the time domain. The PLECS (Plexim) is used for theverification. The current control bandwidth of the IUT is
set to 500 Hz. A ramped speed command is given in orderto accelerate in the rated acceleration time of the MUT(Motor A). After the end of acceleration, the step torquesupplies to the CSTME or the IPMSM from 0 Nm to 4.91
Nm (rated torque).
Fig. 12 shows the CSTME responses with and without
the time delay when the current control bandwidth of the
IUT is set to 500 Hz. The oscillation of torque and q-axis
current increase when the current control bandwidth of the
CSTME is 1032 Hz with the time delay and 1276 Hz
without the time delay although the oscillations decrease
when the current control bandwidth of the CSTME is 1033
Hz in (a) and 1077 Hz in (b). The stability limit becomesfrom Fig. 12 (a) and (b), the results of the stability limit
agree with the root locus analysis in Section III,
respectively. From these results, the stability analysis isverified.
Fig. 13 shows the difference in the CSTME responses
between with and without the time delay when the current
control bandwidth of the CSTME is set to 1300 Hz. As
shown in Fig. 11, the system is stable with and without
delay time when the current control bandwidth of the

fc_emu=1450 Hz

0

Imaginary [s-1]Fig. 8fc_emu/fc_inv[-]

controller of IUT

Coupling
inductor
1 iq
sLrec

3000

without time delay0

stablefc_emu=1300 Hz

with time delay

unstable

fc_emu=1200 Hz

-3000

-6000
-1500

-500

0
500
Real [s-1]Fig.11 The difference of pole placement between with and without
time delay in same bandwidth. The current control bandwidth of
CSTME is set to 1200 Hz and 1300 Hz (Motor A).

Rotational speed [rpm]

7500

5000

TL=0N・m TL=4.91N・m

2500

Rotational speed [rpm]

7500

5000

TL=0N・m TL=4.91N・m

2500
0

0
Torque [N・m]6
3

3

Decreasing Increasing
oscilation oscilation

016

Decreasing Increasing
oscilation oscilation

0

q-axis current [A]28

Torque [N・m]6

q-axis current [A]28
14

Decreasing Increasing
oscilation oscilation

Decreasing Increasing
oscilation oscilation

0
0.5s
0.5s
fc_emu =1277Hz
fc_emu =1033Hz
fc_emu =1276Hz
fc_emu =1032Hz(a) Without time delay. The stability limit is between 1032 Hz and 1033 Hz. (b) With time delay. The stability limit is between 1276 Hz and 1277 Hz.
Fig.12 CSTME response when the bandwidth of the current controller is near to stability limit (Motor A).
0

7500
5000
2500

Rotational speed [rpm]
TL=0N・m TL=4.91N・m

0

6

Rotational speed [rpm]TL=4.91N・m

7180
7160

Torque [N・m]3

6Torque [N・m]

4.5

3

0
24

7210
7200

q-axis current [A]

24

16

20

8

16

q-axis current [A]

12
0.5s
0.01s
With time delay
Without time delay
Fig.13 The difference of CSTME responses between with and without time delay when the current control bandwidth of CSTME is set to 1450 HZ(Motor A).

0

CSTME is 1300 Hz. However, the oscillations occur only
when there is the delay time. No oscillation occurs because
the dominant poles, which are the closest pole to RHP, areon the real poles when there is no the delay time, as shownin Fig. 11. In contrast, the complex conjugate polebecomes the dominant pole when there is the delay time.
Thus, the response becomes oscillatory. Then, theoccurrence of such oscillations in the motor drive testingis unacceptable. Therefore, the design of the current
control bandwidth for the CSTME must not only satisfy
the stability limits of the system, but also ensure that theimaginary part poles should be located at that point, whereif far from the real part poles.
Fig.14 shows the responses of the IPMSM (Motor A)
and the CSTME at stable conditions. The current control
bandwidth of the IUT and the CSTME are set to 500 Hz
and 2000 Hz, respectively. A comparison of the amount ofovershoot that occurs after a torque step agrees within anerror of 4 % or less. Thus, the CSTME imitates the IPMSM
with accuracy. This error is minimized by reducing the
integration time of the current PI controller of the coupling
inductor. This means that the accuracy of the imitation is
improved by increasing the current control bandwidth of

the CSTME. In addition, the delay time is considered toaffect the response of the PI controller. However, theovershoot is almost same with and without the delay time.
This is because the electrical time constant of the motor issufficiently slow compared to the response of the PI
controller.
V. CONCLUSIONSThis paper derives the required current control
bandwidth of the CSTME to prevent system instability.
The system stability with and without the sampling delay
was also analyzed using a root locus. From the analysis
result, the current controller of the CSTME required 2.2
times higher bandwidth than the IUT’s bandwidth in theideal conditions. On the other hands, when the samplingdelay is included, the required bandwidth of the CSTME
becomes more than 3.1 times when the IUT’s current
control bandwidth of less than 1000 Hz.
The future works are the following, analysis with more
rigorous models considering discretization, etc.;
experimental verification of stability under different
conditions such as coupling inductors, switching

7500

Rotational speed [rpm]5000

TL=0N・m TL=4.91N・m

2500
0

7210
7200

Rotational speed [rpm]TL=4.91N・m

7180

0.54 rpm

7160
Torque [N・m]

6

6

3

4.5

0

3

Torque [N・m]0.028 Nmq-axis current [A]

24

24

16

20

8

16

0

12

7500

0.5s
IPMSM
CSTME
(a) Without time delay.
Rotational speed [rpm]5000

TL=0N・m TL=4.91N・m

2500
0q-axis current [A]

0.124 A

0.01s

7210
7200

Rotational speed [rpm]TL=4.91N・m

7180

0.54 rpm

7160
Torque [N・m]

6

6

3

4.5

0

3

Torque [N・m]0.027 Nmq-axis current [A]

24

24

16

20

8

16

0

12

q-axis current [A]

0.124 A

0.5s
0.01s
IPMSM
CSTME
(b) With time delay.
Fig.14 IPMSM and CSTME responses at stable conditions. The delay time of CSTME Ts_emu and the integral time Ti are 10 s and 113 s in thiscondition, respectively (Motor A).

frequency, and so on; consideration of a method to achieve
fast current response for higher performance of the
CSTME.
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