Torque Control Method for Permanent Magnet Synchronous ...

IEEJ Journal of Industry ApplicationsVol.2 No.2 pp.106–112 DOI: 10.1541/ieejjia.2.106

Paper

Torque Control Method for Permanent Magnet Synchronous MotorOperating in Field Weakening Region at Middle Speed Range

Keiichiro Kondo∗a)Senior Member, Satoshi Kitamura∗ Non-member

(Manuscript received March 17, 2012, revised Sep. 11, 2012)

In this paper, a torque control method for permanent magnet synchronous motors (PMSMs) functioning in the middlespeed range of the field weakening control region is proposed. The current resonance due to d axis and q axis couplingcannot be neglected. The current resonance is depressed by the appropriate design of PID controller for the q-axiscurrent. The proposed controller designing method is verified both numerically and experimentally. The influence ofparameter changes is also examined to reveal that the Lq change affect the torque performance more than Lq and Rm

does.

Keywords: PMSM, field weakening control, torque control, PID compensator

1. Introduction

Permanent magnet synchronous motors (PMSMs) havebeen used in various application fields, such as railway ve-hicle tractions, automotives, air conditioners, elevators, etc.,because the efficiency of PMSMs is higher than the one of in-duction motors. PMSMs are driven with the field weakeningcontrol when the terminal voltage of PMSMs reaches to themaximum output voltage of inverters.

Several field weakening control methods for PMSMs havebeen proposed so far (1). In reference (2) and (3), the currentvector direction to weaken the field is changed dependingon the rotor speed to maximize the motor torque and cur-rent ratio. The torque control response is not discussed inboth (2) and (3). In reference (4), a voltage control pattern tominimize torque step change time for the fastest response isderived based on the Lagrange optimization method. How-ever, the voltage pattern is entirely feedforward control sys-tem. Thus the parameter changes are may affect much thetorque response. Since a method proposed in reference (5)is based on field weakening method, the same problems oc-curs with the parameter changes. In reference (6), the error ofthe phase RMS current and its reference is compensated bythe voltage phase angle in the voltage limit range. Using thephase RMS current is effective to limit the current amplitude.However the absolute torque is not controlled accurately inthis method.

The d-axis and q-axis coupling is a problem for highertorque control performance in PMSMs. In the field weak-ening region, only the voltage phase can be manipulated ifthe inverter outputs its maximum voltage. In this case, de-coupling control over d-axis and q-axis is impossible becauseonly a current can be controlled. Feedback control of q-axiscurrent is one of effective measures to control the torque ac-

a) Correspondence to: Keiichiro Kondo. E-mail: [email protected]∗ Engineering Dept., Graduate School of Chiba University

1-33, Yayoicho, Inage-ku, Chiba-shi 258-8540, Japan

curately, because the relation between the q-axis current andthe torque is more linear than the case using the phase RMScurrent (7). Thus, the strategy of the q-axis current feedback tomanipulate the phase angle of the voltage vector in the middleand higher speed range is proposed (8). In the control method,the error of q-axis currents is compensated by an integrationcompensator, which is featured by a simpler controller de-signing procedure. However, the control method using theintegration compensator can be effective only in the higherspeed range, because the integrator cannot depress the affec-tion of current oscillations caused by the coupling over d-axisand q-axis. Thus the method is available only in the case thatthe armature reaction reactance can be neglected due to thehigher rotor frequency than the cut off frequency of the sta-tor circuit. To cope with the problem in the middle speedrange, a control method is proposed to apply PID compen-sator to the q-axis currents controller, instead of integrator (9)

The PID compensator is designed to reduce the peak gain ofthe PMSM impedance, which is caused by the d-axis and q-axis coupling. Thus the controller can decouple the PMSMcurrent control system even in the middle speed range. Thisfeature is preferable for the mobile traction applications suchas railway vehicle tractions and automobile tractions, becausethe wider field weakening range is required to save the in-verter and the motor size and their mass in these applications.The characteristics of the proposed control method in (9) arediscussed further in this paper.

This paper starts with a numerical simulation to study cur-rent oscillation phenomenon due to the coupling over d-axisand q-axis systems. The characteristics of the control systemare analyzed to reveal the current oscillation phenomenon.To design the PID compensator, a linearized model of thePMSM is derived, not neglecting the phase lag characteris-tics due to the d-axis inductance and q-axis inductance in thestator windings. Then a controller is designed so that theopen-loop frequency characteristics of the control system areregarded as an integral element. The results simplify the de-sign of frequency characteristics of the control system. The

c© 2013 The Institute of Electrical Engineers of Japan. 106

Field Weakening Torque Control for PMSM at Middle Speed Range（Keiichiro Kondo et al.）

PID compensator is adopted depending on the rotor angularfrequency. This compensator design provides the torque con-trol performance independent from the rotor frequency. Inthe last part of this paper, the proposed designing method ofthe compensator gains is examined by the step response ofthe torque (q-axis) current to its reference with experimen-tal tests with 1.0 kW class interior permanent magnet syn-chronous motors (IPMSMs). Torque step responses at differ-ent angular frequencies are verified as results. In addition,the torque control performance is theoretically and experi-mentally verified in the case that motor parameters such asresistance and inductances of stator windings change. It is re-vealed that the q-axis inductance cause influences the torquestep performance. This paper contributes to provide a highertorque performance for the wider field weakening range suit-able for the mobile traction applications.

2. Field Weakening Control

2.1 Control Method in Field Weakening Range Inthe speed range where the terminal voltage of the PMSMreaches to the limit of the inverter output voltage, PMSM iscontrolled with the field weakening control. In this speedrange, the terminal voltage Vm is high enough to neglect sta-tor resistance drop. Thus, Vm can be expressed by (1).

Figure 1 shows the voltage vectors and the current vec-tors in the field weakening range. From Fig. 1, d-axis andq-axis current references can be expressed as shown in (2),(3). By substituting (2) and (3) to (1), the armature currentvector phase angle δ∗ can be obtained as (4) when the voltagereaches its maximum value Vmmax.

Vm = ω

√(−LqIq

)2+

(Φ f + LdId

)2 · · · · · · · · · · · · · · (1)

I∗d = −Im sin δ∗ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (2)

I∗q = Im cos δ∗ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (3)

δ∗=sin−1

LdΦ f −√(

LdΦ f

)2+(L2

d−L2q

) (V2m max

ω2−L2

qI2m−Φ2

f

)

Im

(L2

d − L2q

)· · · · · · · · · · · · · · · · · · · · (4)

2.2 Linearity of Torque Control CharacteristicThus, it is more effective that the voltage vector phase an-

gle change compensates the error of Iq and I∗q so as to controltorque rapidly and stably.

Figure 2 shows the field weakening control system which

Fig. 1. Vector diagram of the voltage vector phase anglecontrol

compensates the error between the torque current Iq and itsreference I∗q . From (2), (3) and (4), the current references I∗dand I∗q can be calculated when Vm is set its maximum value.

The voltage references V∗d and V∗q can be calculated bythe current references, the PMSM constant parameters andthe rotor frequency. A feedforward component of the volt-age vector phase angle ϕvFF can be calculated by the voltagereferences. Then the voltage vector amplitude is limited toVm max.(

V∗dV∗q

)= Vm max

( − sinϕvFF

cosϕvFF

)· · · · · · · · · · · · · · · · · · (5)

In addition, according to (6), a feedback component of thevoltage vector phase angle ϕvFB can be calculated. WhereCPID(s) is a PID compensator expressed by (7) and KphP,KphI , KphD are gains for a proportional element, an integratorelement and differential element, respectively. New voltagevector references V∗∗d and V∗∗q obtained as (8) by changingcoordinate.

ϕvFB = CPID(s)(I∗q − Iq

)· · · · · · · · · · · · · · · · · · · · · · · · (6)

CPID(s) = KphP + KphI/s + KphD · s · · · · · · · · · · · · · (7)(V∗∗dV∗∗q

)= Vm max

(cosϕvFB − sinϕvFB

sinϕvFB cosϕvFB

) (V∗dV∗q

)· · · · · · · (8)

3. Design of the Compensator Gains

3.1 Characteristics of the Proposed Control MethodThe block diagram of the proposed torque current con-

trol system is shown in Fig. 3. Figure 4 shows the simplifiedblock diagram of the proposed control system. In Fig. 4, thePID compensator gains can be analytically designed by ne-glecting feedforward control block GFF(s). In this section,GPMS M(s), the transfer function of PMSM model from ϕvFB

to Iq, is derived for the analytical design of the PID compen-sator. If a feedback component of the voltage vector phaseangle ϕvFB is small enough, (8) is arrowed to be approxi-mated to (9). Where cosϕvFB and sinϕvFB are approximatedby cosϕvFB � 1 and sinϕvFB � ϕvFB. V∗d ave and V∗q ave are theequibarium point of the voltage references under the approx-imated linearization. V∗d ave and V∗a ave are expressed by (10)and (11).

From (10) and (11), speed electromotive force ωaveΦ f bya permanent magnet flux is dominant component in V∗q ave.Since V∗q ave is much larger than V∗d ave, V∗d ave can be ne-glected.

Fig. 2. Block diagram of field weakening control ofPMSM/with q-axis current feedback

107 IEEJ Journal IA, Vol.2, No.2, 2013

Field Weakening Torque Control for PMSM at Middle Speed Range（Keiichiro Kondo et al.）

Fig. 3. Block diagram of the proposed control system

Fig. 4. Simplified block diagram of the control system

Table 1. Constant parameters of PMSM

(ΔV∗∗dΔV∗∗q

)=

(0 −ϕvFB

ϕvFB 0

) (Vd ave

Vq ave

)· · · · · · · · (9)

V∗d ave = RmI∗dFF − ωaveLqI∗qFF · · · · · · · · · · · · · · · · · · (10)

V∗q ave = RmI∗qFF + ωave(LdI∗dFF + Φ f ) · · · · · · · · · · · (11)

In Fig. 4, G′PMS M(s) can be expressed as (12) by (9) and (11).

G′PMS M(s) =ωaveVq aveLd

LdLqs2 + Rm(Ld + Lq)s + (R2m + ωave

2LdLq)· · · · · · · · · · · · · · · · · · · (12)

If ωaveΦ f is much larger than ωaveLdId in (12), V∗q qve can beapproximated by (13).

Vq ave � ωaveΦ f · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13)

The inequality expression (14) is obtained.

R2m � ωave

2LdLq · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14)

From (13) and (14), G′PMS M(s) is regarded as the form of (15).

GPMS M(s) =ωave

2LdΦ f

LdLqs2 + Rm(Ld + Lq)s + ωave2LdLq

· · · · · · · · · · · · · · · · · · · (15)

Gloop(s), which is a transfer function of the open-loop fromI∗q to Iq in Fig. 4. can be expressed by (16). Gclose(s), which is

Fig. 5. Current oscillations phenomenon by numericalsimulation simulation

Fig. 6. Frequency characteristics of GPMS M(s) andCPID(s)

a transfer function of the closed-loop from I∗q to Iq in Fig. 4,can be expressed by (17).

Gloop(s) = CPID(s) ·GPMS M(s) · · · · · · · · · · · · · · · · · (16)

Gclose(s) =Gloop(s)

1 +Gloop(s)· · · · · · · · · · · · · · · · · · · · · · · · (17)

From Fig. 3, rapid change of ϕvFB causes current oscilla-tions due to speed electromotive forces interfering betweend-axis and q-axis. In Fig. 5, this phenomenon is shown by anumerical calculation, where angular frequency of PMSM ωis 600 rad/s. The PMSM parameters used in the numericalsimulation are shown in Table 1. Figure 5 shows that angularfrequency of the current oscillations is almost equal to angu-lar frequency of PMSM.

The frequency characteristic of GPMS M(s) is shown inFig. 6, where ω is 600 rad/s. Figure 6 shows that the angu-lar frequency where the peak gain of GPMS M(s) appears isalmost equal to angular frequency of PMSM. Thus, the cur-rent oscillations can be depressed by cancelling the peak gainat the rotor angular frequency.

3.2 The Design of Compensator Gains As shownin Fig. 6, P stands for a point that gives the peak gain ofGPMS M(s) and Q stands for a point that gives the bottom gainof CPID(s). CPID(s) stands for a PID compensator and is atransfer function of ΔIq/φvFB. CPID(s) is designed to cancelthe peak gain of GPMS M(s), by its bottom gain.

The frequency characteristics of the closed-loop transferfunction Gclose(s) is preferable to be the first-order lag el-ement with the time constant of about 10 ms. Thus, thespecification of Gloop(s) must be set as an integral elementwith cut off angular frequency of 100 rad/s. The frequency

108 IEEJ Journal IA, Vol.2, No.2, 2013

Field Weakening Torque Control for PMSM at Middle Speed Range（Keiichiro Kondo et al.）

Fig. 7. Bode diagram of open-loop transfer functionGloop(s)

Fig. 8. Bode diagram of closed-loop transfer functionGclose(s)

characteristic of CPID(s) is designed to cancel the peakgain of GPMS M(s) and to have cut off angular frequency at100 rad/s, as shown in Fig. 8.

The time constant TdFF of the feedforward control in Fig. 3is determined before designing the PID compensator, Thiscontrol method applies low-pass filters to avoid current oscil-lations due to the feedforward components of the voltage ref-erences. Thus, TdFF would be better to be set about 10 ms ormore to avoid the peak gain of GPMS M(s). In addition, TdFF

is set larger than the time constant of the Iq step response, sothat the affection of GFF(s) may be neglected for the simplifydesign procedure. Thus, TdFF is set 30 ms.

The feedback controller is designed as followings. The an-gular frequencies and gains at point P and Q can be analyti-cally derived as follows. (15) is expressed by (18).

GPMS M(s) =a0

b2s2 + b1s + b0· · · · · · · · · · · · · · · · · · · (18)

Where, a0, b0, b1 and b2 are,

a0 = ωave2LdΦ f

b0 = ωave2LdLq, b1 = Rm(Ld + Lq), b2 = LdLq

Thus, gain of GPMS M(s) can be expressed by (19).

20 log10 |GPMS M( jω)|=20 log10

√a2

0

b22ω

4+(b21−2b0b2)ω2+b2

0

· · · · · · · · · · · · · · · · · · · (19)

Therefore, the angular frequency ωP which gives peak gainof GPMS M(s), ωP is calculated by (20).

|GPMS M( jω)| =√

a20

b22ω

4 + (b21 − 2b0b2)ω2 + b2

0

· · · · · · · · · · · · · · · · · · · (20)

ωP can be defined as the angular frequency which gives theminimum value of (21).

1

|GPMS M( jω)|2 =1

a20

{b2

2ω4 + (b2

1 − 2b0b2)ω2 + b20

}· · · · · · · · · · · · · · · · · · · (21)

When ω2p is represented by K, (22) is obtained by differenti-

ating (21) by K.

ddK

{1

|GPMS M( jω)|2}=

1

a20

{2b2

2K + (b21 − 2b0b2)

}= 0

· · · · · · · · · · · · · · · · · · · (22)

Consequently, ωP can be given by (23).

ωP =√

K =

√b0/b2 −

(b1/√

2b2

)2 · · · · · · · · · · · · · (23)

By substituting ωP in (23) into (19), the peak gain ofGPMS M(s) gp can be calculated. The gain of the transferfunction of the PID compensator in the frequency range isexpressed by (24).

|CPID( jω)| =√

K2phP +

(KphDω − KphI/ω

)2 · · · · · · (24)

Therefore, ωM can be obtained by differentiating (24) by ωand setting (25) as zero.

ddω|CPID( jω)| =

2K2phDωM − 2K2

phI/ω3M√

K2phP +

(KphDωM − KphI/ωM

)2= 0

· · · · · · · · · · · · · · · · · · · (25)

Consequently, ωM can be given by (26).

ωM =

√KphI/KphD · · · · · · · · · · · · · · · · · · · · · · · · · · · · (26)

By substituting ωM into (19), gM of the minimum value ofthe CPID(s) can be expressed by (27).

gM = 20 log10 KphP · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (27)

ωM stands for the cut off angular frequency of the PIDcompensator is designed to be equal to ωP, as expressed by(28).

ωM = ωP · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (28)

The gain of Gloop(jωp) at can be expressed by (29).

gP + gM = 20 log10 (ωP/ωC) · · · · · · · · · · · · · · · · · · · · (29)

The gain of Gloop(s) = GPID(s) GPMS M(s) at the cut off angu-lar frequency ωc is set 0 dB, as shown in (30).

20 log10 |CPID( jωC)GPMS M( jωC)| = 0 · · · · · · · · · · · (30)

From (28), (29) and (30), the gains of the PID compensatorKphP, KphI and KphD can be obtained as shown in (31), (32)

109 IEEJ Journal IA, Vol.2, No.2, 2013

Field Weakening Torque Control for PMSM at Middle Speed Range（Keiichiro Kondo et al.）

and (33).

KphD =KphI

ω2P

· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (31)

log10 KphP = log10

(ωP

ωC

)− gP

20· · · · · · · · · · · · · · · · · · (32)

KphI =

√√√√b22ω

4 + (b21 − 2b0b2)ω2 + b2

0 − a20K2

phP(ωC/ω

2P − 1/ωC

)2

· · · · · · · · · · · · · · · · · · · (33)

These gains include angular frequency ω. Thus, these gainsare adopted by ω to keep the control characteristics

4. Experimental Validation of Proposed Method

The results of step response of the q-axis current by thenumerical simulations and the experimental tests are shownin Fig. 9 and Fig. 10, respectively. The PMSM parametersfor this study are used in the Table 1. The step responsesof q-axis current are examined at 600 rad/s and 800 rad/s toevaluate the affection of the rotor speed. In the both cases ofthe rotor frequencies, voltage vector phase angle ϕvFB of thefeedback component enhance the motor torque.

Step responses of Iq and motor torque Tm show the first-order lag with the designed time constant of 10ms and theyare independent from the affection of the different rotor fre-quency. The proposed control system and its designingmethod are verified.

5. Analysis of Parameter Changes of PMSM

As shown in (31)–(33), the nominal values, Rm, Ld and Lq,are used to design the controller gains. Thus, by the motorparameters change, the control performance can be deterio-rated. The torque step responses at two cases of the temper-atures such as −20 centi degrees and 120 centi degrees areexamined, when the nominal value RNominal is 1.0 [Ω] at 20centi degrees and temperature coefficient α is 0.0393 [Ω/deg].

In Fig. 10(I)(a), the peak gain of the transfer functionof PMSM is influenced by the Rm change. However,Fig. 10(I)(b) shows that the cutoff angular frequency of theopen-loop gain is independent from the change of Rm. InFig. 10(I)(c), the closed loop gain is not affected by thechange of Rm in lower frequency range where the gain ishigher. Thus, change of the stator windings resistance Rm

is not major problem for the torque control performance ofthe proposed control system.

50% and 150% of the nominal values of Ld are assumedin order to examine the influences of the d-axis induc-tance Ld change. The nominal value of d-axis inductanceis 12.0 [mH]. Though the peak gain of GPMS M(s) in 150%of the nominal value is higher than the nominal value inFig. 10(II)(a), the cutoff angular frequency of the open-loopgain in Fig. 10(II)(b) is independent from the d-axis induc-tance changes. In Fig. 10(II)(c), the closed loop gain is notaffected by the change of Ld in lower frequency range wherethe gain is higher as well as the case of Rm change. Thus, theLd change also does not cause major problem on the torquecontrol performance in the proposed control method.

However, as shown in Fig. 10(III)(a)–(c), change of the q-axis inductance Lq affects the torque step response more than

(a) ω = 600.0 (rad/s)

(b) ω = 800.0 (rad/s)

Fig. 9. Experimental results of the step response

the case of the Rm and Ld change. Figure 10(III) shows thegain of the transfer functions in cases of 50% and 150% ofthe nominal values of Lq. The nominal value of q-axis in-ductance is 14.0 [mH]. The gains of PMSM transfer func-tion GPMS M(s) and the open loop transfer function Gopen(s)changes due to the Lq change in all over frequency range.This causes the change of the dynamic range of the closed

110 IEEJ Journal IA, Vol.2, No.2, 2013

Field Weakening Torque Control for PMSM at Middle Speed Range（Keiichiro Kondo et al.）

(a) Gain of GPMS M (jω) (a) Gain of GPMS M (jω) (a) Gain of GPMS M (jω)

(b) Gain of Gopen(jω) (b) Gain of Gopen(jω) (b) Gain of Gopen(jω)

(c) Gain of Gclose(jω) (c) Gain of Gclose(jω) (c) Gain of Gclose(jω)

(1). Bode Diagram at Rm changing. (2). Bode Diagram at Ld changing. (3). Bode Diagram at Lq changing.

Fig. 10. Bode Diagram at parameters changing

loop function Gclose(s). Thus, the torque control performanceis affected by the Lq change more than the case of the Rm andLd change. This can be explained by (34) obtained from (19).

|GPMS M( jω)|

=1Lq

√(ω2

aveLdΦ f )2

(Ldω2)2+{R2m(Ld/Lq+1)2−2(ωaveLd)2}ω2+(ω2

aveLd)2

· · · · · · · · · · · · · · · · · · · (34)

The d-axis inductance affects minor the gain of GPMS M(s)because Ld is almost cancelled both in the numerator anddenominator of (34). The affection of the armature resis-tance changing is also weak because Rm

2(Ld/Lq+1)2 is smallenough to neglect the affection. However, the q-axis induc-tance affects more the gain of GPMS M(s), because the gain ofthe PMSM much depends on Lq as shown in (35), which canbe converted from (34).

20 log10 |GPMS M( jω)| = −20 log10 Lq + 20 log10 A

· · · · · · · · · · · · · · · · · · · (35)

This is because only the q-axis current is controlled by the

d-axis voltage that consists mainly of the armature reactionvoltage by q-axis inductance.

6. Verification of Parameter Changes of PMSMby Experimental Tests

The experimental tests validate the results of theoreticalanalysis in section 5. In the experimental tests, the values forthe controller are set as 50% and 150% of the nominal values.

Figure 11 shows the experimental tests results of the stepresponse of q-axis current at 600 rad/s.

Figure 11(a) shows the step response of the nominalizedq-axis current. These are the cases of the 50% and 150% ofnominal resistance of the stator windings Rm. The step re-sponse is almost independent from the Rm change.

Figure 11(b) shows the step response of nominalized q-axiscurrent in the case of d-axis inductance changes. As shownin the gains characteristics of Fig. 10(II), the step response isaffected minor by the Ld changes.

The q-axis inductance change causes major influence onthe step response of the nominalized q-axis current as shownin Fig. 10(III). In the case of the lower value of Lq than the

111 IEEJ Journal IA, Vol.2, No.2, 2013

Field Weakening Torque Control for PMSM at Middle Speed Range（Keiichiro Kondo et al.）

(a) at Rm changing. (b) at Ld changing. (c) at Lq changing.

Fig. 11. Experimental results of step response of nominalized q-axis current at parameters changing

nominal value, the step response is slower and in the case ofthe higher value of Lq than the nominal value, the step re-sponse is faster but the over shoot increase. As far as theovershoot cause major problem in the whole control system,the value of the Lq in the PID compensator is set smaller thanthe range of the possible actual value of Lq.

7. Conclusion

In this paper, q-axis current control method with PID com-pensator in the field weakening range of PMSM are presentedand examined its characteristics. The control system com-pensates the error between Iq and its reference I∗q by manip-ulating the voltage vector phase angle ϕvFB. The proposedmethod is featured to be available in not only the higher speedrange and but the middle speed range by coinciding the fre-quency which gives the peak gains of PID compensator tosynchronous angular frequency of the PMSM. Experimen-tal tests verify the proposed control method. In addition, theinfluence on the torque control performance by the motor pa-rameters changes are examined both theoretically and experi-mentally. These result in the q-axis inductance is more sensi-tive to the torque control performance, but the value of q-axisinductance in the controller is set smaller as far as the overshoot does not causes major problem. This study reveals thatthe proposed control method with PID compensator is avail-able enough to drive PMSM in wider operational speed rangein the field weakening region of PMSM.

References

( 1 ) K. Yasui, Y. Nakazawa, and M. Mochizuki: “A Field Weakening Control forPMSMs of Hybrid Electric Vehicle”, Proc. IEEJ JIASC 2010, (CD-ROM),No.1-O4-3, pp.I-149–152 (2010) (in Japanese)

( 2 ) Y. Nakazawa, R. Kurosawa, K. Sakai, and M. Arata: “A Flux WeakeningControl for Permanent Magnet Reluctance Motor”, IEE Japan, Vol.140, No.4,p.1575 (2000)

( 3 ) S. Shimizu, S. Morimoto, and M. Sanada: “Sensorless Control Performanceof IPMSM with Over-modulation Range at High Speed”, Proc. InternationalConference of EelectricMachinary and Systems (ICEMS) CD-ROM, pp.1–5(2009)

( 4 ) L. Smith, S. Doki, and S. Okuma: “Novel Voltage Limiter for Fast TorqueResponse of IPMSM in Voltage Saturation Region”, IEE Japan Trans. IA,Vol.128, No.12, pp.1346–1356 (2008)

( 5 ) M. Tursini, E. Chiricozzi, and R. Petrella: “Feedforward Flux-WeakeningControl of Surface-Mounted Permanent-Magnet Synchronous Motors Ac-cording for Resistive Voltage Drop”, IEEE Trans, Vol.57, pp.440–448 (2009)

( 6 ) T. Yamakawa, S. Wakao, K. Kondo, and T. Yoneyama: “A New Flux Weak-ening Operation of Interior Permanent Magnet Synchronous Motors for Rail-way Vehicle Traction”, 11th European Conference on Power Electronics andApplications, CD-ROM (2004)

( 7 ) S. Kitamura and K. Kondo: “Study on the Control Method of PermanentMagnet Synchronous Motor at the Limited Voltage and Current Region”, IEEJapan, SPC-09-175, LD-09-65, pp.49–54 (2009)

( 8 ) K. Ohi, K. Tobari, and Y. Iwaji: “High Response Field Weakening Control byVoltage Phase Operation”, IEEJ Trans. IA, Vol.129, No.9, pp.866–873 (2009)

( 9 ) S. Kitamura and K. Kondo: “An enhanced torque control method of perma-nent magnet synchronous motor in the field weakening region”, Proc. Interna-tional Conference on Electrical Machines and Systems (ICEMS) (CD-ROM),pp.781–786 (2010)

Keiichiro Kondo (Senior Member) received B.S. and Ph.D. in the fac-ulty of electrical engineering, department of scienceand technology, of Waseda University in 1991. Heentered Railway Technical Research Institute in 1991and 2000 respectively. Since 2007, Dr. Kondo is anassociate professor of electrical and electronic engi-neering course of graduate school of Chiba Univer-sity. His research interest is power electronics, ACmotor drive, and their application to the railway vehi-cle traction. Dr. Kondo is a member of the Institute

of Electrical Engineers of Japan. He is also a member of the IEEE IndustryApplications, Industrial Electronics, and. He is a Dr.Eng. and ProfessionalEngineer Japan (Mechanical Engineering, Technical Management).

Satoshi Kitamura (Non-member) received the B.E., and M.E., de-grees in electrical and electronics engineering fromChiba University, Japan, in 2009, and 2011, respec-tively. Since 2011, he has been a member of TobuRailway Co. His research interest is PMSM fieldweakning control.

112 IEEJ Journal IA, Vol.2, No.2, 2013