stationary reference frame position sensorless control

IEEJ Journal of Industry ApplicationsVol.6 No.3 pp.181–191 DOI: 10.1541/ieejjia.6.181

Paper

Stationary Reference Frame Position Sensorless Control Based on StatorFlux Linkage and Sinusoidal Current Tracking Controller for IPMSM

Ryota Takahashi∗ Student Member, Kiyoshi Ohishi∗ Fellow

Yuki Yokokura∗ Member, Hitoshi Haga∗ Member

Tenjiroh Hiwatari∗ Student Member

(Manuscript received Feb. 29, 2016, revised Sep. 30, 2016)

Generally, standard direct torque control (DTC) does not require fine current responses from the current controllerbecause the torque and flux of a DTC-based drive are controlled by a closed-loop system without current loops. It isoften difficult for the standard DTC to achieve the desired current regulation and fine harmonic current disturbancesuppression performancew. In order to overcome these problems, this paper proposes a new stationary referenceframe position sensorless control system based on stator flux linkage estimation, and a new sinusoidal current trackingcontroller. In this paper, the current control performance of IPMSMs using the proposed sinusoidal current trackingcontroller is evaluated through numerical simulation and experiments. Finally, using the proposed sinusoidal currenttracking controller, the effectiveness of the proposed stationary reference frame position sensorless control system withthe stator flux control method is confirmed through experimental results.

Keywords: IPMSM, position sensorless control, disturbance suppression characteristics, stationary reference frame, sinusoidaltracking current controller

1. Introduction

Internal permanent magnet synchronous motors (IPMSMs)have been applied for motors in electric vehicles and vari-ous industrial applications. Recently, to reduce the size andcost of the motor drive systems, position sensorless controlmethods have been studied extensively. Direct torque control(DTC) has often used to its position sensorless control basedon stator flux estimation (1)–(4). DTC has the merits of both fasttorque response and low sensitivity to inductance variations.Hence, DTC has been used in many types of AC motor.

DTC has many regulation methods of stator flux and motortorque. DTC can have a fast torque response. The standardtype of DTC uses both a switching table of space voltagevector and hysteresis comparator of torque and flux (1). Othertype of DTC is called Reference Flux Vector Calculator DTC(RFVC-DTC) (2)–(4). RFVC-DTC can have a fine and smoothtorque response without torque ripple. In RFVC-DTC, thetorque error is converted into the torque angle information byPI torque controller. Its voltage reference is determined bythe torque angle information. Generally, the standard DTCand RFVC-DTC do not use the current regulated and do notregulate the motor current directly. Since IPMSM is drivenby motor current, DTC should be regulated by the motor cur-rent. Therefore, the sensorless control method having the PIcurrent controller has been realized (5) (6), whose name is statorflux vector control (SFVC). In this case, its current controlleris located on the rotating reference frame.∗ Nagaoka University of Technology

1603-1, Kamitomioka-machi, Nagaoka, Niigata 940-2188,Japan

Standard DTC, RFVC-DTC and SFVC have the fine torquetracking performance. However, since the standard DTC andRFVC-DTC need not have current controller having a finecurrent response of primary frequency, the standard DTC andRFVC-DTC sometimes can not have a fine harmonic currentdisturbance suppression performance.

On condition of primary frequency, its d-q current informa-tion in rotating reference frame is equal to its α-β current in-formation in stationary reference frame (7). On the other hand,in case of harmonic frequency, the d-q current control doesnot often have the desired performance.

Moreover, the current control performance of IPMSMs us-ing the new sinusoidal tracking current controller is evaluatedby the numerical simulation results and experimental results.

The current control in the stationary reference frame cansuppress the harmonic current better than current controlin the rotating reference frame. Thus, robust performanceagainst the harmonic current is obtained by control of the sta-tionary frame.

In order to obtain robust performance, this paper proposesthat the proposed stationary reference frame position sensor-less control is accomplished with a new current control sys-tem in the α-β stationary frame.

This paper confirms the validity of the proposed method byusing the experimental results.

2. Sinusoidal Current Tracking Control

2.1 Nomeclature Definition diagram of coordinatesis shown in Fig. 1. Here, superscrips and symbol and abbre-viations are shown as follow;

c© 2017 The Institute of Electrical Engineers of Japan. 181

Sinusoidal Current Controller based Stationary Frame Sensorless Control（Ryota Takahashi et al.）

Fig. 1. Coordinate of stationary reference frame

Superscripts

:̂ Estimated quantitiesref : Reference quantitiesres: Response valuedis: Disturbance

Symbol and Abbreviations

vd, vq: Stator q- and d-axes voltages.vα, vβ: Stator α- and β-axes voltages.vM , vT : Stator M- and T-axes voltages.id, iq: Stator q- and d-axes currents.iα, iβ: Stator α- and β-axes currents.iM, iT : Stator M- and T-axes currents.Ra: Stator resistance.φa: Permanent magnet flux linkage.Ld, Lq Stator d- and q-axes inductances.p: Derivative operator.P: Pole pairs.Vdc: DC link voltage.ψ, ψα, ψβ: Stator α- and β-axes flux.ψM , ψT : Stator M- and T-axes flux.T : Torque.ωre, θre: Electrical angular velocity and position.ωrm, θrm: Mechanical angular velocity and position.ωψ, θψ: Stator flux angular velocity and position.ωc: Pole of current control system.ωs: Pole of speed control system.ω f : Pole of flux control system.ωLPF : Pole of low pass filter.ωB: Pole of band pass filter.JM: Inertia moment.Eex: Extended electromotive force.2.2 Stationary Reference Frame Model of IPMSMIn this paper, the current control system for IPMSM is

designed by sinusoidal tracking controller in the stationaryreference frame (i.e., α-β reference frame). At first, the cir-cuit equations d − q reference frame are given in (1). Usingthe rotating frame transformation, (1) is converted into (3),which is the voltage equation in α-β reference frame.

[vd

vq

]=

[Ra + pLd −ωreLq

ωreLd Ra + pLq

] [idiq

]

+

[0

ωreφa

]· · · · · · · · · · · · · · · · · · · · · · · · · · (1)

Eex = (Ld − Lq)(ωreid + piq) + ωreφa · · · · · · · · · · · · (2)[vαvβ

]=

[Ra + pLα −pLαβ−pLαβ Ra + pLβ

] [iαiβ

]

+ωre

[2Lαβ Lα − Lβ

Lα − Lβ −2Lαβ

] [iαiβ

]

Fig. 2. Structure of current control system and EEMFmodel

+ωreφa

[ − sin θre

cos θre

]· · · · · · · · · · · · · · · · · · · (3)

where

Lα =12

[Ld + Lq + (Ld − Lq) cos 2θre] · · · · · · · · · · · · (4)

Lβ =12

[Ld + Lq − (Ld − Lq) cos 2θre] · · · · · · · · · · · · (5)

Lαβ = −12

[(Ld − Lq) sin 2θre] · · · · · · · · · · · · · · · · · · · · (6)

In this paper, an extended electromotive force (EEMF)model (8) is used for design of current-controller. The EEMFcircuit equations of IPMSM in d−q reference frame are givenby (7).[

vd

vq

]=

[Ra + pLd −ωreLq

ωreLq Ra + pLd

] [idiq

]+

[0

Eex

]· · · · · · · · · (7)

Using the rotating frame transformation, (7) is converted into(8), which is the EEMF-type voltage equation in α-β refer-ence frame. Using (8), the plant model of sinusoidal currenttracking controller is defined as shown in Fig. 2.[

vαvβ

]=

[Ra + pLd ωre(Ld − Lq)

−ωre(Ld − Lq) Ra + pLd

] [iαiβ

]

+ Eex

[ − sin θre

cos θre

]· · · · · · · · · · · · · · · · · · · · (8)

2.3 Design of Current Control System based on Sinu-soidal Current Tracking Controller In α-β referenceframe, the current controller must have the internal model ofsinusoidal wave function, such as co-sine function, as shownin Fig. 2.

In this paper, the EEMF model is used for design of cur-rent controller, and the internal model of current regulator isco-sine function. The proposed current control system basedon EEMF model is realized as shown in Fig. 2. In Fig. 2, thecoupling EEMF component are treated as the disturbancesfor the current control system.

The transfer function from irefα to ires

α is given by (9).

Grefres =iresα

irefα

=−b1s − b0

s3 + a2s2 + a1s + a0· · · · · · · · · · · · · (9)

a0 =1Ld

(Raω2re + f3ω

2re − f2) · · · · · · · · · · · · · · · · · · · (10)

a1 =

(ω2

re −f1Ld

)· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (11)

182 IEEJ Journal IA, Vol.6, No.3, 2017


(a) Disturbance suppression characteristics of the positive-phaseharmonic components

(b) Disturbance suppression characteristics of the negative-phaseharmonic components

Fig. 3. Disturbance suppression characteristics using d-q PI current control

a2 =Ra

Ld+

f3Ld· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (12)

b0 =f2Ld· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (13)

b1 =f1Ld· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (14)

The current control system is designed by using (9). On thebasis of the poles placement method, the poles of the sinu-soidal current tracking controller are designed so as to havethe desired roots. The feedback gains of the sinusoidal cur-rent tracking controller are given by (15)–(17). Using thesegains, the poles of the current control system are arranged inmultiple roots in the band. The zero also has a stable place-ment. Therefore, the current control system has stable opera-tion using the feedback gains of (15)–(17).

f1 = Ld(ω2re − 3ω2

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

f2 = Ld(3ωcω2re − ω3

c) · · · · · · · · · · · · · · · · · · · · · · · · · (16)

f3 = 3Ldωc − Ra · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (17)

2.4 Evaluation based on Extended Transformation ofthe Disturbance Suppression Characteristics Using theextended transfer function (9) (10), the both disturbance suppres-sion characteristics of d-q PI current control and α-β sinu-soidal current control are evaluated in this paper by using theextended transfer function, which is introduced in Appendixof this paper. The extended transfer function can evaluate theboth frequency characteristics of d-q PI regulator and α-β-sinusoidal regulator on the positive and negative harmonicsphase components. Here, j is the complex coefficient. Thetransfer function from idis

α to iresα in d-q PI regulator is given

by (18).

(a) Disturbance suppression characteristics of the positive-phaseharmonic components

(b) Disturbance suppression characteristics of the negative-phaseharmonic components

Fig. 4. Disturbance suppression characteristics using α-β sin current control

Gdisdq−PI =

iresαβ

idisαβ

=−s2 + n1s + n0

s2 + m1s + m0· · · · · · · · · · · · · · · · (18)

m0 =KI − j(Ra + KP)ωre

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

m1 =(Ra + KP − jLdωre)

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

n0 =jRaωre

Ld· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (21)

n1 =−Ra + jLdωre

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

The transfer function from idisα to ires

α in the α-β sinusoidalcontrol is given by (23).

Gdisαβ−sin =

iresαβ

idisαβ

=−s3 − q2s2 − q1s − q0

s3 + a2s2 + a1s + a0· · · · · · · · · (23)

q0 =Ra

Ldω2

re · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (24)

q1 = ω2re · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (25)

q2 =Ra

Ld· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (26)

Using (18) and (23), each bode diagram of d-q PI regulatorand α-β sinusoidal regulator is obtained for the positive-phasedisturbance suppression characteristics, as shown in Fig. 3(a)and Fig. 4(a). In Fig. 3(a) and Fig. 4(a), the fundamental fre-quency performance of d-q PI regulator is equivalent equalto that of α-β sinusoidal regulator. However, the harmonicdisturbance suppression performance of α-β sinusoidal reg-ulator is slightly better than that of d-q PI regulator. Com-paring the two disturbance suppression characteristics, the



Fig. 5. Experimental system for evaluation on distur-bance suppression performance d-q PI current regulatorand α-β sinusoidal current regulator

(a) FFT analysis u-phase current responses with d-q PI regulator.

(b) FFT analysis results u-phase responses with α-β sinusoidal regulator.

Fig. 6. Experimental results of u-phase current FFTanalysis

harmonic disturbance suppression performance of the α-β si-nusoidal regulator is one order higher than that of the d-q PIregulator. Therefore, the harmonic disturbance suppressionperformance of the α-β sinusoidal regulator is slightly bettercompared with the d-q PI regulator.

Similarly, Fig. 3(b) and Fig. 4(b) show each bode diagramof the negative phase disturbance suppression characteristics,respectively. The negative-phase harmonic disturbance re-jection performance of α-β sinusoidal regulator is better thanthat of d-q-PI regulator.

As the result, the effectiveness of α-β sinusoidal controlleris confirmed through the experimental results of Fig. 6. Therated values and specifications of tested motor are shown inTable 1, respectively. In the experiment, the motor torquecurrent is maintained at iq = 1 A, which is 40% load. Themotor speed is maintained at 100 rpm. In order to confirmthe disturbance suppression characteristics, the experimentalresults are shown in Fig. 6(a) and Fig. 6(b). The robust per-formance of αβ − sin is better than dq-PI. 7th and 13th are apositive phase disturbance. Because the order of the transfer

Table 1. Rated values and specifications of tested motor

Ra 2.8 [Ω]Ld 28 [mH]Lq 70 [mH]P 3

JM 1.152*10−3 [kgm2]Carrier frequency PWM Inverter 10 [kHz]

Rated current of u-phase 3 [A]Rated speed 1800 [rpm]Rated power 750 [W]

Table 2. Specification of tested speed control system

Poles of the speed control system ωs 80 [rad/s]Poles of the current control system ωc 2000 [rad/s]

Fig. 7. Speed control system using I-P speed controller

function of αβ − sin is high, αβ − sin can reduce the positivephase disturbance better than the dq-PI. 5th and 11th is a neg-ative phase disturbance. αβ − sin can be reduced more thandq-PI because αβ − sin can be suppressed even for negativephase. From the above results, the current control systemusing the sinusoidal tracking controller can reduce the cur-rent harmonics better than the current control system usingthe PI controller. Therefore, the current control system us-ing the sinusoidal tracking controller is expected to suppresstorque ripple and motor noise generated by the structure ofthe winding and the space harmonic flux. The disturbancesuppression characteristics of the current control system us-ing the sinusoidal tracking controller in the modified IPMSMcan also be found in the Appendix.2.5 Experimental Results of Sinusoidal Current Tra-

cking Controller with Position Sensor Using the α-βsinusoidal current controller, the speed control system withposition sensor is constructed. The transfer function fromω

refrm to ωres

rm is given by (27).

Gre f res =ωres

rm

ωrefrm

=KIs

Jms2 + KPss + KIs· · · · · · · · · · · · (27)

where KPs and KIs represent the proportional and integralgains of the speed controller. The speed controller is an I-Ptype controller. The speed control system is shown in Fig. 6.KPs and KIs are calculated by the use of (27) and the poleplacement method. Using (9) and (27), the specifications ofthe tested current control system and the tested speed controlsystem are designed as shown in Table 2.

Figure 8 shows the experimental results of speed controlsystem based on α-β sinusoidal current controller with posi-tion sensor. The proposed speed control system based on α-βsinusoidal current controller has good responses.

3. Position Sensorless Control based on αβ-sinCurrent Controller

3.1 Sensorless Control Method of Torque (Method 1)Here, the principle of proposed position sensorless control

is presented in Fig. 9. The motor torque of IPMSM is defined



Fig. 8. Experimental results of speed step response us-ing speed control system based on sinusoidal currenttracking controller with position sensor

Fig. 9. Coordinate of position-sensorless control in sta-tionary reference frame

by (28). The stator flux linkage vector is estimated by using(29) and (30) (11) (12).

T = Pψ ∗ iref

= P(ψαiβ − ψβiα) · · · · · · · · · · · · · · · · · · · · · · · · · · · · (28)

ψ̂α =

∫ t

0(v∗α − Raiα)dt + ψ̂α|t=0 · · · · · · · · · · · · · · · · · (29)

ψ̂β =

∫ t

0(v∗β − Raiβ)dt + ψ̂β|t=0 · · · · · · · · · · · · · · · · · · (30)

Fig. 10. Stator flux estimator using APF based on BPF

The phase θψ in the α-axis, its angular speed ωψ, and theabsolute value |ψ| of the stator interlinkage magnetic flux vec-tor are calculated using (31)–(33), respectively. The angu-lar frequency of the stator flux is calculated by the quasi-differentiate of the phase of the stator flux. This paper usesωLPF in Fig. 10 because the quasi-differentiate is needed forthe differential operation and LPF. The motor torque currentreference iref is defined in (34). θi is the motor current phaseof α-axis, which is given by (35). Using (34) and (35), thispaper proposes that the αβ-axis current references are cal-culated by using (36) and (37). As the results, this paperproposes a new stationary reference frame position sensor-less control based on sinusoidal tracking current controllerfor IPMSM.

θ̂ψ = tan−1 ψ̂β

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

ω̂ψ =sωLPF

s + ωLPFθ̂ψ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (32)

|ψ̂| =√ψ̂2α + ψ̂

2β · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (33)

iref =T ref

P|ψ̂| · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (34)

θ̂i = θ̂ψ +π

2· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (35)

irefα = iref cos θ̂i · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (36)

irefβ = iref sin θ̂i · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (37)

3.2 Stator Flux Estimation of Using APF based onBPF (29) and (30) can not be calculated in the actualsystem because (29) and (30) have a complete integrationcalculation process. In order to overcome this problem, thispaper uses the stator flux estimation of using the all pass fil-ter (APF) based on band pass filter (BPF) (13) (14). Stator fluxestimation using APF based on BPF is shown in Fig. 9. Thecoordinate of stator flux estimator with APF based on BPF isshown in Fig. 10.

(I)

uα = vα − Raiα · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (38)

uβ = vβ − Raiβ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (39)

(II)This paper uses the APF whose transfer function of is

shown in (40).

GAPF =s − kB

s + kB· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (40)

vap fα = GAPFuα · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (41)

vap fβ = GAPFuβ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (42)

where vap fα and vap f

β are the value after the APF. Here, kB is



determined as shown in (43).

kB = ωB · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (43)

In this paper, using (43), the phase characteristics is shiftedto − π2 degrees.

(III)The drift occurs when the stator flux is estimated by (29)

and (30). BPF is used to avoid the drift. However, thephase characteristic of the estimated value of the stator fluxis changed by the BPF. Therefore, it is necessary to use (44)in order to obtain the phase characteristic that is equal to anideal integrator.

GAPFideal =s + kB

s − kB· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (44)

However, (44) has an unstable pole. In order to realize (44),this paper used a vector rotator. The description of a vectorrotator is shown below.

θv = tan−1 uβuα· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (45)

The output vector phase of APF is shown in (46).

θap fB = tan−1v

ap fβ

vap fα

· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (46)

The vector rotator is shifted to ϕ = θv − θap fB . The rotator isdescribed as shown in (47).

⎡⎢⎢⎢⎢⎣ vap f ′α

vap f ′β

⎤⎥⎥⎥⎥⎦ =[

cos 2ϕ − sin 2ϕsin 2ϕ cos 2ϕ

] ⎡⎢⎢⎢⎢⎣ vap fα

vap fβ

⎤⎥⎥⎥⎥⎦ · · · · · · · · · (47)

where vap f ′α and vap f ′

β are the value after a vector rotator.(IV)As the result, using APF based on BPF, the stator flux link-

age is estimated without phase error.

ψ̂α =ωBs

s2 + 2ωBs + ω2B

vap f ′α · · · · · · · · · · · · · · · · · · · · · (48)

ψ̂β =ωBs

s2 + 2ωBs + ω2B

vap f ′β · · · · · · · · · · · · · · · · · · · · · (49)

B =

√(ω2

re − ω2B)2+ 4ω2

reω2B

ωBω2re

· · · · · · · · · · · · · · · · · · (50)

|ψ̂| = B√ψ̂2α + ψ̂

2β · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (51)

Fig. 11. Coordinate of stator flux estimator with APFbased on BPF in stationary reference frame

Fig. 12. Bode diagram of the stator flux estimator of us-ing APF based on BPF

Fig. 13. Proposed position sensorless speed control system using sinusoidal current tracking controller withoutflux control loop (Method 1)



ωresrm (s)

ωrefrm (s)

=ω2

s

s2 + 2ωss + ω2s· · · · · · · · · · · · · · · · · · · · · (52)

where B is a correction equation of the gain characteristic. Asthe DC gain of BPF becomes −∞ as shown in Fig. 12, the off-set of the current sensor is completely attenuated. In addition,the gain characteristic in Fig. 12 is affected by the angular fre-quency of the BPF. The phase characteristic in Fig. 12 is notaffected by the angular frequency of the BPF. In addition, thephase characteristic is equal to an ideal integrator.

Therefore, this paper realizes the proposed position sen-sorless speed control system using the new sinusoidal currenttracking controller as shown in Fig. 12, which is Method 1of this paper. The control system of Method 1 is composedof only a stationary reference frame. Therefore, this controlsystem does not require a coordinate transformation into arotating coordinate. This is because it converts the output ofthe speed controller to the current command on the stationaryreference frame by (34)–(36). The Method 1 control systemdoes not require coordinate transformation to a rotating co-ordinate because it does not depend on the phase estimationaccuracy.

(51) is obtained by using the angular frequency of thespeed control system from (27). (51) is used for the inter-nal model of the sinusoidal tracking current controller.3.3 Sensorless Control Method of Torque and Flux

(Method 2) In high-speed region of operation, it is nec-essary to carry out a flux-weakening control. To control thestator flux, this paper perform the coordinate conversion fromα-β axis to M-T axis (15) (16). The proposed magnetic flux con-troller is shown in Fig. 14. The current references iref

M and

irefT in Method 2 is changed into iref

α and irefβ as shown in

(53). As the result, Fig. 15 shows the proposed position sen-sorless speed and flux control system using new sinusoidalcurrent tracking controller, which is Method 2 of this paper.On condition of iref

M = 0 and irefT = iref , (53) becomes (54).

Therefore, on condition of on irefM = 0 in Method 2, Method 2

becomes equivalent equal to Method 1.

⎡⎢⎢⎢⎢⎣ irefα

irefβ

⎤⎥⎥⎥⎥⎦ =[

cos θ̂ψ − sin θ̂ψsin θ̂ψ cos θ̂ψ

] [irefM

irefT

]

=

[irefM cos θ̂ψ − iref

T sin θ̂ψirefM sin θ̂ψ + iref

T cos θ̂ψ

]

=

[irefM sin θ̂i + iref

T cos θ̂i

−irefM cos θ̂i + iref

T sin θ̂i

]· · · · · · · · · · · (53)

⎡⎢⎢⎢⎢⎣ irefα

irefβ

⎤⎥⎥⎥⎥⎦ =[

iref cos θ̂i

iref sin θ̂i

]· · · · · · · · · · · · · · · · · · · · · · · · (54)

4. Experimental Results

This paper confirms the validity of the proposed methodsby the experimental results. Table 3 shows the angular fre-quency of the controller and the carrier frequency used in theexperiment.4.1 Experimental Results of Speed Control Fig-

ures 16 and 17 show the experimental results of sensorlessspeed control IPMSM, whose flux current condition is zero.Figure 16 shows the experimental results of Method 1. Fig-ure 17 shows the experimental results of Method 2 on condi-tion that iref

M = 0. The poles of tested current control systemof Method 1 and Method 2 are designed to 2,000 rad/s (13) (14).Figures 16 and 17 confirm that Method 1 and Method 2 ofthe proposed sensorless speed control systems have stablespeed and torque responses. Moreover, both speed responsesof Method 1 and Method 2 are almost the same as those ofFig. 8, which are the speed responses of a speed control sys-tem with a position sensor. However, the ripple of iref during

Fig. 14. Flux control loop of Method 2

Fig. 15. Proposed position sensorless speed and flux control system using sinusoidal current tracking controller(Method 2)



Table 3. Motor parameters and simulation conditions

Poles of the speed control system ωs 80 [rad/s]Poles of the flux control system ω f 80 [rad/s]

Poles of the current control system ωc 2000 [rad/s]Cut-off frequency of low-pass filter ωLPF 640 [rad/s]

Pole of band-pass filter ωB 10 [rad/s]Carrier frequency fs 10 [kHz]

Fig. 16. Experimental results of speed step response inMethod 1

the 1.2–1.4 s interval is larger than at any other time. Thereason for this is that the phase estimation value of the statorflux linkage by the load torque becomes oscillatory.

Figure 18 shows that the experimental results of step speedresponse of Method 2 from −700 rpm to 700 rpm. Figure 18confirms that the proposed sensorless speed control systemwell regulates the motor speed throughout zero speed area.4.2 Experimental Results of Flux-weakening ControlWhen the voltage vector becomes larger thanVmax, the sta-

tor flux command (4) is determined by (55). Vmax is the maxi-mum voltage of inverter.

ψref =−RaiT +

√V2

max − (RaiM)2

ω̂ψ· · · · · · · · · · · · · · · (55)

In this paper, the tested PWM inverter has the triangular wavecomparison modulation method. Therefore, the maximumvoltage of tested the inverter is given by (56).

Fig. 17. Experimental results of speed step response oncondition of iref

M = 0 in Method 2

Vmax =12

√32

Vdc · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (56)

To confirm the effectiveness of the flux-weakening control,Fig. 19 shows the experimental results of acceleration experi-ment for the voltage saturation region. Vdc is set to 200 V. Theexperimental results confirm that the proposed flux weaken-ing control has the fine and stable flux control response asshown in Fig. 19. The proposed sensorless speed control sys-tem well regulates the motor speed in the region of voltagesaturation. Therefore, the proposed flux-weakening controlhas the stable speed response in the region of voltage satura-tion.

5. Conclusion

This paper proposes a new stationary reference frame po-sition sensorless control based on stator flux linkage and newsinusoidal current tracking controller for IPMSM.

At first, this paper proposes a new sinusoidal current track-ing controller and carries out its performance analysis based



Fig. 18. Experimental results of speed step responsefrom −700 rpm to 700 rpm on condition of iref

M = 0 inMethod 2

on the extended transformation. This analysis points outthe harmonic disturbance suppression performance of α-β-sinusoidal current controller. The numerical simulation re-sults and experimental results confirm that the disturbancesuppression characteristics of new α-β-sinusoidal currenttracking controller is higher than that of d-q PI current con-troller.

Next, this paper newly proposes the two types of positionsensorless control systems based on the proposed sinusoidalcurrent tracking controller. Method 1 is the position sen-sorless control method. Method 2 is the position sensorlessspeed control of both stator flux and torque. The experimen-tal results confirm that Method 1 and Method 2 have stablespeed and torque responses. Moreover, the flux-weakeningcontrol of Method 2 is well achieved. Since the proposedflux-weakening control in Method 2 has no information ofinductance parameters, it has a fine stator flux control in theregion of voltage saturation.

References

( 1 ) I. Takahashi and T. Noguchi: “A new quick-response and high-efficiency con-trol strategy of an induction motor”, IEEE Trans. on Industry Applications,Vol.22, No.5, pp.820–827 (1986)

( 2 ) F. Niu, K. Li, and Y. Wang: “Direct Torque Control for Permanent-MagnetSynchronous Machines Based on Duty Ratio Modulation”, IEEE Trans. onIndustrial Electronics, Vol.62, No.10, pp.6160–6170 (2015)

( 3 ) Y. Inoue, S. Morimoto, and M. Sanada: “A Reference Value Calculation

Fig. 19. Experimental results of acceleration controlwith flux weakening control in Method 2

Scheme for Torque and Flux and an Anti-Windup Implementation of TorqueController for Direct Torque Control of Permanent Magnet SynchronousMotor”, IEEE Trans. on Industry Applications, Vol.130, No.6, pp.777–784(2010)

( 4 ) T. Inoue, Y. Inoue, S. Morimoto, and M. Sanada: “Mathematical Modeland Control Method of Maximum Torque Per Ampere for PMSM in StatorFlux Linkage Synchronous Frame”, IEEJ Trans. on Industry Applications,Vol.135, No.6, pp.689–696 (2015)

( 5 ) M.-H. Shin, D.-S. Hyun, S.-B. Cho, and S.-Y. Choe: “An Improved StatorFlux Estimation for Speed Sensorless Stator Flux Orientation Control of In-duction Motors”, IEEE Trans. on Power Electronics, Vol.15, No.2, pp.312–318 (2000)

( 6 ) T. Murata, T. Tsuchiya, and I. Takeda: “Vector Control for Induction Ma-chine by Primary Flux Linkage Control”, Trans. of the Society of Instrumentand Control Engineers, Vol.25, No.11, pp.1194–1201 (1989)

( 7 ) R. Takahashi and K. Ohishi: “Vector control using a Sinusoidal CurrentTracking Controller in Stationary Reference Frame for SPMSM”, The Papersof Technical Meeting on Mechatronics Control, IEE Japan, Vol.14, No.162,pp.17–22 (2014) (Japanese)

( 8 ) S. Ichikawa, M. Tomita, S. Doki, and S. Okuma: “Sensorless Control of Syn-chronous Reluctance Motors Based on Extended EMF Models ConsideringMagnetic Saturation With Online Parameter Indentification”, IEEE Transac-tions on Industry Applications, Vol.42, No.5, pp.1264–1274 (2006)

( 9 ) H. Nakano, H. Eda, M. Naitoh, Y. Yamamoto, R. Kondo, and J. Shimizu:“Novel Analysis Method Based on Extended Bode Diagram for High-pass



Filter Using Rotating Coodinate Transformations”, IEEJ Trans. IA, Vol.119-D, No.2, pp.175–181 (1999)

(10) H. Nakano, M. Jibiki, A. Nabae, and Y. Okamura: “Variable Frequency In-verter with Sinusoidal Voltage Outputs Using Rotating Coordinate Transfor-mation”, IEEJ Trans. IA, Vol.115-D, No.6, pp.735–742 (1995)

(11) R. Takahashi, K. Ohishi, H. Haga, and Y. Yokokura: “Vector control usinga Sinusoidal Current Tracking Controller in Stationary Reference Frame forIPMSM”, The Papers of Joint Technical Meeting on Semiconductor PowerConverter and Motor Drive, IEE Japan, Vol.15, No.25, pp.149–154 (2015)(Japanese)

(12) R. Takahashi, K. Ohishi, H. Haga, and Y. Yokokura: “Stationary referenceframe sensorless vector control based on primary flux linkage and sinusoidalcomplete tracking current controller for IPMSM”, Proc. of IECON 2015 -41st Annual Conference of the IEEE Industrial Electronics Society, pp.2006–2011 (2015)

(13) K. Tanaka, M. Hasegawa, and A. Matsumoto: “Position Estimation UsingAll-pass Filter for PMSM Position Sensorless Control”, The Papers of JointTechnical Meeting on Semiconductor Power Converter and Motor Drive, IEEJapan, Vol.15, No.46, pp.101–106 (2015) (Japanese)

(14) K. Tanaka, M. Hasegawa, and A. Matsumoto: “Extremely Precise PositionEstimation Using All-pass Filter and BPF for PMSMs Postion SensorlessControl”, The Papers of Joint Technical Meeting on Semiconductor PowerConverter and Motor Drive, IEE Japan, Vol.15, No.121, pp.13–18 (2015)(Japanese)

(15) R. Takahashi, K. Ohishi, H. Haga, and Y. Yokokura: “Vector control usinga Sinusoidal Current Tracking Controller in Stationary Reference Frame forIPMSM”, The Papers of Joint Technical Meeting on Semiconductor PowerConverter and Motor Drive, IEE Japan, Vol.15, No.98, pp.51–56 (2015)(Japanese)

(16) R. Takahashi, K. Ohishi, H. Haga, and Y. Yokokura: “Position Sensor-less Speed Control Based on Stator Flux Linkage and Stationary ReferenceFrame for IPMSM(Second report)”, The Papers of Joint Technical Meetingon Semiconductor Power Converter and Motor Drive, IEE Japan, Vol.16,No.8, pp.43–48 (2016) (Japanese)

Appendix

1. Extended Transfer FunctionIn order to confirm the effectiveness of the α-β sinusoidal

current control, it is compared with the current control systemon a d-q synchronous frame, whose name is d-q PI currentcontrol. The input and output frames of d-q PI current con-trol are different from them of α-β sinusoidal current control.In order to analyze the performance of d-q PI current control,this paper uses the rotating coordinate transformation e jωret

and e− jωre t (9) (10). The d-q PI current control is equivalentlyconverted on α-β stationary frame.

app. Fig. 1 shows the extended transformation of the equiv-alent d-q PI current controller on α-β stationary frame. Inapp. Fig. 1, the voltage reference on α-β stationary frame vref

αβis defined in (A5). Furthermore, (A5) is rewritten as (A6).

vrefαβ = v

refα + jvref

β · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (A1)

ierrαβ = iref

αβ − iresαβ = ierr

α + jierrβ · · · · · · · · · · · · · · · · · · · · (A2)

T−1 =

[cosωret j sinωretj sinωret cosωret

]= e jωret · · · · · · · · · (A3)

T =

[cosωret − j sinωret− j sinωret cosωret

]= e− jωre t · · · · · · · (A4)

⎡⎢⎢⎢⎢⎣ vrefα

jvrefβ

⎤⎥⎥⎥⎥⎦ = T−1

[KP s+KIs 00 KP s+KI

s

]T

[ierrα

jierrβ

]· · · · · · · · · (A5)

vrefαβ

ierrαβ

=KP(s − jωre) + KI

s − jωre· · · · · · · · · · · · · · · · · · · · · · (A6)

Where, Kp and Ki are the d-q PI current controller gains.app. Fig. 2 shows extended transformation of the equivalent

app. Fig. 1. Equivalent d-q PI current controller on α-βstationary frame

app. Fig. 2. Extended transformation of equivalent d-qPI current control system on α-β stationary frame

app. Table 1. Different IPMSM parameters

Ra 0.78 [Ω]Ld 6.43 [mH]Lq 10.37 [mH]P 5

JM 3.3*10−4 [kgm2]

d-q PI current control system on the α-β stationary frame.The transfer function to the current response ires

αβ from the dis-

turbance idisαβ is defined as (A7).

Gdisdq−PI =

iresα

idisα

=−s2 + n1s + n0

s2 + m1s + m0· · · · · · · · · · · · · · · · (A7)

m0 =KI − j(Ra + KP)ωre

Ld· · · · · · · · · · · · · · · · · · · · · · (A8)

m1 =(Ra + KP − jLdωre)

Ld· · · · · · · · · · · · · · · · · · · · · · (A9)

n0 =jRaωre

Ld· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (A10)

n1 =−Ra + jLdωre

Ld· · · · · · · · · · · · · · · · · · · · · · · · · · (A11)

2. Evaluation based on Extended Transformation ofthe Disturbance Suppression Characteristics

The current control system using the sinusoidal trackingcontroller in the modified IPMSM obtained similar distur-bance suppression characteristics as shown in Fig. 4. Thecurrent control system, in the case of the modified IPMSMshown in app. Table 1, obtained the disturbance suppressioncharacteristics shown in app. Figs. 3 and 4.



(a) Disturbance suppression char-acteristics of the positive-phase harmonic components.

(b) Disturbance suppression char-acteristics of the negative-phase harmonic components.

app. Fig. 3. Disturbance suppression characteristics us-ing d-q PI current control

(a) Disturbance suppression char-acteristics of the positive-phase harmonic components.

(b) Disturbance suppression char-acteristics of the negative-phase harmonic components.

app. Fig. 4. Disturbance suppression characteristics us-ing α-β sin current control

Ryota Takahashi (Student Member) received B.S. degree in Electri-cal, Electronics and Information Engineering fromNagaoka University of Technology, Japan in 2014.Now he is a candidate of the M.S. degree in Elec-trical, Electronics and Information Engineering. Hisresearch interests include motor control.

Kiyoshi Ohishi (Fellow) received the B.S., M.S., and Ph.D. degrees,all in electrical engineering, from Keio University,Yokohama, Japan, in 1981, 1983, and 1986, respec-tively. From 1986 to 1993, he was an Associate Pro-fessor with Osaka Institute of Technology, Osaka,Japan. From 1993 to 2003, he was an Associate Pro-fessor with Nagaoka University of Technology, Ni-igata, Japan. Since August 2003, he has been a Pro-fessor at the same university. He is an administrationcommittee member of the IEEE Industrial Electronics

Society, the Institute of Electrical Engineers of Japan (IEEJ), the Japan Soci-ety of Mechanical Engineers (JSME), the Society of Instrument and ControlEngineers (SICE), and the Robotics Society of Japan (RSJ).

Yuki Yokokura (Member) received his B.E. and M.E. degrees in elec-trical engineering from the Nagaoka University ofTechnology, Niigata, Japan, in 2007 and 2009, re-spectively. He received his Ph.D. degree in integrateddesign engineering from Keio University, Yokohama,Japan, in 2011. From 2010 to 2011, he was a JSPSresearch fellow (DC2 and PD). Since 2011, he was avisiting fellow at Keio University, and a postdoctoralfellow at Nagaoka University of Technology. Since2012, he has been with Nagaoka University of Tech-

nology. His research interests include motion control, motor drive, powerelectronics, and real-world haptics.

Hitoshi Haga (Member) received B.S., M.S. and D.Eng. degrees inenergy and environmental science from the NagaokaUniversity of Technology, Nagaoka, Japan, in 1999,2001, and 2004, respectively. From 2004 to 2007, hewas a Researcher with Daikin Industries, Ltd., Osaka,Japan. From 2007 to 2010, he was an Assistant Pro-fessor with the Sendsai National College of Technol-ogy, Sendai, Japan. Since 2010, he has been with theDepartment of Electrical Engineering, Nagaoka Uni-versity of Technology. His research interests include

power electronics.

Tenjiroh Hiwatari (Student Member) received B.S. degree in Elec-trical, Electronics and Information Engineering fromNagaoka University of Technology, Japan in 2016.Now he is a candidate of the M.S. degree in Elec-trical, Electronics and Information Engineering. Hisresearch interests include motor control. He is a stu-dent member of the Institute of Electrical Engineersof Japan (IEEJ).


stationary reference frame position sensorless control

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