Position Sensorless Vector Control of

Permanent Magnet Synchronous Motorsfor Electrical Household Appliances

Kiyoshi Sakamoto*, Yoshitaka Iwaj i*, Tsunehiro Endo* *,

Tsukasa Taniguchi*, Toru Niki***, Mitsuhisa Kawamata***, and Atsuo Kawamura***** Hitachi Research Laboratory, Hitachi Ltd., Ibaraki, JAPAN

** Power and Industrial Systems Division, Hitachi Ltd., Ibaraki, JAPAN* ** Hitachi Appliances, Inc., Ibaraki, JAPAN

* ** * Yokohama National University, Yokohama, JAPAN

Abstract-A position sensorless vector control for aPermanent Magnet Synchronous Motor (PMSM) suitablefor electrical household appliance motor drives is describedin this paper. As a position sensorless control, a simpleposition estimate equation is presented. The derivation ofthe equation is described. A simplified vector controlmethod for position sensorless PMSMs is proposed. Theproposed method does not employ any automatic speedregulator or automatic current regulator. However, sincethe motor supply voltage Vd and Vq are calculated on thecontrol rotation axis, the drive performance of our methodis almost the same as that of a conventional vector controlunder a steady-state condition, i.e. constant load andconstant speed. Simulation and experimental results areshown. Finally, the authors applied the proposed method toa battery-driven cordless vacuum cleaner. By experiment, astable drive of 50,000 min'1 was confirmed.

Index Terms-position sensorless control; vector control;permanent magnet synchronous motor; cordless vacuumcleaner.

I. INTRODUCTION

In the field of electrical household appliances,especially air-conditioners and refrigerators, PermanentMagnet Synchronous Motors (PMSM) have become thestandard ac motors for variable speed drives, because oftheir several advantages, such as superior power densityand high efficiency, compared with induction motors.The first air-conditioner product, which uses an inverterdriven PMSM, was developed in 1982 in Japan. Since1998, the ratio of inverter-driven household air-conditioners sold in Japan has risen to over 90 percent.This trend might spread over the world given recentglobal energy and environmental problems.

As a drive method for PMSM for electrical householdappliances, a position-sensorless trapezoidal current drive,i.e. 120-degree commutation drive, is widely usedbecause of its simplicity and low-cost implementation.However, the distorted current waveform generatespulsating motor torque and motor loss. Presently, the useof sinusoidal current drive, i.e. 180-degree commutationdrive, is increasing.A major example of a sinusoidal current drive is the

position-sensorless vector control. Many research papers

have focused on this control [1-3]. However the positionestimation methods proposed by the papers, such as theKalman filter, the state observer, and the disturbanceobserver, are relatively complicated and their calculationrequirements are large. Furthermore, vector control,which includes a speed-control loop and current-controlloop, requires a short control interval. Therefore, a highperformance Micro-Controller Unit (MCU) or DigitalSignal Processor (DSP) is needed for the implementationof the control. Adoption of such an expensivecontroller/processor is unrealistic for electrical householdappliance motor drives.

In this paper, a simplified vector-control methodsuitable for implementation with a low-cost typical MCUis proposed. The position estimation algorithm proposedby the authors is described. The configuration of theproposed controller and the gain design methodology arepresented. Simulation results are given to verify theeffectiveness of the proposed drive system. Finally, theauthors applied the proposed control to a battery-drivencordless vacuum cleaner (maximum motor speed is50,000 min-'), demonstrating the high-speed motor drivecapability of the proposed method.

II. POSITION ESTIMATION ALGORITHM

In this section, the derivation process of the proposedposition estimation algorithm ofPMSM [6] is described.

A. Voltage Equation ofSalient Pole PMSMThe well-known voltage equation of the salient pole

PMSM in the synchronous reference frame d-q axis is asfollows:

[V ] iR]+P[Ld i +wr[ L 'i [Es] (1)

where cor is the rotor angular velocity; Ld, Lq are the d andq axes inductances; Vd, vq are the d and q axes voltages; id,iq are the d and q axes currents; R is the stator windingresistance; p is the differential operator with respect totime; and Eo is the voltage of the back electromotiveforce (EMF).

In the sensorless control system, rotor angular positionand velocity o,r are not measured; thus voltages and

1-4244-0844-X/07/$20.00 ©2007 IEEE. 1 11 9

dVcc = R dc + PLd + 2 coL, i q1

dt L iOx

1 cosAO]

(6)

However, equation (6) includes 0cr, which is anunobservable value of the controller. Substitutingequation (6) into dAO/dt of equation (7), equation (8) isobtained:

d AO(d-=d d-d)ddt dt dt d)

(

p2r

(7)

Fig. 1. Relation between two synchronous reference frames. The daxis is the rotor frame and the dc axis is the assumed rotor frame.

currents on the d-q axis cannot be obtained. Thereforsynchronous reference frame dc-qc axis, which is fion the assumed rotor, is introduced.

Fig. shows the two rotating axes of the PM'where the assumed dc-qc axis is shifted from the realaxis. The difference between the two axes is definedposition error AO given in (2):

AO=Odc Odwhere Od is the real angular position of the d-axis relatito the stationary a-axis and Odc is the assumed angularposition of the dc-axis relative to the stationary a-axis.

Converting from the dc-qc axis value into the d-q a)

value, equation (3) can be used:

V cossAO -sinAO Vdc

[Vq] si:AO cosAO ][vqc]

B. Position Error EquationThe voltage equation (1) can be transformed i

another expression as follows:

[d R[ d +PLd[. d] 2 Lq[L q]

±v Q d±P(L 2q d

[KE2 ° r + p Ld) iq ±2 °(Ld Lq) id.J

The fourth term of (4) is the summation of the back Eand induced voltage caused by motor pole saliency.term is called the extended EMF [4]. In the folloMNexplanation, Eo, expresses the extended EMF termfollows:

E0 =KE r+P(Lq Ld) iq + r(Ld Lq) id

The voltage equation of the dc-qc axis is obtainedsolving as follows:

dV 1= R d +PLd d +CDLqi c

+dAS L -ia+ UsinA00(Ld -Lq) [coOx

(8)

Equation (8) does not include 0r, and is suitable forderiving the position error equation.

Combining the Eo, term, equation (9) is obtained:

(9)EOx coA -= v1Ri-PLd i I-dLqL i

ive - ~~~~~~~~~dt( d q) i H

To obtain the position error information, the size of theextended EMF is not necessary but the phase angle of theextended EMF is important. Getting tangent tanzl0, thesize of the extended EMF Eo, is eliminated:

tanAOVdC -(R+pLd)idC +{(Ld Lq)(pAO)} q (10)

Vqc- (R +PLd)qc -{|L Lq)(PAO)} ' dc

Equation (10) includes the time derivation ofthe motorcurrent and the position error zAS. We assume that thetime derivative of the motor current is negligible underthe condition where motor load and motor speed are

constant. We also assume that the time derivation of theposition error zlObecomes zero under the same conditions.Eliminating the time derivation values, a practicalposition error equation can be obtained as follows:

(1 1)AOc = tan' dc Rid +0) iLq *qc]Vqc -R jiqc -aCILq * dcj

where /10, is the estimated position error value. Note thatby substituting L-Lq=L in (l1), an equation for non-

(5) salient PMSMs can be obtained.

by III. SIMPLIFIED VECTOR CONTROL

In this section the authors would like to propose a

simplified vector control for position sensorless PMSMs.The proposed control structure is shown in Fig. 2. Acharacteristic of our method is that the control structureof the proposed control is very simple compared with the

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qc q

rdc

Ct)r -YSpeedReference

Fig. 2. Simplified vector control system for position sensorless PMSMdrive.

conventional one. This simplified vector control structurewas reported on in the 1980s for use in inductionmachines [5]. The authors apply the idea to PMSM drives.

As shown in Fig. 2, our method does not use anautomatic speed regulator (ASR) or automatic currentregulator (ACR). Thus, the proposed method has noadvantage over the conventional vector control especiallypertaining to the case of disturbance load torque.

However, since the motor supply voltages Vd and Vqare calculated on the dc-qc axis, the drive performance ofour method under the steady state condition, i.e. constantload and constant speed conditions, is almost the same asthat of the conventional vector control. This is animportant difference between the well-known V/F typecontrol and our method.

Another feature of the proposed control is that numberof control parameters is smaller than for the conventionalmethod. Thus, controller adjustment is finished with lesswork.

The proposed simplified vector control is characterizedby using a voltage command calculator, a q-axis currentcommand generator, and a PLL controller. We describethe detail of each constituent block below.

A. Voltage command calculatorThis part calculates the voltage command Vdc* and vqc*

using the motor electrical parameters, motor frequencyreference, and current reference. The calculating formulais shown in equation (12), which is obtained byneglecting the time derivative term of equation (1).

Vd I[vc]R[] + C9 L .J+LK l] (12): clc ] 0 cI 0 0 d [d E 1

where o, * is frequency reference of the motor.

B. q-axis current commandgeneratorIn the conventional vector control, the ASR determines

the q-axis current command, iq*, as a motor torquecommand. On the other hand, in our method, the q-axiscurrent command is generated through the LPF equation(13) from detected motor current as follows:

q 1 + TiqS qc(13)

Since the detected motor current iqc changes withmotor load variation, the value of the q-axis currentcommand is adjusted properly.

Note that determining the time constant parameter ofthe LPF (13) is important. The response of the LPFoutput should be designed to be lower than the responseof the PLL controller described in the following.

C. PLL controllerThe position error ASO expresses the lead-lag

relationship between the assumed axis and the actual axis.Using this lead-lag relation, the PLL controller adjuststhe assumed rotor speed o,, i.e. the inverter outputfrequency.

Actually, the PLL controller is implemented in the useof proportional control as follows:

A1 = -KPsAOC. (14)

If z1O, is positive, the assumed axis is ahead of theactual axis, and the PLL controller reduces the assumedrotor speed o,. Similarly, if z1O, is negative, the assumedaxis is lagging the actual one, and the PLL controllerincreases co,.

The dc-axis phase Odc is obtained by an integrationcalculation as follows,

Odc =frdt. (15)

D. Other comments concerning the proposed methodThe setting of the d-axis current command id* is

important for high efficient drive. The current referenceof the d-axis, id*, is set to minimize the amplitude of themotor current in order to decrease losses.

Changing the speed reference oi) * at a rapid rate islimited because the voltage command is calculated fromthe speed reference directly as shown in (12). To generatec)r , the use of a ramp function is recommended.

IV. GAIN DESIGN

The proposed control has two control parameters, atime constant parameter of the LPF (13) and a gain Kp ofthe PLL controller. In the following, the gain designmethod, based on the resonant characteristics of PMSMis described.

A. Resonant characteristics ofPMSMFig. 3 shows a salient pole PMSM motor model in the

rotational reference frame. The relation between thevoltage and current shown in Fig. 3 is obtained from thevoltage equation (1). To analyze the electrical response ofthe motor, we assume that the motor speed co, is constant.For simplicity, we also assume that the position error A1Oequals zero and the motor speed PoV2 is substituted byc] -

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From Fig. 3, the transfer function from Vd to id isobtained as follows:

= R +sLqG=

s2LdLq + s R(Ld + Lq)+ R2 + 012LdLq(16)

Using the motor parameters of Table 1, the transfercharacteristics of Go can be plotted as Fig. 4. Fig. 4shows that Go has resonant characteristic and the resonantpeak becomes sharp with higher o, values.

In order to find the resonant characteristics, equation(16) is changed to a 2nd_order system equation as follows: Fig. 3. A model of salient pole PMSM in the rotational reference frame.

R + sLq C 2= q -

° R2 + C LLS &si i

2R

(,01 +LL

whereL~LqR . (Ld + Lq)

2VLE (R2+ 2LdLq)

(17)

(18)

Equation (17) indicates that the resonant frequency CoI

and the damping coefficient 4 vary with changing tl. Ift), is the higher value, ozh, comes close to o, and the valueof 4 is reduced. Thus, the resonant oscillation of PMSMcan hardly be damped at higher rotation speed.

B. Resonant suppression strategy ofSimplified VectorControl

Generally, in order to suppress the resonance of thePMSM mentioned above, a decoupling control isemployed. The decoupling controller calculates the d-qaxis interference value and compensates the voltagecommand reference. However, complete decoupling isimpossible, because the computation interval of thecontroller output is limited and the motor's electricalparameters are different from the actual values.

Simplified vector control avoids the resonance inanother way. The method is limiting the variation of thevoltage command reference. If the frequency of thevoltage reference is lower than the resonant frequency ozI,no resonant oscillation occurs and the PMSM systembecomes stable.

In the following, we clarify the critical resonantcondition. The relation between the resonant frequency(I)n and the damping coefficient X is expressed byequation (19):

R-(Ld+Lq) (19)

2- LdLq * n

The case of coefficient 4=1 is known as the criticaldamping condition. Thus, we can derive the stablecondition by solving for ; >1.0 . Equation (19) is

changed to the following inequality:

91=0 100 =25% °1=50% p1=75% p1 100% (233Hz)90

........... ........... .......

10 .0 ...0.0

...... ....... ....... .. ... .......

-90 ,_10 ioo 100 O

Inverter frequency[Hz]Fig. 4. Transfer characteristics from d-axis voltage to d-axis current

Actual Position Estimatedposition error position

Od AO K 0dc

+SPLL controller

Fig. 5. Simplified model of PLL controller.

COnR *(Ld + Lq)

2*LdLq(20)

Here we call the right value of (20) a critical dampingfrequency tnO:

0)nOR (Ld + Lq)

(21)2 LdLq

C. Gain Design Methodology

The PLL gain Kp should be set at the critical dampingfrequency tnO

(22)

Selecting the gain Kp as shown in equation (22), thetransfer characteristic from AS0 to Odc becomes the LPFresponse and the cutoff frequency is COJo because the PLLcontroller can be simplified as Fig. 5. Therefore, thefrequency component PLL controller output is less than0nO and the PMSM system becomes stable.Note that the response speed of the LPF (13) is also

important. It is recommended that the LPF setting beabout 0.1 times slower than the PLL response.

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inputVd -

output> id

C.

ctQ.)

Kps = 0)n 0 '

V. SIMULATION AND EXPERIMENT

To confirm the validity of the proposed control, severalsimulations and experiments were made. Thespecifications for the test motor used in this simulationare shown in Table 1.

In this case, the critical damping frequency C0obecomes 74rad/s. Therefore we set the control parametersto K, =80rad/s and Tiq=125ms. The PWM carrier signal

200

---.---.---------.---.........................................

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.620

0

-200 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

150

100 . A .

50 ...........

-50°0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

20lo ............ ............

10 .

-200 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

40

20

> 20 _ . .

-400 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

150

100. -

50

500 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6[s]

Fig. 6. Performance of speed response. (Simulation)

240

30 .

220(

400.1 0.2 0.3 0.4 0.5 0.6

frequency is set to 5kHz. The 3-phase voltage reference iscomputed every 1OOVts. The computation interval of (12)

TABLE 1. SPECIFICATIONS OF THE TEST MOTOR.

Rated Power 3.7 kW

Rated Speed 3500 r/min

Pole Number P 8

Inductance Ld, Lq 2.5, 3.3 niH

Resistor R 0.21 Q

Rotor Inertia 0.0034 kg cm2

(a) Phase current and inverter frequency

L20 °H-lIEIL... ' 'i

-20 r

400 0.1 0.2 0.3 0.4 0.5 0.6

200

100tLI

400.1 0.2 0.3 0.4 0.5

-500

(b) Phase current and estimated axis error AOc

Fig. 7. Performance of speed response. (Experimental result)

0.6

20

-2 .........................................................................

-400 0.1 0.2 0.3 0.4 0.5 0.6

40

. -20 i

-400 0.1 0.2 0.3 0.4 0.5 0.6

200.iqc

100 --............... .....

0* .-I-._

Fig. 9. Load variation response. (Experimental result)

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0 0.1 0.2 0.3 0.4 0.5

Fig. 8. Load torque variation response. (Simulation).

0

.1.;illltillb,,i.';:

-.C:)ct0 -

't

0 a)-4- ;z0 M.

0-4-

6

0.6 Is]

is set to 900 ts, and the computation interval of (11) and(14) is set to 500is.

Fig. 6 shows the simulation result of the speedresponse. In this simulation, the load torque of the testmotor is set to zero. The frequency reference increasesfrom 30Hz to 230Hz.The result of this simulation shows that the motor

torque rise is delayed, and furthermore, that ASO occurs atthe speed variation point. However, zAO becomes zeroduring speed up. Within this simulation, the proposedcontrol method has adequate capability.

Fig. 7 shows the experimental result of applying ourcontrol system to an actual apparatus. The motor phasecurrent, inverter frequency, o,, and estimated positionerror zIO, are shown. The motor current amplitude isdifferent from the simulation because of the wind loss ofthe actual motor. Except for this point, the experimenttends to agree well with the simulation results.

Fig. 8 shows the simulation result of the torque stepresponse. In this simulation, 100% load torque is added tothe motor during the maximum rated rotation speed.From this increase in the load the motor speed 0crdecreases, and the inverter frequency, o,, follows cr,After applying the load, the motor torque Tm is adjustedfor about 0.4s to balance with the load.

Fig. 9 shows an experimental result of the torque stepresponse. The motor current is quite similar to thesimulation but its amplitude is fluctuating. It seems thatthe mechanical model difference causes the fluctuation.We chose a simple 1-mass model for the motormechanical model of the simulation.

VI. APPLICATION EXAMPLE OF HOUSEHOLD APPLIANCES

The proposed method has been applied to varioushousehold appliances, such as room air conditioners andrefrigerators [7]. In this paper, we will outline itsapplication to a cordless vacuum cleaner as one case.A cordless vacuum cleaner has some drawbacks

because all the power is supplied from a battery. Forexample, the problem is that the suction power is poorand available operating time is short. These problemsresult from the use of a commutator motor. To improvethe performance, substituting a PMSM for thecommutator motor has been investigated [8].

In order to boost the suction power, a rotation speed ofabout 50,000r/min is necessary for the PMSM. Thus, themotor driver of cordless vacuum cleaner requires highrotation-speed drive capability. The authors applied thesimplified vector control to driving such a high-speedmotor.

Fig. 10 shows the external view of the test motor. Thespecifications of the test motor are shown in Table 2. Thetest motor is designed to operate using a 24V DC battery.The structure is an interior permanent-magnetsynchronous type. The output power of the drive circuit is500W. As a micro-controller unit, a 32bit SH7046 RISCprocessor made by Renesas Technology is employed.

The experimental apparatus is shown in Fig. 11. Fig.

Fig. 1U. External view o0 the test motor.

DC24V

measurement

Fig. 11. Experimental apparatus.

TABLE 2. SPECIFICATIONS OF THE TEST SYSTEM.

Maximum Rated50,000 r/min

Speed

Pole Number P 2

Inverter Output 500 W

DC voltage 24 V

Fig. 12. Startup waveforms.

PWM carrier frequency: 8kHzFig. 13. Motor phase current waveform in high-speed region

(50000minm1).

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12 shows the motor current and motor frequency signalwaveforn recorded while the motor was accelerating. Inthis case, the acceleration to 50,000r/min (top speed) wascompleted in just 5s.

Here, it is necessary to explain the start sequence indetail. At the beginning of rotation, an open-loop start-upmethod, i.e. the synchronous drive method, is used in thisexperiment. The start-up method flows more current thanthe vector control. You can find the start-up period by thedifference of motor current amplitude shown in Fig. 12.

After the start-up, the proposed simplified vectorcontrol is activated. During acceleration to the top speed,significant fluctuation of the motor current was notobserved. Fig. 13 shows a close-up of the motor currentwaveforn at the top speed. The motor current involves ahigh frequency component. These components are causedby the back electromotive force with harmonic distortionand use of the pulse width modulation (PWM) control. Inthis experiment, the PWM carrier frequency was set to8kHz.We conclude from the experiment described above

that the proposed simplified vector control can be appliedto a high speed PMSM drive. The proposed control mightbe applied not only to vacuum cleaners but also high-speed fan motor drives and spindle motor drives.

VII. CONCLUSIONS

A simplified vector control for position sensorlessPMSMs is proposed. Configuration of the proposedmethod and the position estimation method are shown.The methodology of the control gain setting is introduced.The effectiveness of the proposed control is verified bysimulation and experiments.

Using the results of this paper, the cordless vacuumcleaner, type CV-XG20, shown in Fig. 14 has been madeavailable in stores since October 2003.

REFERENCES[1] T. Takeshita, M. Ichikawa, J-S Lee, and N. Matsui, "Back

EMF Estimation-Based Sensorless Salient-Pole BrushlessDC Motor Drives", T IEE Japan, Vol. 11 7-D, No.] pp. 98-104 (1997-1) (in Japanese)

[2] L. A. Jones and J. H. Lang, "A state observer forpermanent magnet synchronous motor," IEEE Trans.Industrial Electronics, Vol. 36, No. 3, 1989, pp. 374-382.

[3] S. Bolognani, R. Oboe, and M. Zigliotto, "Sensorless full-digital PMSM drive with EKF estimation of speed androtor position," IEEE Trans. Industrial Electronics, Vol. 46,No. 1, Feb. 1999, pp. 184-191.

[4] S. Ichikawa, Z. Chen, M. Tomita, S. Doki, and S. Okuma,"Sensorless Controls of Salient-Pole Permanent MagnetSynchronous Motors Using Extended Electromotive ForceModels", T. IEE Japan, Vol.122-D, No.12 pp.1088-1096,Dec. 2002. (in Japanese).

[5] T. Okuyama, N. Fujimoto, and H. Fujii, "SimplifiedVector Control System without Speed and VoltageSensors", T. IEE Japan, Vol.1 10-D, No.5 pp.477-486, May1990. (in Japanese).

[6] K. Sakamoto, Y. Iwaji, T. Endo, and Y. Takakura,"Position and Speed Sensorless Control for PMSM DriveUsing Direct Position Error Estimation," Proc. ofIndustrial Electronics Society, 2001. IECON '01. The 27thAnnual Conference ofthe IEEE, vol.3, pp.1680-1685, 2001

[7] D. Li, T. Suzuki, K. Sakamoto, Y. Notohara, T. Endo, C.Tanaka, T. Ando, "Sensorless Control and PMSM DriveSystem for Compressor Applications." Proc. of PowerElectronics and Motion Control Conference, 2006. IPEMC'06. CESIIEEE 5th International, vol.2, pp. 1-5, Aug. 2006

[8] T. Taniguchi, H. Mikami, K. Sakamoto, K. Ide, H. Harada,F. Jyoraku, "Basic Study of High-Speed Brushless DCmotor with Battery System," Proc. of The 2005International Power Electronics Conference, IPEC 2005,pp. 1033-1037, April. 2005

Fig. 14. Cordless vacuum cleaner. CV-XG20

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