Sensorless Control Algorithm of BLDC Motors with

Current Model

Je-Wook Park, Woo-Young Ahn and Jang-Mok Kim

Dept. of Electrical Engineering

Pusan National University

Busan, South Korea

Byung-Moon Han

Dept. of Electrical Engineering

Myungji University

Seoul, South Korea

Abstract— This paper proposes a new sensorless control

algorithm of BLDC(Brushless DC) motors with current model

based on the 120 degree conduction mode. The rotor speed and

the position can be estimated by using the current model of

BLDC motor which is modified version of the conventional

current model of PMSM(Permanent Magnet Synchronous Motor)

sensorless method. The rotor position and the speed can be

obtained by using the difference of the actual current and the

model current. The position error caused by the parameter

errors of the current model, current distortion at commutation

points and nonideal trapezoidal shape of back-EMF is also

compensated by using simple PI controller and the feedback loop

of the real current. The validity of the proposed sensorless

control algorithm is verified through several experiments.

Index Terms—Component, formatting, style, styling, insert.

(key words)

I. INTRODUCTION

The rotor position sensors of BLDC motor including hall

sensors and encoders have some disadvantages such as drive

cost, reliability and the drive volume. To solve these problems,

many sensorless control algorithms have been studied to

control BLDC motors without rotor position sensors. The

conventional back-EMF based methods have narrow operating

range because it isn’t easy to detect the back EMF at low speed

and additional hardware circuit is required [1]-[5]. The flux

linkage estimation methods [6], [7] use measured voltages and

currents for calculating the flux linkage. The position

correction and estimation are obtained by using the estimated

flux linkage. However, this method has an accumulated

estimation error at low speeds because of the large integration

time period. The freewheeling current method [8] estimates the

rotor position by using the freewheeling currents of the open

phase. The zero crossing point of the freewheeling current is in

the middle of the commutation point. However, for

implementation of this method, six comparators have to be

installed to detect the freewheeling currents and six isolated

power sources are required for the reference signal of each

comparator. The torque constant estimation method uses the

ratio of the back-EMF and the rotor speed as a position

estimation signal [9]. This method has wide operating range

because the ratio of the back-EMF and the rotor speed is

constant in all speed range. However, the performance of this

method depends on the pre-set threshold value which causes

the reliability problem of the sensorless control algorithm.

This paper proposes a new sensorless control algorithm of

BLDC motors with current model based on the 120 degree

conduction mode. The sensorless control algorithm with

current model is already presented previously based on the

vector control [10]. This method has good performance in

wide speed range and high reliability because the estimated

position is continuously updated according to the difference of

the model and actual current. Therefore, this method is applied

to the BLDC motor to enhance the performance and the

reliability of the sensorless control algorithm.

The current model is modified based on the 120 degree

conduction mode and the effect of the current distortion at the

commutation points is also compensated. This method doesn’t

require additional hardware circuit and the validity of the

proposed sensorless control algorithm is verified through

several experiments.

II. ROTOR POSITION ESTIMATION

The equivalent circuit of BLDC motor and a PWM inverter

are shown in Fig. 1.

The voltage equation of a BLDC motor is shown in (1).

c

b

a

c

b

a

c

b

a

c

b

a

e

e

e

i

i

i

dt

d

L

L

L

i

i

i

R

R

R

V

V

V

00

00

00

00

00

00

(1)

where

R : phase resistance

L : LS – LM

LS : inductance of each phase

LM : mutual Inductance

Va,Vb and Vc : phase voltages

ia, ib and ic : phase currents

ea, eb and ec : back-EMFs of each phase

978-1-4673-4569-9/13/$31.00 ©2013 IEEE 1648

PWM Inverter

L

L

L

R

BLDCM

N

e b

e c

e a

ib

ic

ia

Vdc

R

R

Fig. 1. The PWM inverter and equivalent circuit of BLDCM.

For the 120° conduction mode, only two phases are

activated. Thus, the voltage equation of BLDC motor can be

simplified as (2) [9].

edt

diLRiV (2)

),,max( cba VVVV , ),,max( cba iiii , 2

lu eee

where eu and el are back-EMFs of upper and lower activated

phases.

Rearranging (2) for derivative of the current, (3) can be

obtained.

eRiVLdt

di

1 (3)

where

eKe , dt

d

Ke : back EMF constant

For computer-based control, the difference equation of

current can be expressed as (4).

Tdt

dinini )()1( (4)

where, n and T are sampling number and period, respectively.

From (3) and (4), the sampled current can be expressed as (5).

enRiVL

Tnini )()()1( (5)

Therefore, the model current im(n+1) can be obtained as

follows.

mm enRiVL

Tnini )()()1( (6)

Taking difference between (5) and (6), following relation

can be obtained.

mm eeL

Tninini )1()1()1( (7)

From (7), the estimated back-EMF em(n+1) can be obtained

as (8).

)()()1( niT

Lnene mmm (8)

The rotor speed and the position can be estimated as (9) and

(10) respectively.

e

mm

K

ne )1( (9)

TK

nenn

e

mmm

)1()()1(

(10)

However, the estimated position by using (10) has error

because the parameter errors of the current model, current

distortion at commutation points and nonideal trapezoidal

shape of back-EMF is not considered.

III. POSITION ERROR COMPENSATION

In 120°conduction mode, the current is distorted during

commuation periods because the current of activating phase is

delayed by time constant of the BLDC motor, but the

deactivated phase current is eleminated immidiately through

freewheeling diode as shown in Fig. 2. Moreover, the back

EMF is not ideally trapezoidal, the current is sharply increased

near the commutation point.

ia ib

ic

Two-phase

conduction

Commutation

period Fig. 2. Current waveforms of the two-phase conduction and commutation

period.

To explain the current distortion caused by position error,

the on-period and off-period is difined for each phase. The on-

period is the first quarter of the 120° conducting region and the

off-period is the last quarter of the 120° conducting region as

shown in Fig. 3.

Va

A On B Off C On A OffB On C Off B On

Vb

Vc

Fig. 3. The PWM inverter and equivalent circuit of BLDCM.

1649

If the estimated position is ahead of the actual position, the

current increases in every on-periods because the back-EMF of

the BLDC motor is low at the on-period. On the other hand, if

the estimated position is behind of the actual position, the

current increases in every off-periods because the back-EMF is

low at the off-period.

Therefore, to obtain the position error by using phase

currents, the current error must be difined considering on-off

period as (11).

)( : period Off

: periodOn

*

*

iii

iii

err

err

(11)

where i* is the current command from the output of the speed

controller.

The position error can be obtained by using

PI(proportional-Integeral) controller expressed as (12).

][ dtiKiK errierrp (12)

where ∆Ө is the position error, Kp and Ki are PI gain of the

position error compensator.

The overall block diagram of the proposed sensorless

control algorithm for BLDC motors is shown in Fig.4.

∆Ө

PI

Speed Controller

PI

Current Regulator

PWM Inverter

BLDCM

-+

-+

wm

wm*

Hall Sensor

vab

vac

vbc

vba

vca

vcb

(Monitoring)

MA

X -

-

ia

ib

V*

Proposed Sensorless Control Block

V*V

*

Position

R

L

i(n+1)z-1

TLT

z-1

im(n+1) em(n+1)

i(n)

V*(n+1)

em(n)em(n)

s1

Ke

1 wm

i(n+1)

i(n+1)

PI

+

- - ++ -

++

-

Current Error

Calculation

Position Error Compensation

i(n+1)

i*(n+1)

ierr

Ө

Ө

Ө

i*(n+1)

Current-Reference Model

Fig. 4. Overall block diagram of the proposed sensorless control algorithm.

IV. EXPERIMENTAL RESULTS

The specification of the implemented BLDC motor is given

in Table I. The hall sensors are installed in the BLDC motor for

a comparison of the actual and the estimated position.

PARAMETERS OF THE BLDC MOTOR TABLE I.

0.0083[Nm/A]Torque Constant100[W]Rated Power

1.13[mH]Stator Inductance2,500[r/min]Rated Speed

0.5[ ]Stator Resistance0.4[Nm]Rated Torque

10Poles24[V]Rated Voltage

Fig. 5 shows the experimental results of the proposed

sensorless control algorithm without position error

compensation. Fig. 5(a) shows the speed response and phase

current. The rotor speed has ripple because of the position error

and the phase current contains large ripple component. Fig. 5(b)

shows the comparison of the estimated position and the actual

position and the phase current. The position error is maximum

25° and the phase current is distorted because of this error.

Fig. 6 shows the experimental results of the proposed

sensorless control algorithm with the position error

compensation. The straight increase of the speed at the

transient state of Fig, 5(a) show that the good performance of

the position estimation in the transient state. Fig. 5(b) shows

the comparison of the estimated position and the actual

position and the phase current. The maximum position error is

2° and the phase current has no distortion.

Fig. 7 shows the rotor speed and the phase current when the

0.1[Nm] step load torque is given. The load torque is given to

the BLDC motor from a loaded motor at 0.2[sec] as shown in

Fig. 7(a). The rotor speed is decreased to about 2,000[rpm] and

the phase current is increased when the step load torque is

given to the BLDC motor. The rotor speed restored 2,500[rpm]

within 0.7[sec]. Fig. 7(b) and (c) shows the estimated position

and three phase currents at S1 and S2 of Fig. 7(a), respectively.

The phase currents have good shape both of no load and the

0.1[Nm] load condition.

1650

Actual position

100[msec]

[sector]

10[sec]

[A]

2,500

6

1

(b)

(a)

-2

2

[A]

0

5

-5

Rotor speed

Speed command

Phase current

[rpm]

Current reference

Current reference

Phase current

Estimated position

Fig. 5. Sensorless control without position error compensation. (a) Speed

command, rotor speed, current reference and phase current. (b)

comparison of actual and estimated position and phase current.

Actual position

100[msec]

[sector]

10[sec]

[A]

2,500

6

1

(b)

(a)

-2

2

[A]

0

5

-5

Rotor speed

Speed command

Phase current

[rpm]

Current reference

Current reference

Phase current

Estimated position

Fig. 6. Sensorless control with position error compensation. (a) Speed

command, rotor speed, current reference and phase current. (b)

comparison of actual and estimated position and phase current.

Estimated Position

10[msec]

[sector]

0.50[sec]

ia

[A]

2,500

6

1

(b)

(a)

-2

2

[A]

S2

S1

1,500

2

-2

Rotor speed

Speed command

Load torque injection

S1

[rpm]

ia ib ic

Estimated Position

10[msec]

[sector]

6

1

(c)

-2

2

[A]

S2

ia ib ic

Fig. 7. Sensorless control on the external load disturbance. (a) The rotor

speed and the phase currents. (b)The estimated position and the three

phase currents at no load. (c) The estimated position and the three phase

currents.

V. CONCLUSION

This paper proposed a new sensorless control algorithm for

BLDC motor based on the current model. The current model of

BLDC motor is proposed .to estimated rotor position with

difference of the model and actual current. The position error

caused by parameter errors, current distortion at the

commutation point and the shape of back-EMF is also

compensated by using a PI controller and the difference of the

current reference and actual current. This method doesn’t

require additional hardware circuit and has good reliability in

wide operating range because the continuous position angle

1651

can be obtained. The validity of the proposed method was

verified through several experiments.

REFERENCES

[1] K. Iizuka, H. Uzuhashi, M .Kano, T. Endo and K. Mohri,

“Microcomputer control for sensorless brushless motor,” IEEE

Trans. Industry Applications, vol. 27, pp. 595–601, May/June

1985.

[2] C.-T. Lin, C.-W. Hung, and C.-W. Liu, “Sensorless Control for

Four-Switch Three-Phase Brushless DC Motor Drive”, Conf.

Rec. 2006 IEEE Int. Conf. Industry Applications, vol. 4,

pp.2048–2053.

[3] J. Moreira, “Indirect sensing for rotor flux position of permanent

magnet ac motors operating in a wide speed range,” IEEE Trans.

Industry Applications, vol. 32, pp. 401–407, Nov./Dec. 1996.

[4] M. Jufer and R. Osseni, “Back-EMF indirect detection for

selfcommutation of synchronous motors,” in 1987 Proc. EPE

Conf., pp. 1125–1129.

[5] J. X. Shen, Z. Q. Zhu, and D. Howe, “Sensorless flux-

weakening control of permanent magnet brushless machines

using third-harmonic back-EMF,” in 2003 Proc. IEEE IEMDC,

pp. 1229–1235.

[6] N. Ertugrul and P. Acarnley, “A new algorithm for sensorless

operation of permanent magnet motors,” IEEE Trans. Industry

Applications, vol. 30, pp. 126–133, Jan./Feb. 1994.

[7] R. Wu and G. R. Slemon, “A permanent magnet motor drive

without a shaft sensor,” IEEE Trans. Industry Applications, vol.

27, pp. 1005–1011, Sept./Oct. 1991.M. Young, The Technical

Writer's Handbook. Mill Valley, CA: University Science, 1989.

[8] S. Ogasawara and H. Akagi, “An approach to position

sensorless drive for brushless dc motors,” IEEE Trans. Industry

Applications, vol. 27, pp. 928–933, Sept./Oct. 1991.

[9] J. W. Park, S. H. Hwang and J. M. Kim, “Sensorless Control of

Brushless DC Motors with Torque Constant Estimation for

Home Appliances,” IEEE Trans. Industry Applications, vol. 48,

pp. 677–684, Mar/Apr 2012.

[10] N. Matsui, “Sensorless PM Brushless DC Motor Drives,” IEEE

Trans. Industrial Electronics, vol. 43, pp. 300-308, Apr 1996.

1652

Powered by TCPDF (www.tcpdf.org)