Fuzzy Back-EMF Observer for Improving Performance of Sensorless Brushless DC Motor Drive

Byoung-Gun Park, Tae-Sung Kim, Ji-Su Ryu, and Dong-Seok Hyun, Fellow, IEEE

Department of Electrical Engineering, Hanyang University 17, Haengdang-dong, Seongdong-gu

Seoul, 133-791 Korea

AbstractIn this paper, a novel sensorless brushless DC (BLDC)

motor drive using the fuzzy back-EMF observer is proposed to improve the performance of conventional sensorless drive methods. Most existing sensorless methods of the BLDC motor have low performance at transients or low speed range and occasionally require additional circuit.

To cope with this problem, the estimation of a back-EMF using the fuzzy logic is suitable for high performance because the back-EMF of the BLDC motor has a trapezoidal shape. The proposed algorithm using fuzzy back-EMF observer can achieve robust control for the change of an external condition and continuously estimate speed of the rotor at transients as well as steady state. The robustness of the proposed algorithm is proved through the simulation and is compared with other sensorless drive methods.

I. INTRODUCTION

The brushless DC (BLDC) motor has been used in many

applications such as appliance, computer, automatic office machine, robots for automation of manufactory, drives of many electronics and minuteness machine. The BLDC motor has advantages of the DC motor such as simple control, high torque, high efficiency and compactness. Also, brush maintenance is no longer required, and many problems resulting from mechanical wear of brushes and commutators are improved by changing the position of rotor and stator in DC motor. To alternate the function of brushes and commutators, the BLDC motor requires an inverter and a position sensor that detects rotor position for proper commutation of current [1]. However, the problems for the cost and reliability of rotor position sensors have motivated research in the area of position sensorless BLDC motor drives. In recent years, many sensorless drive methods have been proposed for improving the performance of BLDC motors without a position sensor [2]-[5]. However, most existing sensorless drive methods of the BLDC motor have low performance in transient state or low speed range and occasionally require additional circuits. This paper presents the fuzzy back-EMF observer based on fuzzy function approximation and a novel sensorless control algorithm using this observer. Because fuzzy logic [6] can estimate a variable shape function such as back-EMF of the BLDC motor, both changed and constant back-EMF are excellently estimated by the fuzzy back-EMF observer.

Therefore, the correct back-EMF estimation achieves the position and speed estimation of the BLDC motor is more robust against other parameter deviations. The robustness of the proposed algorithm is proved through simulations compared with other sensorless drive methods.

II. BLDC MOTOR DRIVE SYSTEM

Generally, the BLDC motor drive system can be modeled as

an electrical equivalent circuit that consists of a resistance, an inductance and back-EMF per a phase. The electrical equivalent circuit and drive performance of this system is sh wn in Fig 1. o

ae

be

ce

aibidcv

1S

av

cvbv

aR aL

bR bL

cR cL

3S 5S

4S 6S 2S

n

(a)

(b)

Fig. 1. General performance of BLDC motor system. (a) The electrical equivalent circuit. (b) Waveforms of back EMF, phase current, and developing torque.

6740-7803-9547-6/06/$20.00 2006 IEEE.

Assuming that self and mutual inductances are constant, the voltage equation of three phases is given by

+

+

=

c

b

a

c

b

a

c

b

a

c

b

a

c

b

a

c

b

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eee

iii

dtd

LL

L

iii

RR

R

vvv

000000

000000

(1)

T he torque equation is given by

m

ccbbaae

ieieieT

++= (2)

where va, vb, and vc are phase voltages. Ra, Rb, and Rc are phase resistances. ia, ib, and ic are phase currents. La, Lb, and Lc are phase inductances. ea, eb, and ec are phase backEMFs. m is rotor speed.

III. PROPOSED SENSORLESS CONTROL METHOD

A. The Proposed Sensorless Control Algorithm

The overall structure of the proposed sensorless drive system is given in Fig. 2.

PIcontroller

currentHysteresis

voltagesline-to-line

Calculate

currentsline-to-line

Calculate

signalsncommutatio

Generate

functionncommutatio

Calculate

speedCaculate

s1

aibici

P2

abe bce cae

abi caibci

abebcecae

em

m

m sI

dcV

dcV

0

Mode

1CF 2CF 3CF

signalgating:,, cba SSS

ai bi ci

aSbScS observer

EMFback-Fuzzy

Fig. 2. The overall structure of the proposed fault tolerant drive system. The hysteresis current controller is used for each phase

current control. The line-to-line voltage is calculated based on the DC-link voltage and switching status of the inverter. In a typical sensorless drive system of the BLDC motor, the forced alignment of the rotor is the way setting an initial position. This method is also used in the proposed sensorless drive algorithm. The fuzzy back-EMF observer provides an estimated value of the back-EMF. The speed, the rotor position and the commutation function are calculated by the estimated back-EMF. The commutation signal generation block generates commutation signals based on calculated values of the position an the commutation function. d

B. Fuzzy Back-EMF Observer

The fuzzy back-EMF observer consists of two parts. One is the current observer based on a system state equation of the BLDC motor and the other is the fuzzy function approximator

that represents the back-EMF disturbance model using fuzzy logic approach. The structure of the proposed fuzzy back-EMF ob erver is shown in Fig. 3. s

sL2

abi

abe

ss 2Rs2L1+

ss 2Rs2L1+

Fig. 3. Block diagram of the proposed fuzzy back-EMF observer. Since the neutral point of the BLDC motor is unknown when

manufactured, this observer is considered by the following lin -line equation: e-to

abs

abs

abs

sab vL

eL

iLR

dtdi

21

21

22

+= (3)

he equation (6), (7) is represented by system state equation. T

FwBuAxx ++=

dtd

Cxy =

(4)

(5)

Where

[ ] [ ] [ ] [ ] [ ]ababababsss

s eviiLLL

R=====

=

=

= wuyxCFBA ,,,,1,

21,

21,

22

Back-EMF is regarded as disturbance in (4). This disturbance

is difficult to presuppose. Generally, a disturbance model can represent most

disturbance models by increasing the degree of polynomial differential equation. However, this disturbance model can not exactly represent the back-EMF of trapezoidal shape, so a fuzzy function approximator that can estimate voluntary non-linear function is applied to the back-EMF disturbance model in this paper. The inputs of the fuzzy function approximator are the line-to-line current error of the BLDC motor and the differential value of the error. These inputs are given by

ababab ii)i(err = nabnabab ierrierricerr )()()( )1( =

(6)

(7) The fuzzy function approximation includes three stages:

fuzzification, inference mechanism and defuzzification. 1) Fuzzification: Fuzzification permits to convert inputs into

fuzzy variables by using membership functions. Each input and output has seven sets associated with seven linguistic labels: Negative Large (NL), Negative Medium (NM), Negative Small (NS), Zero (ZE), Positive Small (PS), Positive Medium (PM),

675

Positive Large (PL) (Fig. 4). All fuzzy sets are defined on the same discourse universe [-1,1].

)icerr( ab

)e( ab

)ierr( ab

Fig. 4. Membership function. 2) Inference mechanism: In this step, the value of the fuzzy

output is determined using a rule base. A typical rule is described as:

IF (condition 1) AND (condition 2) THEN (conclusion)

The approximation law of the fuzzy function approximator

contains 49 rules. The inference method which has been chosen is the Max-Min method [7] which was proposed by Mamdani.

)()()(

)()()()()()(

49

2

1

abPLPLPL

abNLNMNL

abNLNLNL

ecerrerrDOF

ecerrerrDOFecerrerrDOF

==

====

M (8)

Table I shows the rule-base. The database contains

descriptions of the input and output variables.

TABLE I FUZZY RULE-BASE

)i(e ab

)i(ce ab

3) Defuzzification: The output of the inference mechanism is

fuzzy output variable. The fuzzy function approximator must convert its internal fuzzy output variables into crisp values so that the actual system can use these variables. One of the most common ways is the Center of Area (COA) method [7]. The

de uzzified output is given by f

=

== Ni

abiout

N

iabioutabi

e

eeabe

1

1

)(

)(

(9)

If the defuzzified output at time k is , the overall

crisp output of the observer will be )( keab

)k(e)1k(e)k(e ababab += (10)

C. Commutation Function

In this paper, the commutation function is defined by the estimated back-EMF using the proposed fuzzy back-EMF ob erver. Fig. 5 shows the commutation function. s

0 50 100 150 200 250 300 350-150

-100

-50

0

50

100

150

Electrical Angle

eab/ebc ebc/ecaeca/eab

Fig. 5. Commutation function. Although similar commutation function was already

proposed [8], the proposed commutation function in this paper is easy to decide the threshold of commutation function because it has a negative value before commutation. Also, since this commutation function is consisted of the estimated back-EMF, it is robust for noise.

T

he commutation functions are as follows:

Mode 1 and 4: ca

bc2 e

eCF =)(

Mode 2 and 5: bc

ab3 e

eCF =)(

Mode 3 and 6: ab

ca

eeCF =1)(

(11)

(12)

(13) D. The Estimation of Speed and Position

There is following relation between the dimension and speed of back-EMF in BLDC motor.

eeKE = (14)

where E is back-EMF dimension, Ke is back-EMF constant, and

is electrical angular velocity. eThe speed can be also estimated by using back-EMF that the

state observer offers as follows:

676

ee

KE =

em P2 =

(15)

(16)

where is estimated mechanical angular velocity. P is the number of poles.

m

T

he rotor position is obtained by integrating speed.

0 += dte (17)

where 0 is initial position of rotor.

IV. SIMULATION RESULT Simulations are performed to prove robustness of the

proposed algorithm compared with observers using the back-EMF disturbance model consisted of polynomial differential equations. The specification of the BLDC motor is as Table II.

TABLE II

RATINGS AND PARAMETERS OF BLDC MOTOR

Rated Voltage V 160 (V)

Rated Torque Te 0.662 (Nm)

Rated Speed Nr 3500 (rpm)

Resistance Rs 0.75 ()

Inductance Ls 0.0031 (H)

Fig. 6 is results of the back-EMF disturbance model using the

first order differential equation. An estimation of constant back-EMF shows satisfied results as Fig. 6(a), (b). But in the case of the back-EMF changes, the estimated value shows a delay. As a result, transient state of the rotor speed and a commutation signal has a delay as in Fig. 6(c), (d).

Fig. 7 is results of the back-EMF disturbance model using the second order differential equation. Contrary to the first order differential model, an estimation of a changing back-EMF shows good performance. But in the case of constant back-EMF shows good estimation results as in Fig. 7(a), (b). As a result, the rotor speed on steady state has ripple as Fig. 7(c). But a commutation signal is high performance because an estimation of changed back-EMF is superior as Fig. 7(d).

Fig. 8 is results of the proposed fuzzy-back EMF observer to solve problems of the polynomial differential disturbance model. Because fuzzy logic can estimate a variable shape function as back-EMF of the BLDC motor, both constant and varying back-EMF are excellently estimated by the fuzzy back-EMF observer as fig. 8(a), (b). As a result, the performance of both the rotor speed on entire states and the commutation signal is much superior compared with observers using the back-EMF disturbance model consisted of polynomial differential equations.

0 0.02 0.04 0.06 0.08 0.1

-50

0

50eab

eab^

(a)

0.03 0.032 0.034 0.036 0.038 0.04

-50

0

50eab

eab^

(b)

0 0.02 0.04 0.06 0.08 0.10

1000

2000

3000

m

m^

(c)

0.03 0.032 0.034 0.036 0.038 0.040

0.5

1

1.5

CS CS^

Time [sec]

(d) Fig. 6. Simulation results of the observer using first order disturbance model.(a) Rotor speed. (b) Line-to-line back-EMF. (c) Extended line-to-line back-EMF. (d) Commutation signal.

V. CONCLUSION Conventional sensorless methods of the BLDC motor have

low performance in transient state or low speed range and occasionally require additional circuit.

To cope with this problem, this paper proposed a fuzzy back-EMF observer using the commutation function by closed loop continuously estimates a back-EMF of trapezoidal shape. Also, the proposed algorithm using this fuzzy back-EMF observer can achieve robust control for the change of an external condition and continuously estimate a speed of the rotor at transients as well as steady state.

As a result, the proposed sensorless drive method without additional circuit has higher performance than conventional sensorless methods. In addition, this proposed sensorless method can be easily applied to industry applications requiring low-cost and reliable style drive of BLDC motor. The technical validity of the proposed algorithm has been shown through computer simulation using the Matlab.

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0 0.02 0.04 0.06 0.08 0.1

-50

0

50 eab

eab^

(a)

0.03 0.032 0.034 0.036 0.038 0.04

-50

0

50

eab

eab^

(b)

0 0.02 0.04 0.06 0.08 0.10

1000

2000

3000

m

m

^

(c)

0.03 0.032 0.034 0.036 0.038 0.040

0.5

1

1.5

CS CS^

Time [sec]

(d) Fig. 7. Simulation results of the observer using second order disturbancemodel. (a) Rotor speed. (b) Line-to-line back-EMF. (c) Extended line-to-line back-EMF. (d) Commutation signal.

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[3] J. C. Moreira, Indirect Sensing for Rotor Flux Position of Permanent Magnet AC Motors Operating Over a Wide Speed Range, IEEE Trans. Ind. Appl., vol. 32, no. 6, pp. 1392-1401, Nov./Dec. 1996.

[4] H. R. Andersen and J. K. Pedersen, Sensorless ELBERFELD Control of Brushless DC Motors for Energy-Optimized Variable-Speed Household Refrigerators, EPE Conf. Rec., vol. 1, pp. 314-318, Sep. 1997.

[5] Hyeong-Gee Yee, Chang-Seok Hong, Ji-Yoon Yoo, Hyeon-Gil Jang, Yeong-Don Bae and Yoon-Seo Park, Sensorless Drive for Interior Permanent Magnet Brushless DC Motors, Electric Machines and Drives Conf. Record, 1997, IEEE International 18-21 pp. TD1/3.1-TD1/3.3, May 1997.

[6] Lefteri H. Tsoukalas and Robert E. Uhrig, Fuzzy and Neural Approaches in Enginerring, John Wiley & Sons, Inc., 1997.

0 0.02 0.04 0.06 0.08 0.1

-50

0

50eab

eab^

(a)

0.03 0.032 0.034 0.036 0.038 0.04

-50

0

50

eabeab^

(b)

0 0.02 0.04 0.06 0.08 0.10

1000

2000

3000

m

m

^

(c)

0.03 0.032 0.034 0.036 0.038 0.040

0.5

1

1.5

CS CS

Time [sec]

(d) Fig. 8. Simulation results of the proposed Fuzzy back-EMF observer. (a) Rotor speed. (b) Line-to-line back-EMF. (c) Extended line-to-line back-EMF.(d) Commutation signal. [7] C. C. Lee, Fuzzy Logic in Control Systems: Fuzzy Logic

Controller-Part & Part , IEEE Trans. Syst. Man. Cybern., vol. 20, no. 2, pp. 404-435, March/April 1990.

[8] Tae-Hyung Kim and M. Ehasani, Sensorless Control of the BLDC Motors From Near-Zero to High Speeds, IEEE Trans. Power Electron., vol. 19, no. 6, pp. 1635-1645, Nov. 2004.

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