Third International Workshop on Advanced Computational Intelligence August 25-27,2010 - Suzhou, Jiangsu, China

AI -Based Sensorless Speed Estimation of 3-Phase BLDC Motor J. Srisertpol, A. Srikaew, and P. Jawayon

Abstract-This paper describes a signal-based speed estimation of 3-Phase Brushless Direct Current (BLDC) motor using the relationship between commutation signal and Back

Electromotive Force (Back-EMF). Both signals can directly be measured from each phase of motor's terminal. The

relationship function between both signals is approximated and

filtered to find Haft of phase voltage-Crossing Point and using Artificial Intelligence find coefficient of function and filter's parameters of each speed.

I. INTRODUCTION

BRUSHLESS DIRECT CURRENT MOTOR (BLDC) motor has been used increasingly in both industrial and household applications [1]-[12] such as CD player, hard disk

drives, medical tools, air conditioners etc. This is because the BLDC motor has better efficiency, good reliability, low maintenance, and power density .

Currently, detection of speed and position of BLDC has two approaches. Firstly, the rotor's commutation signal is obtained by using the Hall-effect sensor. Secondly, by using the zero-crossing detection circuit, the rotor commutation signal of each phase can be estimated [3]-[7]. Mostly, the zero-crossing detection circuit uses op-amp to compare phase back-EMF voltage with half of supply voltage. Therefore, there are many software-based methods proposed to find the zero-crossing of back-EMF voltage for reducing the addition circuit. In [12], an artificial neural network (ANN) and a model reference adaptive system are used for finding a zero-crossing of back-EMF in which the performance of the estimation is based on the properties of the motor. In [13], the relation between the size of back­EMF voltage and the motor speed are applied to control the speed of motor using fuzzy logic in high speed range (more than 10,000 revolutions per minute). In [9], the artificial neural network is deployed to estimate the back-EMF from voltage and current of each phase in low speed range.

This paper presents the relationship of back-EMF voltage, which is included within each phase voltage of motor. Phase voltage can be measured directly from each terminal of the

The authors would like to thankfully acknowledge the research grant from National Electronics and Computer Technology Center (NECTEC) and Suranaree University of Technology.

1. Srisertpol is with the School of Mechanical Engineering, Suranaree University of Technology III University Avenue, Muang District Nakhon Ratchasima 30000 (e-mail: jiraphon@sut. ac.th ).

A. Srikaew is with the School of Electrical Engineering, Suranaree University of Technology III University Avenue, Muang District Nakhon Ratchasima 30000 (e-mail: ra@sut.ac.th).

P. Jawayon is with the School of Mechanical Engineering (Mechatronics), Suranaree University of Technology III University Avenue, Muang District Nakhon Ratchasima 30000.

978-1-4244-6337-4/10/$26.00 @2010 IEEE 537

motor. The function to estimate commutation signal from phase voltage is then created by using artificial intelligence techniques to find relations between each speed and commutation signal's function. The resulting commutation signal's frequency is then used as a frequency cut-off of low-pass filter for estimating back-EMF signal from phase voltage. The filtered phase voltage signal or back-EMF estimation can increase accuracy for estimating speed. The testing speed ranges in this work are approximately from 2,000 to 7,000 rpm.

In this paper, a mathematical modeling of the BLDC motor and its electrical drives are described in Section II. Section III presents speed estimation scheme for the BLDC motor. Section IV and V are experimental results and conclusions.

II. PRINCIPLE OF BLDC MOTOR

A three-phase brushless DC motor has three induction coils with equivalent circuit of BLDC motors as described in the following section.

A. Mathematical Model of the BLDe Motor

The equivalent circuit of BLDC motors shown in Fig.1 provides dynamic equations of BLDC motor as in equation (1), (2) and (3). [v,,] [1 0 0Ila] [L-M

� =R 0 1 0 Ib + 0 � 0 0 1 � 0

o L-M

o

when Va> Vb, Vc Ia,h'!c Ea,Eb,Ec R L M Te T, w

B

J

T= EaJa + EbJb + EJc e 0)

dO) J-+BO)=Te -7; dt are phase voltage [V], are phase current [A], are phase back EMF [V], is phase resistance [Q], is self-inductance [H], is mutual inductance [H], is electromagnetic torque [N.m], is load torque [N.m], is mechanical velocity [rad/s], is damping constant, and .

f" ' [k 2 IS moment 0 mertIa g.m[.

(1)

(2)

(3)

Fig.l.The equivalent circuit of BLDC motor.

B. The BLDC Motor Control

BLDC motors are driven by a three-phase inverter with six-step commutation sequence. The inverter is commutated every 60 degree electrical when Ha, Hb and Hc are Hall effect sensor signal of each phase.

Va

Vb

Ve

, i ,

L--j------!H i H � , , ! f-! --+-�

H �-+'--�! --�i --�!--� , H: �"i; f-I -+-�r"

i I"�

He , " i,i t--4-i ---+---11 " " t--:-:--+-:---+-:-::--l i , i 001 i 011 i 010 i 110 i 100 i 101 i 001 , 011 i

60 120 180 240 300 360 Electrical

Fig. 2. Six step commutation sequence

C. BLDC Motor's Back-EMF

When the 2 coils are induced to rotate through a magnetic field, the induced voltage is created in this coils, call that "Back Electromotive force" or "Back-EMF". The relation between Back-EMF signal and Hall effect sensor of each phase is shown in Fig. 3.

Ha

H I ,

r1 Hb ,

! He I i

Ea NJ � ! ! i i Eb

Ec

Fig. 3. BLDC motor back-EMF and the Hall effect signal of each phase

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III. SPEED ESTIMA nON SCHEME

Fig. 3. show that phase angle of half point of back-EMF voltage of each phase lags from Hall effect sensors signal about 30 degrees. The half point of this back-EMF voltage can be estimated by half of phase voltage of motor [4] as in Fig. 4.

25 F---,---IImH'It--iM 20

o

� • 15

: � 10 � "-

time (ms)

Fig. 4. The zero, Vn/2 and Vn crossing of each phase terminal of BLDC motor

Flowchart of calculating this half of phase voltage and then speed estimation is displayed in Fig. 5.

v, Define band and

Select interest signal

Moving Average

Commutation Estimation

"[m " I " . I " ,

........ , ... , ... ,.." ........

JrJ .. "[fjJ " -, ... �- ....

: , .. , ,-,-,-' .. ,' '"

Regression Equation of s, d, [\ and

Commutation's Period

Speed and Position Estimation

Speed

Fig. 5. Speed estimation scheme

:g,'- '-�

" l '

4 ' .... _ _

A. Define Band and Select Signal Range

The half point of back-EMF crossing includes the half point of phase signal voltage (Vnl2) in which a band of interesting signal must be defined as in equation (4) before estimating the speed.

where

(I) {Vn , Vn _ J � V � Vn + J V; = 2 2 2 ' 2 2

0 ' otherwise

J is window size of interesting band,

Vi is phase voltage at i, Vn is supply voltage, vF) is selected signal at i.

(4)

The selected signal is demonstrated in Fig. 6. The signals that pass the selected band depend on the window size of interesting band (0).

o >

time (ms)

Fig.6. Phase voltage (V,) and selected signal (V,(/)

time (ms)

Fig,7. Selected signal (Ij(/)) and passed the MA signal (V,(2)

B. Find the Selected Signal's Edge

Once the selected signal is defined, the envelope of the selected signal can be found by Moving Average (MA) as shown in equation (5). The envelope of the selected signal in Fig.7 shows the highest density area of the half point of

539

phase voltage crossing.

where V(1) } (2) Vi

(J'

i-I LVP)

V(2) I j=i-O"

is selected signal at j, is MA filtered signal at i, is window size of MA.

C. Commutation signal estimation

(5)

The selected signal which is filtered by the MA function shows the highest density area of the half point of phase voltage crossing. The local maximum in this area can be estimated by (6) and (7). The result is shown in Fig. 8.

Lmax. = I I I-I {V(2) , V(2) > L max I Lmax;, otherwise

L [V(2) V(2) ] s. ={l' max E i-fl' i

l-fJ 0 , otherwise

where Lmaxi is local maximum Si_P is estimated commutation signal at i-fJ

vF) is filtered signal at i fJ is previous time range from i

2.5

� 1.5

0.5·

0-o

l���,Jt;(2)J

/

time (ms)

Lmax /

Input Signal ( Vi(2)

10

Fig.8. The MA filtered signal (v,12) and estimated commutation sig:nal (S .• )

D. Estimate Back-EMF by Low-Pass Filter

(6)

(7)

The phase voltage signal is included in the back-EMS signal. Both signals can be separated by using low-pass filter with frequency cut-off derived from the above method. This work uses Butterworth low-pass filter to separate back-EMF from phase voltage signal as shown in Fig. 9.

0 >

30 Phase Voltage Signal Filtered Signal

25

20 I � 15

10

I r= Irr

.50,:--�--:-�,--------,:--��---:--��--J10

time (ms)

Fig. 9. Phase voltage signal and filtered signal

E. Speed Calculation

The rotor speed can be calculated from frequency of estimated commutation of each phase using equation (8).

n= f xl20 (8) Zpol

where n is motor shaft speed [rpm], f is frequency of commutation signal [Hz], Zpol is number of motor's magnetic poles.

F. Relation between (1, <5, fJ and Commutation Signal's

Period

In each commutation frequency or each speed, variables cr,

° and � in each step are different. Therefore, the relation between variables cr, 0, � for each speed must be calculated to be able to use in all speed range.

450�-�-�-�-�-�-�-�-�

400

350

300

250

200

150

100

50

-- a parameter

a Fitness CUM

-- 0 parameter

- - 0 Fitness cur.e

-- 13 parameter

Fitness CUM

- �-----�--

� 300 400 500 600 700 Commutation Signal Period(O.000025 s)

800 900

Fig. 10. Fitness curve of relation between cr, 0, � and commutation signal's period

In this paper, the Genetic Algorithm (GA) [14] is applied to estimate coefficients of the polynomial equation of relation between the variables cr, 0, � and commutation signal's period. The exact value and polynomial equation of the relation between variables cr, 0, � and commutation signal's period are depicted in Fig. 10.

540

X 10" 12

-- Actual data 10 20 Populations

-- 100 Populations

250 Populations

-- 500 Populations

1000 Populations

·2 0�----,'1 0:::-0 -2::-"-00:----:3-'-= 00:----:-400:-:---------::-'500:::--6::-"- 00:----:7-'-=00:---=-800:-:-------=-'90.0 Commutation Signal Period (0.000025 5)

Fig.ll. Fitness curve of relation equation between cr, 0, � and commutation signal's period when vary population size of GA

Fig. 11 shows that the mean square error decreases when population size of each generation increases. The fitness curve from GA, the more accurate of relation between cr, 0, � and commutation signal's period. The calculation time, however, increases also.

Relation between cr, 0, � and the previous commutation signal's period Ti-1 is shown in equation (9)

r�1 = ro.0�02 fJ 0.0004

-0.0192 -0.0894 0.0802 5.097 4 1r'0� 1 35.2124 '0.1 58.6711 1

IV. EXPERIMENTAL RESULTS

(9)

In this work, the motor is MAXON EC 45 Flat motor 45 mm, brushless, 50 Watt with the data (provisional) as shown in Table I. The motor control is MAXON l-Q-EC Amplifier AECS 35/3.

TABLE! MOTOR DATA

Symbol Parameter

v v Nominal voltage No load speed

Imax Nominal current (max. continuous current)

R Terminal resistance phase to phase L Terminal inductance phase to phase Te Torque constant

J Rotor inertia P pole permanent magnet

phased coil stator Maxon EC 45 Flat motor 45 mm, brushless, 50 Watt

Data

24.0 V 6800 rpm

2.58 A

1.03 n 0.450 mH

33.5 mNml A

135 gcm2

16 3

Speed estimation method is divided into two steps. The first step is to find the frequency of the commutation signal using the each function in section III. The resulting frequency can be used to estimate speed but the result has more error. Therefore, once the commutation signal's frequency is known, the frequency cut-off of Butterworth low-pass filter can be applied to get the high accuracy for speed estimation.

30 Estimated Commutation

Signal 25

20

15

g 10

time (ms)

Fig.12. Hall effect signal, phase voltage and output signal at speed 2,108 rpm

�[l. • -"---_. . j o 1 2 3 4 5 6 7 8 9 10 �[ : : ; --.. -�. ; j o 1 2 3 4 5 6 7 8 9 10

::Le -----_·' . 1 a 1 2 3 5 10

time (ms)

Fig. 13 . The adaptation of parameter (cr, 0 and �) at speed 2,108 rpm

0

5

0

5

0 / 5

0

Ovemead ,,/ Time

5 time (ms)

l J 10

Fig. 14. % Error of estimated speed before filtering at speed 2,108 rpm

time (ms)

Fig.15. Phase voltage, filtered and output signal at speed 2, I 08 rpm

541

30

25

Overhead 20 7me

� 15 f.

10

0 I 0 5 10

time (ms)

Fig.16. % Error of estimate speed at speed 2, I 08 rpm

Low speed range, Hall effect sensor signal, phase voltage signals and estimated signals at speed 2,108 rpm in Fig. 12, shows that the signal is estimated to have periods near the period of Hall effect sensors signals. The adaptation of the parameters cr, 0 and � at speed 2,108 rpm shows in Fig. 13. The percentage error of estimated speed without using the low-pass filter shows in Fig 14. Once the frequency from previous step is used as the frequency cut-off of low pass filter, the frequency of the back-EMF can be estimated as shown in Fig. 15. The frequency of the back-EMF is used to estimate for speed again which is more accurate but over head time of calculation increases. The percentage error of the estimated speed is shown in Fig. 16.

30

5 rF � Hall Effect Sensor signal

/Phase Voltage

r" � I l r � 11 r n

0 I I I 5

0 I '6 >

5 J 0 l � II Estimated Commutation

5 Sign�1

10 time (ms)

Fig. 17. Hall effect signal, phase voltage and output signal at speed 6,885 rpm

t�� 2.5

0 1 2 3 4 5 6 7 8 9 10

�� o 1 2 3 4 5 6 7 8 9 10

rr;;:� 700 1 2 3 4 5 6 7 8 9 10

time (ms)

Fig.18. The adaptation of parameter (cr, 0 and �) at speed 6,885 rpm

30

25

20 Overhead

� Time 15

;!.

10

time (ms)

Fig. 19. % Error of estimated speed before filtering at speed 6,885 rpm

" >

20

15

10

Phase Voltage Signal

A/A A 1\ Filtered Signal

� A A

-50:---C-----:---:---C-----:---:--:----:----:--------:, O' time (ms)

Fig.20. Phase voltage, filtered and output signal at speed 6,885 rpm

25

20

10 Overhead Time

time (ms)

Fig.21. % Error of estimated speed at speed 6,885 rpm

7000

6000

5000

4000

3000

2000

1000

o

.r--

I � �

I L '--� I

I L I �

� � ... I

AC1ua,Led ESlima,l speed

o 10 time(ms)

Fig.22. The estimated and actual speed in each speed

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TABLE II SPEED,% ERROR AND OVER HEAD TIME OF ESTIMATED SPEED

Speed error Over head time (ms) (rpm) (%) 2108 1.28 8.23 2523 2.11 7.62 3038 1.26 6.68 3605 1J 4.81 3994 2.1 4.4 4600 0.87 4.2 5145 0.54 3.8 5649 1.01 3.14 6040 0.52 3.17 6637 0.79 2.8 6885 1.04 23

High speed range, Hall effect sensor signal, phase voltage signals and estimation signals at speed 6,885 rpm in Fig. 17. show that the signal is estimated to have periods nearby the period of Hall effect sensors signals. The adaptation of the parameters cr, 8 and � at speed 6,885 rpm is shown in Fig. 18. The percentage error of estimation speed without using the low-pass filter is shown in Fig 19. Once the frequency from previous step is used as the frequency cut-off of low pass filter, the frequency of the Back-EMF can be estimated as shown in Fig. 20. The approximate of frequency of the back-EMF is used to estimate for speed again which is more accurate but over head time of calculation increases. The percentage error of estimated speed is shown in Fig. 21.

Fig. 22 and Table II show the estimated speed in range of 2,000 to 7,000 rpm. At high speed rang overhead time are decreased. The estimated speed error is less than the lower speed range.

V. CONCLUSION

A novel AI-based speed estimation of 3-phase BLDC motor is presented in this paper. The performance of the proposed method is verified by the experimental results in a speed range of 2,000 to 7,000 rpm. The proposed method can reduce the cost of speed measuring and can use in speed control. The proposed speed estimation that method can estimate the speed of BLDC motor with the over head time less than 9 ms and average estimated speed error less than 2.5%.

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