performance analysis of sensorless controlled bldc motor ... · speed but in positive direction...

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 13, Number 7 (2018) pp. 5223-5235

© Research India Publications. http://www.ripublication.com

5223

Performance Analysis of Sensorless Controlled BLDC Motor Using Direction

Independent U-function

Umesh Kumar Soni1, Maloth Naresh2 and Ramesh Kumar Tripathi3

1,2,3 Department of Electrical Engineering, MNNIT Allahabad, 211004, Uttar Pradesh, India.

Abstract

In this paper, the performance of proposed Direction

Independent U-function based sensorless controlled brushless

DC motor has been analyzed. The proposed U-function based

virtual hall sensor has the good control characteristics as

compared with the real solid state hall sensors. Analysis of the

proposed method has been done with the view point of

position estimation error, speed estimation error, dynamic

tracking response with different observer gains and speed

accuracy. The simulation studies have been carried out with

different speed and load torque references. U-function based

virtual hall sensing provides the commutation positions which

is the exact replication of the actual solid state hall sensor and

provides excellent control over all four quadrants with added

sensitivity at starting and reversal. The proposed method has

excellent sustainability in the vibration and load disturbance

togetherwith the step load changes. The method has added

stability for both directions of rotation.

Keywords: Sensorless control; Brushless Motor;

Commutation; Back EMF, U-function.

INTRODUCTION

Brushless DC motors has widely applications in computers,

aerospace, medical, robotics, electric vehicles, and industries

due to the reason that these motors posses high power/weight

ratio, high torque to current ratio and high efficiency [1, 2].

Variable voltage variable frequency voltage source inverters

or current source inverters are used to operate brushless DC

motors. The self commutated BLDC motors are commutated

either by the Hall effect or encoder based position sensors

fixed in the rotor periphery or by sensorless schemes [3]. Frus

and Kuo [4] first intilaized the milstone research in sensorless

control. Due to the limitations of hall sensing or encoder

based control in terms of increased machine size, reduced

reliability and higher noise, sensorless methods are preferred

[5]. Various detection based sensorless control schemes are

detection of interval of freewheeling diode conduction [6]-[8],

back EMF ZCP detection [9]-[22], third harmonic back EMF

detection [11],[23], back EMF Integration till ZCP [24],[25].

There are many disadvantages in the detection of the back

EMF. Indirect and direct methods of back EMF detection has

circuit losses, delays due to filtering and deteriorated motor

performance due to effect of detection circuit in the phase

variables [20]. Various PWM strategies used in detection set

up unwanted oscillations in torque and degrade the motor

performance [14, 26]. Observer based control techniques

[27]-[35] were introduced to overcome these problems.

Unknown observer method has widely been implemented [33,

38] especially in the field of the fault detection. Unknown

Input Observer (UIO) assumes the back EMF information to

be unknown and the estimation of unknown value of back

EMF is done with the appropriate Kalman gain matrix. After

estimation of phase to phase back EMF, some special

functions e.g. Commutation Function (CF) [33], Speed

independent position function (SIPF) [36] were devised.

These are achieved in the form of a train of high magnitude

impulses. The magnitude and width varies as there is

disturbance in motor performance and so the threshold cannot

be appropriately set. These methods not work properly for

high speeds. To overcome this problem simple function

named ZDP for getting commutation pulses was introduced

[37], in which the simulation study was carried out and

detected phase back EMF was used for calculation of Zero

Difference Points (ZDP). Determining the threshold in ZDP

method is easy and the position detection is precise over wide

speed range. Together it is fault tolerant and free of

acquisition and measurement noises. Also the method

provided the very first commutation signal at starting

comparatively to ZCP based method based on initial rotor

position. ZCP of estimated Line to line back EMF were used

for getting phase back EMF ZDPs in [38]. All above method

proved unsuitable for the four-quadrant application and give

unstable results. So a new function named direction

independent U-function has been introduced in the proposed

work which is useful in the four quadrant application and low

to high speed operation as well. The estimated speed is used

as feedback to the U-function and speed proportional current

control loop. Two methods have been used for speed

estimation in proposed work. One method provides exact

speed but in positive direction only, while the other method

[39] provided rippled speed in both directions. So the

properties of both estimated speeds are applied. Proposed

method has excellent robustness towards estimation and

acquisition noise. In [40] the U-function has been introduced

first for sensorless control of BLDC motor. Main motivation

for the direction independent U-function is that, if direction

changes during reversal, the hall signal sequence only changes

and one of hall sensor signal level doesn’t instantly change

during that sector. So U- function also must be direction

independent and stable. Furthermore, the control should be

self sustained for all speeds. It should be able to control the

speed and torque in all four quadrants, without additional

logics. Function should have the transition edges exactly

coinciding with solid state hall signal transition edges. The



5224

hall signal sequence from the solid state hall sensors should

exactly match with the virtual hall sensor signals. The

proposed U-function has the required properties. The

performance analysis of the same has been accomplished in

further sections.

MODELLING OF VSI FED BLDC MOTORS

The equivalent circuit of PWM Inverter fed Brushless DC

motor drive system is shown in Fig. 1.

N

cnibni

anisL

sL

sL

6T

5T

4T

3T

2T

1T

anvb nv

c nvdcV

Ea

Eb

Ec

R

R

RM M

M

Figure 1. VSI fed BLDC motor drive.

The voltage equation for all the three phases with respect to

neutral can be expressed as Eq. (1) assuming that the

inductance and resistance parameters for all phases are equal

and time and rotor position doesn’t affect the self and mutual

inductances.

a n an an an

bn bn bn bn

cn cn cncn

v i i eR 0 0 L 0 0d

v = 0 R 0 i + 0 L 0 i + edt

0 0 R 0 0 Li i ev

(1)

Where, a nv , bnv and cnv are phase to neutral voltages and

a ni , bni and c ni are phase to neutral currents. The per phase

stator inductance L is calculated from the stator self inductance

Ls and mutual inductance M between phases i.e. sL = L -M .

The ideal waveforms of trapezoidal phase back EMFs with

relative position of rectangular current have been shown in

Fig.2.The developed electromagnetic torque is determines by

the values of phase currents and phase back EMFs as given by

Eq.(2).

an an bn bn cn cn

e

e .i +e .i +e .iT =

ωr (2)

be

be

ce

ce

ae

ae

be

ai

ai

ai

bi

bi

bi

ce

ae Phase A

ci

ci

ci

r r t

r r t

r r t 0

0

0

Phase B

Phase C

Phase Back EMF Phase Current

ZC

P1

ZC

P2

ZC

P3

ZC

P4

ZC

P5

ZC

P6

0 30 60 90 120 150 180 210 270240 300 33030 rotor angle

1T 2T 3T 4T6T

r r t Motor Starting Point

0

1T 2T 3T 5T4T 5T 6T 6T 1TMode I II III IV V VI I

Te

Figure 2. Waveforms of phase back EMF, phase currents and

Electromagnetic torque developed [37].

PROPOSED SENSORLESS BRUSHLESS DC MOTOR

DRIVE

A. Back EMF Estimation

The phase back EMFs cannot be measured directly due to

unavailability of neutral point of motor. So the phase to phase

back EMF can be estimated from known phase currents and

line voltages using the following equation,

an bn an bn an bn an bn

d R 1 1(i -i )=- (i -i )+ (v -v )- (e -e )

dt L L L (3)

Similarly for other phase groups also, the equations can be

written. The quantities an bnv -v , ani , bni in Eq.(3) are

known state variables as they can be measured. The phase to

phase back EMF an bne -e is unknown disturbance quantity.

The above equation can be written in state space matrix form

as,

x=Ax+Bu+Fw , y=Cx+Du (4)

an bn an bn an bn

an bn

R 1 1A= - ,B= ,F= -

L L L

x= i -i , u= v -v , w= e -e ,

y= i -i ,C= 1



5225

The disturbance quantity w is can be expressed as a

polynomial of order , which satisfies the condition that w is

completely observable dynamic model.

0

, 1ii

iw a t

Augmented state space matrix involving unknown disturbance

in phase to phase back EMF can be determined by the

representation as below:

a a a ax =A x +B u (5)

a ay=C x

(6)

Where,

an bn

a an bn an bn

an bn

i -ix = ,u= v -v , y= i -i

e -e

a a a

R 1 1- -

A = , B = ,C =[1 0]L L L

0 0 0

As the system in equations (4) and (5) are observable

system, the complete state space equation can be reduced in

the form of observer given by (7) and shown by Fig.3.

1/ L1

sKTz ˆ ˆ

an bni i

an bni i

/R L

11

0abu

Sw

itch

ing

Va

ria

ble

s

Voltage

generator

dcV

1K

2K

1/ L

1

sKTz ˆ ˆan bne e

iab

U-Functions &

Virtual Hall

Signals

abv

ˆ ˆan bne e

ˆ ˆbn cne eˆ ˆcn ane e

ˆr

Figure 3. Proposed sensorless scheme integrated with

estimation scheme.

a a a aˆ ˆ ˆx =A x +B u+K(y-y) (7)

Where, iab an bn an bnˆ ˆε =(i -i )-(i -i )

is the estimation error in

phase currents in phase-A and phase-B. Similarly other

estimation errors can also be defined. Observer gain matrix is

defined by,

K1K=

K2

(8)

From the variation of estimated quantities

i

ˆde=K2.ε

dt (9)

The variables e and i are generalized errors in the actual and

estimated values of line to line currents and line to line back

EMF.The complete equation showing the difference between

the actual and estimated value is given by.

i i

e e

R 1d ε ε- -K1 -= L L

ε ε-K2 0dt

(10)

The objective is to find out the optimal value of the observer

gains so that the observer error can be reduced approximately

to zero. The observer gain calculation can be obtained by

method discussed in latter section.

B. Observer Gain Calculation

The state feedback gain matrix can be determined Ackermans

[39] method in which the system poles are placed at preferred

positions. Let the desired eigen values are 1λ and 2λ . The

characteristic polynomial is obtained as below,

21 2 1 2 1 2α(s)=(s-λ )(s-λ )=s -(λ +λ )s+λ .λ (11)

Where 1 1 2 0 1 2-α =λ +λ , α =λ .λ

The characteristic polynomial can be expressed in terms of

matrix A by the Caley-Hamilton Theorem as

21 0α(A)=A +α A+α .I (12)

The observer gain matrix G with observability matrix Q can be

determined by

-1 1

0

RK1 0 - +α

K= =α(A).Q = LK2 1-α L

(13)

1 0C R 1Q= =CA - -

L L

(14)

Different Eigen values can be chosen for the best performance

considering the mutual balance between the fast convergence

which occurs when eigen values are set near minus infinity,

sluggishness in case of small eigen values and sensitivity

towards the noise and other disturbances while large eigen

values are selected.

C. Rotor Speed and Position Estimation

The actual speed of the motor depends upon the load torque

applied and internal electromagnetic torque developed by



5226

motor, which is obtained by solving the following differential

equation for ωr ,

re l r

dωT =T +J +Bω

dt (15)

The coefficients J and B are Inertia and friction coefficient

respectively.

The estimated speed can be calculated by the following

equation using line to line back EMF information and back

EMF constant.

an bn bn cn cn an

re

ˆ ˆ ˆ ˆ ˆ ˆmax e -e , e -e , e -e2ω = .

P 2K (16)

The rotor angle can be calculated using

r r 0ˆ ˆθ = ω dt+θ (17)

Where, 0θ is initial angle of rotor with the phase-A axis and

Ke is per phase BEMF constant. The proper tracking of actual

and estimated value is needed so as to protect motor from

going into the saturation especially when motor reverses and

direction becomes negative. So, for the direction estimation,

another speed estimation method was followed in [39], which

can be useful for direction detection, as discussed below.

Referring to the Fig.4, the line to line back EMF can be

transformed to dq form as below [39].

ds ab ca

1ˆ ˆ ê = (e -e )

3 (18)

qs bc

1ˆ ê =- e

3 (19)

qs-1e

ds

eθ =tan

e

(20)

Where, dse and qse are the direct and quadrature back EMFs.

cae

bce

âbe

ˆbe

ce

ce

be

ae

ae

ˆ3 dse

ˆdse

qse ˆ ˆ3bc qse e

ˆcae2 2ˆ ˆds qse e

ê

Figure 4. Vector representation of back EMFs

Estimated rotor angle and rippled angular speed from the

above method,

rr2 e r2

ˆdθ2ˆ ˆ ˆθ = .θ , ω =P dt

(21)

The estimated speed obtained from the Equation (16) is always

achieved positive magnitude, while the magnitude is close to

actual speed. So direction measurement is necessary for getting

the direction with near exact value. Direction of the rotation

can be obtained by the ratio of estimated rippled speed with the

magnitude of rippled speed. The ratio of the rippled speed vs

magnitude of rippled speed may be equal to 1or -1. This value

is multiplied with the Exact estimated speed magnitude from

Eq.(16), to get near exact speed with direction information. So

both the methods are used together at same time to get the

rippleless exact speed with direction information is obtained.

Therefore the rippleless exact speed is given by,

an bn bn cn cn an r2r

e r2

ˆ ˆ ˆ ˆ ˆ ˆmax e -e , e -e , e -e ω2ω = . .

ˆP 2K ω

(22)

The different types of speeds relative to the reference speed

obtained by performing the simulation with proposed method

are shown in Fig.5, which are calculated by Eq. (15), Eq.(16),

Eq. (21) and Eq. (22). The reference speeds of 3000 , -2000

and 500 rpm were applied at the instants 0, 0.2 and 0.6 seconds

respectively with the load of 0.5 Nm.

(a)

0 0.2 0.4 0.6 0.8-4000

-2000

0

2000

4000

Time

Sp

ee

d (

rp

m)

Reference Speed

Exact estimated Speed with direction information (Eq. 22)

actual Speed (Eq. 15)

Exact estimated speed without direction information(Eq.16)

Estimated rippled speed with direction (Eq.21)



5227

(b)

Figure 5 (a) Actual speed, exact estimated speed without

direction, rippled speed with direction information and exact

estimated speed with direction information relative to the

reference speed are shown. (b) zoomed view from 0.162 to

0.26 sec. The motor has been operated with the load of 0.5 Nm

with various reference speeds of 3000, -2000 and 500 at

instants 0, 0.2 and 0.6 seconds respectively.

D. Direction Independent U-Function

The proposed U-function has the property that it crosses the

zero axis only at the actual solid state hall transition edges

unlike Commutation Function and Speed Independent

Position Function. U-functions need not the setting of

threshold values as were needed in other functions for

sensorless operation. The position of phase mmf axis may be

obtained wherever the derivative of U-function is zero. The

U-function is defined by the following equation based on the

line to line back EMFs.

2 2 2ab bc ca

abab

E +E +EU =

3E (23)

2 2 2ab bc ca

bcbc

E +E +EU =

3E (24)

2 2 2ab bc ca

caca

E +E +EU =

3E (25)

Whenever reversal of the direction starts, the back emf

polarity and sequences become opposite which can generate

ambivalence in decision for right commutation. For this

problem, the direction normalization is done. The direction

independent U-functions are given by,

2 2 2ab bc car

abr ab

E +E +EωU = .

ω 3E

(26)

2 2 2ab bc car

bcr bc

E +E +EωU = .

ω 3E (27)

2 2 2ab bc car

car ca

E +E +EωU = .

ω 3E (28)

Where, the angular speed r may be positive, negative or

zero. U-functions cross the zero axis only at real Hall sensor

transition edges. The U-function based virtual hall sensor

behaves as it is fixed as real solid state hall sensors. The

virtual hall sensor signal outputs are obtained by comparing

U-functions to zero, which may be High or Low (logic 1 or 0)

which is shown in Fig.6 and illustrated in Table.1.

Table 1. Actual versus u-function based virtual hall

sensors

Condition of

U-function

U-function

based Virtual

Hall Sensor

States

Corresponding

Real Hall

Sensor States

caU <0 vaH =1 aH =1

caU >0 vaH =0 aH =0

abU <0 vbH =1 bH =1

abU >0 vbH =0 bH =0

bcU <0 vcH =1 cH =1

bcU >0 vcH = 0 cH =0

Uca, Ha Uab, Hb Ubc, Hc

U-f

unct

ions

Ubc

<0

Ubc

>0

Uab

<0

Uca

<0

Uca

>0

Uca

>0

Uab

>0

Ubc

<0

Uab

<0

Ha

Hc

Hb

Vir

tual

Hal

l S

igna

ls

180° 180°

1

0

10

1

0

Figure 6. Virtual hall sensors obtained from U-functions

compared to zero.

E. Overall Block Diagram

Complete block diagram of the proposed U-function based

sensorless controlled VSI fed brushless DC motor system has

been shown in Fig.7.

0.18 0.2 0.22 0.24

-1000

0

1000

2000

3000

Time

Sp

ee

d (

rpm

)

Reference Speed

Exact estimated Speed with direction information (Eq. 22)

actual Speed (Eq. 15)

Exact estimated speed without direction information(Eq.16)

Estimated rippled speed with direction (Eq.21)



5228

BLDC

MotorAC to DC

Converter

PFC

Converter

3 Phase VSI

PWM

AC

Sou

rce

Voltage

Generator

Rectangular

3-Ph. Current

& PWM

generator

ia

ib

ic 3 P

hase C

urren

t

Sen

sin

g

PI

PI

Te

TL

Nref

Iref

Current

Limiter

H1 L1 H2 L2 H3 L3

H1 L1 H2 L2 H3 L3

N

U-function based

Virtual hall signal

Decoder

Vdc

Ia, Ib, Ic

BEMF & Speed

Estimation

Proposed U-functions

calculation Va,Vb,Vc

KpT, KiT

KpN, KiN

Feed-Forward

control

Figure 7. Block diagram of the complete system.

The three phase currents and line voltages are taken as

feedback for rectangular reference current generator and

Unknown input observer. The Back EMFs obtained from the

observer are used for U-function calculation and speed

estimation. Based on the virtual hall signals from calculated

U-functions, the switching sequence signals are decoded. The

current from reference current generators and the actual phase

current are compared and then hysteresis current controllers

provides the PWM signals to the switches of VSI based on the

switching signals obtained from sequence signals. The effect

of increasing feed-forward torque error proportional current

control gain KpT leads to fast speed response with higher

starting torque and current but leads to uncontrolled torque

with ripple. Higher value of speed error proportional gain KpN

leads to fast response, less rise time but increased torque

ripple. So the PID parameters of torque as well as speed error

proportional current controllers need to be set properly to keep

speed rise time and torque ripple in reasonable limit. Also the

steady state errors are affected by these parameters. To keep

the starting torque and current within permissible limits, a

current limiter is used.

SIMULATION RESULTS

The simulation diagram as shown by Fig.8 has been designed

on PC with MATLAB R2011b. The simulation results have

been obtained and analyzed for various load and speed

references using the motor and controller parameters as shown

in Table.2. Different case studies have been done in

succeeding sections. During the starting or zero (or near zero)

speed condition at any time, only the reference speed is fed to

the current controller so as to lead the system in reference

direction. When a very small speed is achieved and motor

starts running in either direction, the rippled speed feedback

having direction information (from Eq.21) is given after a

delay of 0.1 miliseconds. The difference of reference and

rippled speed (with direction information as per Eq.21) is fed

as error for current controller. Again after a small delay, the

exact speed with direction information (Eq. 22) is fed to the

current controller.

Table 2. Simulation parameters for Motor and

Controller

Parameter Value

Per Phase Inductance 8.5mH

Per phase Resistance 2.875 ohm

Voltage Constant 49 V peak L_L /

Krpm

Torque Constant 0.46792 Nm/A-peak

Flux linkage by rotor

magnets 0.23396 V.sec

Rotor Inertia 0.0008 kg.m2

Viscous damping 0.001 N.m.sec

Pole Pairs 1

Nominal DC link voltage

Vdc 300 volt DC

Kalman gain K1 3500

Kalman Gain K2 -100000

Forward Gain K 1

Threshold for phase back

EMF ZDP Vdc/1500

Hysteresis band 0.000005

PWM generator Kp, Ki 0.00005, 0.00000005

Torque proportional control

KpT , KiT

1.075, 0.000005

Speed Proportional Control

KpN,KiN

0.006, 0.000006

Saturation 0.000006

Current limiter 20,-20



5229

Figure 8. Simulation block diagram in MATLAB/ SIMULINK Plateform.

A. Case .1 Dynamic response

1) Reference and Actual Values of Speed, Torque and Current: The speed ,torque and current response of the system

with the reference speed and load variation as per the Table.3

is shown in Fig.9. The load torque applied to the motor are 3

Nm , 2 Nm and 4 Nm respectively at 0, 0.15 and 0.4 seconds

respectively. The speed references at 0, 0.15 , and 0.3

seconds are -2000, 1000 and 500 rpm respectively. The

simulation time is 1 sec.

Table 3. Loading Torque and reference speed

Time (Sec.) 0 0.15 0.3 0.4

Load torque

(Nm) 3 2 2 4

Reference

Speed(rpm) -2000 1000 500 500

Figure 9. Reference speed and actual speed achieved, current

and torque

0 0.1 0.2 0.3 0.4 0.5-2000

-1000

0

1000

Nre

f, N

0 0.1 0.2 0.3 0.4 0.5-20

0

20

Ph

ase

Cu

rren

t 0 0.1 0.2 0.3 0.4 0.5-10

0

10

Time

Tre

f, T

e



5230

2) Three Phase Currents and Back EMF Waveform:The

three phase currents and the line to line estimated back EMF

waveforms are shown in Fig.10, for the variations of load and

reference speed as per Table.3.

Figure 10. Three phase currents and line to line BEMFs.

3) U-functions based Virtual Hall signals & Actual hall signals: When U-functions are compared with zero, they give

the virtual hall signal values (Logical 1 or 0). Because the

value of U-function has very high magnitude at phase back

EMF ZDPs or hall signal transition edges, so a limiter (max

10) is used to show the U-functions properly as in Fig. 11(a).

0 0.1 0.2 0.3 0.4 0.5-10

0

10

0 0.1 0.2 0.3 0.4 0.50

0.5

1

0 0.1 0.2 0.3 0.4 0.50

0.5

1

Time

U-f

un

cti

on

sV

irtu

al H

all

Sig

na

ls

Ac

tua

l H

all

Sig

na

ls

Figure 11. U-functions, virtual hall signals and corresponding

actual hall signals

Zoomed view (time axis from 0.13 to 0.2 seconds) in Fig.

11(b) shows the additional sensitivity and stability of

sensorless virtual hall sensor scheme using U-function during

speed reversal and load disturbance at 0.173 second. It can be

seen that virtual hall sensor signals using U-function gives

extra short duration pulse signal during the reversal, while the

sequence is same as the real hall signals at all other instants.

Also during starting, the virtual hall signals are seen

performing in more sensitive manner.

0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2-5

0

5

0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20

0.5

1

0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20

0.5

1

Time

U-f

un

cti

on

sV

irtu

al H

all

Sig

na

ls

Ac

tua

l H

all

Sig

na

ls

Figure 11(b) Zoomed view (time axis) showing the stability

of U-function method

B. Case 2 Dynamic response

1) Reference and Actual Values of Speed, Torque and Current: The response of the system with the reference speed

and load variation as per the Table.4 is shown in Fig.12. With

high load torque and reference speed, the power requirement

is high. So current is not controlled and the motor has high

torque ripple as can be seen in the Fig.12.

Table 4. Load and reference speed variation

Time (Sec.) 0 0.15 0.2 0.3 0.4

Load torque

(Nm) 5 -1 -1 -1

4

Reference Speed

(rpm) 5000 5000

-

2000 1000

1000

Figure 12. Speed reference, actual speed, load versus actual

torque and currents.

0 0.1 0.2 0.3 0.4 0.5-20

0

20

Th

ree

Ph

as

e

Cu

rre

nts

0 0.1 0.2 0.3 0.4 0.5-100

0

100

Time

Lin

e T

o L

ine

BE

MF

0 0.1 0.2 0.3 0.4 0.5-2000

0

2000

4000

Nre

f, N

r (r

pm

)

0 0.1 0.2 0.3 0.4 0.5

-20

0

20

Ph

ase C

urr

en

t(A

) 0 0.1 0.2 0.3 0.4 0.5-10

0

10

Time

Te,

Tre

f (N

m)



5231

2) Three Phase Currents and Back EMF Waveform:

The three phase currents and the line to line estimated back

EMF waveforms are shown in Fig.13, for the variations of

load and reference speed as per Table.4.

Figure 13. Back EMF and three phase currents for loading

and speed reference as per Table.4.

3) U-functions based Virtual Hall signals & Actual hall signals: for the loading pattern as per Table.4, the U-function

based virtual hall signals and actual hall signals are shown in

Fig.14 (a). Zoomed view (time axis from 0.18 to 0.35

seconds) in Fig. 14(b) shows the additional sensitivity and

stability of sensorless virtual hall sensor scheme using U-

function during speed reversal at 0.248 second and 0.319

second. It can be seen that virtual hall sensor signals using U-

function gives extra short duration pulse signal during the

reversal from negative to positive to negative at 0.248 second,

whereas the sequence is same as the real hall signals at all

other instants. During the reversal when speed is going

positive from negative at 0.32 second, the virtual hall sensor vcH from U-function for phase C (i.e. ) goes LOW for short

duration. Also during starting, the virtual hall signals are seen

performing in more sensitive manner.

Figure 14(a) U-functions based virtual hall sensor signals and

actual hall sensor signals for loading pattern as per Table.2

Figure 14(b) Zoomed view of U-functions, virtual hall

signals, actual hall signals at 0.248 and 0.319 seconds.

C. Dynamic response to load disturbances and fluxuations imposed at different step loading conditions

The robustness of the proposed U- function based sensorless

scheme has been checked for the load disturbance imposed at

the step load changes of 3, 2 and 4 Nm at 0-0.15, 0.15-0.4

and 0.4-0.5 seconds respectively for a fixed forward motoring

speed reference of 2000 rpm. Fig.15 shows that the speed of

the motor is not differing much with reference speed and

remains unaffected by noise and disturbance in load.

Figure 15. Performance verification with load disturbance

and fluctuations applied at different step loadings.

D. Position Estimation Error for Different Observer Gains K1 and K2

For the improvement in the position tracking performance

with U-function based sensorless method, first the system

performance has been investigated with fixed value of K1 and

varying the value of K2 at fixed speed reference of 2000 rpm

0 0.1 0.2 0.3 0.4 0.5-20

0

20

Th

ree P

hase

Cu

rren

ts (

A)

0 0.1 0.2 0.3 0.4 0.5

-200

0

200

Time (sec.)

Lin

e t

o L

ine

BE

MF

s (

V)

0 0.1 0.2 0.3 0.4 0.5-5

0

5

U-F

un

cti

on

s

0 0.1 0.2 0.3 0.4 0.50

0.5

1

Vir

tual

Hall

Sig

nals

0 0.1 0.2 0.3 0.4 0.50

0.5

1

Time

Actu

al

Hall

Sig

nals

0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34-5

0

5

U-F

un

cti

on

s

0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.340

0.5

1

Vir

tual

Hall

Sig

nals

0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.340

0.5

1

Time

Actu

al

Hall

Sig

nals

0.1 0.2 0.3 0.4 0.51800

1900

2000

Nre

f, N

r (r

pm

)

0.1 0.2 0.3 0.4 0.5-20

0

20

Ph

as

e

Cu

rre

nt

(A)

0.1 0.2 0.3 0.4 0.50

5

Time

Dis

turb

an

ce

Lo

ad

(N

m)



5232

and Load Torque of 2Nm. It can be observed from Fig.16, that

increasing the observer gain K2, turns into the reduced the

slope of position estimation error. After this, the Kalman gain

K2 is kept fixed and K1 is varied and then both are varied.

Figure 16. Effect of varying the observer state feedback gain

K2 on Position error

The position error (radians) is constant 0.25x10-3 for

K1=10000 and K2 = -3.5x107 for the reference speed of 2000

rpm as shown in Fig.20.

Figure 17. Position estimation error for different observer

gains.

E. Actual speed feedback vs. Estimated Speed feedback

For the reference speed of the 5000 rpm and 1 Nm load, the

speed performance of U- function based sensorless technique

has been investigated with the feedback of actual speed and

estimated speed as shown in Fig.18. The percentage

difference in later condition is only 0.2 percent.

Figure 18. Performance of U-function method when actual

speed estimated speed is used as feedback for speed control.

F. Reference Tracking of Estimated and Actual Speeds

The reference tracking performance of the proposed U-

function based sensorless technique has been evaluated as

shown in Fig.22 (a) and (b). In case (a), the speed references

of -3000, 3000 and -5000 rpm is applied with 2 Nm load

input, while in case(b) the references of 3000, -3000 and 5000

rpm is given at instants 0, 0.2 and 0.4 seconds respectively.

(a)

(b)

Figure 19. The performance of proposed U-function based

sensorless method for various speed references at load of 2Nm

showing the reference tracking behavior of actual speed and

estimated speed.

0 0.1 0.2 0.3 0.4 0.5-0.15

-0.1

-0.05

0

0.05

Time

Po

sit

ion

esti

mati

on

err

or

(K1=

3000)

K2=-500000

K2=-100000

K2=-700000

K2=-1000000

K2=-3000000

K2=-5000000

0 0.1 0.2 0.3 0.4 0.5-5

-4

-3

-2

-1

0

1

2

3

4x 10

-3

Time

Po

siti

on

Est

imat

ion

Err

or

K1=3000, K2=-5000000

K1=5000, K2=-5000000

K1=10000, K2=-5000000

K1=10000, K2=-10000000

K1=10000, K2=-20000000

K1=10000, K2=-35000000

0.2 0.25 0.3 0.35 0.4 0.45 0.54885

4890

4895

4900

Time

perf

orm

an

ce o

f U

-fu

ncti

on

Speed(RPM)

actual speed feedback

estimated Speed feedback

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-5000

-4000

-3000

-2000

-1000

0

1000

2000

3000

Time

refe

ren

ce ,

est

imat

ed a

nd

acu

alS

pee

ds

(rp

m)

Estimated Speed

Actual Speed

Reference Speed

0 0.2 0.4 0.6 0.8 1-4000

-2000

0

2000

4000

6000

Time

refe

ren

ce,

esti

mate

d a

nd

actu

al

sp

eed

(rp

m)

estimated Speed

actual Speed

Reference Speed



5233

G. Percentage Steady state error between actual and estimated speed with direction:

The percentage error using proposed method obtained based

on the reference speed, has been shown in Fig.20.

(a)

(b)

Figure20 (a) Percentage error in the estimation of speed with

speed reference of 2000 rpm. (b) Percentage error with input

reference speed of 5000 rpm.

Fig. 20 (a) shows the forward motoring case for speed

reference of 2000 rpm with Kalman gains K1=1x104 and K2

=-3.5x107 while the reference speed of drive is 2000 rpm and

0.5 Nm load torque. Fig.20 (b) represents the percentage error

in the estimation of the speed with input reference speed of

5000 rpm.

H. Effieciency Versus Load Torque

The efficiency versus load torque plot for the solid state hall

sensor based control as well as for sensorless control using U-

function based Virtual Hall sensor has been shown in Fig.21.

The reference speed has been given 3000 rpm. It has been

observed in simulation study that the sensorless control

through U-function based virtual hall sensors perform better

than actual solid state hall sensor based control at higher load

torques. The bifurcation in efficiency plots starts from 6 Nm

load torque for the drive parameters selected as per Table.2.

Figure 21. Plot of efficiency versus load torque for actual and

U-fucntion based virtual hall sensor control reference speed of

3000 rpm.

CONCLUSION

In the proposed work, a Direction Independent U-function

based sensorless commutation technique has been introduced

for brushless DC motor. The exact estimated speed value with

direction information was used as feedback for current control

loop as well as in U-functions. The line to line back EMF

estimated out of unknown input observer has been used for

speed magnitude calculation. The U-function based virtual

hall sensor signals are more sensitive at starting and reversal

instants. The positions are stable as solid state hall sensors. At

starting, the system with feedback may give unstable results,

so for 0.0001 seconds time the feedback is not given to

current control loop, so as to lead the system in reference

direction. The method has been observed to be self-

sustainable in the condition of the load disturbance, vibration

and step load variations when using proposed technique with

speed and load proportional current control. It has been

observed that for higher observer gain obtained with

corresponding Eigen values, the position estimation and speed

estimation error reduce to very low value and remain constant.

Percentage estimation error at steady state is limited to 0.1 to

0.2 %. Proposed method has provided excellent tracking of

reference speed and torque. It works for all four quadrants

with positive as well as negative reference torque and speed.

The proposed sensorless system is completely free of actual

(hall or encoder based) speed and position feedback and

works only on estimated line to line back EMFs. The

proposed method has higher efficiency at higher loads than

the actual hall sensor base control.

REFERENCES

[1] M.V.Kesava Rao, Department of Electrical

technology, IISc Bangalore, “Brush Contact Drops in

DC machines”, Accepted 25-6-1934, Bangalore

Press.

[2] Y.S. Jeon, H.S. Mok, G.H. Choe, D.K. Kim, J.S.

Ryu, “A New Simulation Model of BLDC Motor

with Real Back EMF waveform”, 7 th workshop on

Computers in power Electronics , 2000 (COMPEL

2000), page 217-220.

[3] Padmaja yedmale, “Brushless DC (BLDC) Motor

Fundamentals”, AN885, 2003 Microchip

Technology.

[4] J. R. Frus and B. C. Kuo, “Closed-loop control of

step motors using waveform detection,” in Proc. Int.

Conf. Stepping Motors and Systems, Leeds, U.K.,

1976, pp. 77–84.

[5] S. Tara , Syfullah Khan Md “Simulation of

sensorless operation of BLDC motor based on the

zero cross detection from the line voltage”

International Journal of Advanced Research in

Electrical Electronics and Instrumentation

Engineering, vol 2, issue 12 , December 2013, ISSN

2320-3765.

[6] R. L. Lin, M.T. Hu, S.C. Chen, and C.Y. Lee, “Using

phase-current sensing circuit as the position sensor

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-0.2

0

0.2

Time (sec.)

% E

rro

r in

es

tim

ate

d

sp

ee

d (

rpm

)

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-0.1

-0.05

0

0.05

0.1

Time

% E

rro

r in

th

e e

sti

ma

ted

sp

ee

d(r

pm

)

0 2 4 6 80.5

0.6

0.7

0.8

0.9

1

Load Torque (Nm)

Eff

icie

nc

y (

pu

)

U-function based Virtual hall sensor

Actual Hall Sensor



5234

for brushless DC motors without shaft position

sensor,” IEEE Conf. Digital Object Identifier, Vol. 1,

pp. 215-218, Nov. 1989.

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

position sensorless drives for brushless DC motors”,

IEEE Trans. On Industry Applications vol.27, no.5

pp.928-933, 1991.

[8] C. G. Chen, T. H. Liu, M. T. Lin, and C. A. Tai,

“Position control of a sensorless synchronous

reluctance motor,” IEEE Trans. Digital Object

Identifier, Vol. 51, Issue 1, pp. 15-25, Feb. 2004.

[9] K. Iizuka, H. Uzuhashi, and M. Kano,

“Microcomputer control for sensorless brushless

motor,” IEEE Trans. on Industry Applications, vol.

27, pp. 595-601, 1985.

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

Mohri, “Microcomputer Control for Sensorless

Brushless Motor, Industry Applications,” IEEE

Trans, vol. IA-21, pp. 595-601, 1985.

[11] J.C. Moreira, “Indirect sensing for rotor flux

position of permanent magnet AC motors operating

over the wide speed range”, IEEE trans. on Industry

Applications, vol. 32, no. 6, pp. 1394-1401, 1996.

[12] H. G. Yee, C. S. Hong, J. Y. Yoo, H. G. Jang, Y. D.

Bae, and Y. S. Park, “Sensorless drive for interior

permanent magnet brushless DC motors,” Proc. of

IEEE International Conf. on Electric Machines and

Drives, 18-21, pp.TD1/3.1-3.3, 1997.

[13] J. S. Kim, and S. K. Sul, “New approach for high-

performance PMSM drives without rotational

position sensors,” IEEE Trans. Power Electronics,

Vol. 12, pp. 904-911, Sep. 1997.

[14] J. Shao, D. Nolan, and T. Hopkins, “A novel direct

back EMF detection for sensorless brushless

DC(BLDC) motor drives,” 17th Annual IEEE

Applied Power Electronics Conference and

Exposition, Vol. 1, pp. 33-37, Mar. 2002.

[15] G. J. Su and J. W. Mckeever, “Low cost sensorless

control of brushless DC motors with improved speed

range,” IEEE Trans. on Power Electronics, vol. 19,

pp. 296-302, 2004.

[16] Q. Jiang, C. Bi, and R. Huang, “A new phase delay-

free method to detect back EMF zero crossing points

for sensorless control of spindle motors,” IEEE

Trans. Magn., vol. 41, no. 7, pp.2287-2294, 2005.

[17] Y. Kang, S. B. Lee, and J. Yoo, “A microcontroller

embedded AD converter based low coast sensorless

technique for brushless dc motor drives,” IEEE Conf.

Industry Applications, Vol. 3, pp. 2176-2181, Oct.

2005.

[18] C. G. Kim, J. H. Lee, H. W. Kim, and M. J. Youn,

“Study on maximum torque generation for sensorless

controlled brushless dc motor with trapezoidal back

EMF,” IEE Proceedings of Electric Power

Applications, Vol.152, Issue 2, pp. 277-291, Mar.

2005.

[19] J. Shao, “An improved microcontroller-based

sensorless brushless DC (BLDC) motor drive for

automotive applications”. IEEE Trans. Ind. Appl.

42(5): 1216- 1222 (2006).

[20] Yushui, Yugang Xin, Weicheng Zhang, “An

improved BEMF Detection Method for sensorless

BLDC motor” IEEE international conference in

Industrial technology, ICIT 2008.

[21] P. Damodharan and Krishna Vasudevan, “Sensorless

Brushless DC Motor Drive Based on the Zero-

Crossing Detection of Back Electromotive Force

(EMF) from the Line Voltage Difference”, IEEE

Trans on energy conversion, vol. 25, no. 3,

September 2010.

[22] Lai Y.-S. Lin Y.-K., “A unified approach to zero

crossing point detection of back EMF for Brushless

DC motor drives without current and hall sensors”.

IEEE Trans. Power Electron. 26(6), 2011).

[23] J.X. shen ,Z.Q. Zhu and D. Howe, “sensorless flux

weakening control of permanent magnet brushless

machine using third harmonic back EMF”, IEEE

transactions on Industry applications, vol 40 no 6 pp.

1629-1636, 2004.

[24] T.M. Jahns, R.C. Becerra, and M. Ehsani,

“Integrated current regulation for a brushless ECM

drive” ,IEEE trans. on power Electronics, Vol No. 6,

No.1, pp 118-126, 1991.

[25] H.R Anderson and J.K. Pedersen, “Sensorless

ELBERFELD control of brushless DC motors for

energy optimized variable speed household

refrigerators,” EPE confrec,vol.1, pp. 314-318, 1997.

[26] J. X. Shen, K. J. Tseng, "Analyses and

Compensation of Rotor Position Detection Error in

Sensorless PM Brushless DC Motor Drives," IEEE

Trans. Energy Conversion, vol. 18, no. 1, pp. 87-

93,March 2003.

[27] Fakham H, Djemai M, Busawon K. “Design and

practical implementation of a back-EMF sliding-

mode observer for a brushless DC motor”, IET

Electr. Power Appl. 2008;2(6):353–61.

[28] R. Wu and G. R. Slemon, “A permanent magnet

motor drive without a shaft sensor,” IEEE

Transactions on Industry Application, vol. 27, pp.

1005–1011, Sept. /Oct. 1991.

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

sensorless operation of permanent magnet motors,”

IEEE Trans. Ind. Applicat., vol. 30, pp. 126–133,

Jan./Feb. 1994.

[30] J. S. Kim, and S. K. Sul, “New approach for high-

performance PMSM drives without rotational

position sensors,” IEEE Trans. Power Electronics,

Vol. 12, pp. 904-911, Sep. 1997.

[31] Jium –Ming Lin , Ming –Chang Lin, Hsin –Ping

Wang, “LEQG/LTR controller design with extended

kalman filter for sensorless brushless DC



5235

driver.”,Computer. Methods Applied Mechanical

Engineering 190(2001) pp.5481-5494, Elsevier.

[32] Ki- hong Park, tae-Sung Kim, Sung-Chan Ahn,

Dong-Seok Hyun, “Speed Control of High

Performance Brushless DC Motor drives by load

Torque Estimation”, 34th IEEE Power Electronics

Specialist Conference, 2003 PECS 03, pp. 1677-

1681.

[33] Tae-Sung Kim,Byong –Gun Park, Dong-Myung

Lee, Ji-su Ryu and Dong –Seok Hyun, “A new

Approach to sensorless control method for brushless

DC Motors”, International Journal of Control

Automation and Systems, vol. 6 No.4 PP 477-487,

August 2008.

[34] S.A.KH. Mozaffari Niapour, M. Tabarraie , M.R.

Feyzi, “Design and analysis of speed-sensorless

robust stochastic L-induced observer for high-

performance brushless DC motor drives with

diminished torque ripple” Energy Conversion and

Management, 64 (2012) 482–498.

[35] S.A.KH. Mozaffari Niapour, M. Tabarraie , M.R.

Feyzi, “A new robust speed sensorless control

strategy for high performance brushless DC motor

drives with reduced torque ripple”, Control

Engineering Practice(Elsevier), 24(2014), 42-54.

[36] Tae-Hyung Kim ,M. Ehsani, “Sensorless control of

BLDC motors from near zero to high speeds”, IEEE

Transactions on Power Electonics , ISSN 0885-

8993,vol 19, No. 6, p.1635-1645, Nov 2004.

[37] Umesh Kumar Soni and Ramesh Kumar Tripathi,

“Novel Back EMF Zero Difference Point Detection

Based Sensorless Technique for BLDC Motor”,

Proceedings of IEEE 18th Annual International

Conference on Industrial Technology, ICIT 2017,

22-25 March 2017, Toronto, Canada, pp.330-335.

[38] Umesh Kumar Soni and Ramesh Kumar

Tripathi,”Novel Estimated back EMF ZDP based

sensorless controlled BLDCM using Unknown Input

Observer”, Proc. of International Seminar on

Intelligent Technologies and Its Applications, pp.

121-126, Indonesia, 28-29 August, 2017.

[39] Mitesh B. Ashtik, Pragnesh Bhatt, Bhavesh R.

Bhljia, “ Analysis of Sensorless Control of brushless

DC motor using unknown input observer with

different gains”, Journal of Electrical Engineering,

Vol. 68(2017) no. 2, pp.99-108.

[40] U. K. Soni and R. K. Tripathi, "Direction

independent U-function based sensorless control of

BLDC motor," 2017 IEEE International Conference on Industrial and Information Systems (ICIIS), Peradeniya, Sri Lanka, 2017, pp. 1-6.

performance analysis of sensorless controlled bldc motor ... · speed but in positive direction...

Documents