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Research Article ISSN: 2319-507X

Shital Wasu, IJPRE, 2013! "#lu$e 1%&':2()-259 IJPRE

Available Online At www.ijpret.com

INTERNATIONAL JOURNAL OF PURE AND

APPLIED RESEARCH IN ENGINEERING ANDTECHNOLOGY

A PATH FOR HORIZING YOUR INNOVATIVE WORK

BACK EMF DETECTION METHODS FOR SENSORLESS BRUSHLESS DC MOTOR

DRIVES USING MATLAB/SIMULINK

SHITAL M.WASU, PROF. UDAY B. SARODE

1.

Studet M.E. !P"#e$ S%&te'(, E)e*t$+*) E--. Det., PVG& COET, Pue.0. A&&+&tt P$"e&&"$, E)e*t$+*) E--. Det., PVG& COET, Pue.

Accepted Date:

02/30/0314Pu!"#$

Date:

31/35/0314

Ke%&'(d#Bldc Motor;

State Space Model;

Sensor less,

Back Emf Zero Crossing

Detection

C"$$e&"d+- Aut6"$

M$. Mu)+7 Pte)

A#t(act

Brushless dc (BLDC) motors and their dries are penetrating

the market of home appliances, !"#C industr$, and

automotie applications in recent $ears %ecause of their high

efficienc$, silent operation, compact form, relia%ilit$, and lo&

maintenance' raditionall$, BLDC motors are commutated in

si*step pattern &ith commutation controlled %$ positionsensors' o reduce cost and compleit$ of the drie s$stem,

sensor less drie is preferred' he eisting sensor less control

scheme &ith the conentional %ack EM+ sensing %ased on

motor neutral oltage for BLDC has certain dra&%acks, &hich

limit its applications' o oercome these dra&%acks this paper

presents a state space modelling, simulation and control of

permanent magnet %rushless DC motor' B$ reading the

instantaneous position of the rotor as an output, different

aria%les of the motor can %e controlled &ithout the need ofan$ eternal sensors or position detection techniues' -n this

paper BLDC motor &ith ideal %ack*EM+ is modelled and

simulated in M#L#B . S-M/L-01' Simulation model of the

controller and BLDC drie are also presented' -n order to

alidate the model arious simulation models are studied'

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1. INTRODUCTIONBrushless dc (BLDC) motors hae %een

desired for small horsepo&er control

motors due to their high efficienc$, silent

operation, compact form, relia%ilit$, and

lo& maintenance' !o&eer, the control

compleit$ for aria%le speed control and

the high cost of the electric drie hold %ack

the &idespread use of %rushless dc motor'

2er the last decade, continuing technolog$

deelopment in po&er semiconductors,

microprocessors.logic -Cs, ad3usta%le speed

driers (#SDs) control schemes and

permanent*magnet %rushless electric motor

production hae com%ined to ena%le

relia%le, cost*effectie solution for a %road

range of ad3usta%le speed applications'

!ousehold appliances include clothes

&ashers, room air conditioners,

refrigerators, acuum cleaners, free4ers,

etc' 5ater heaters, hot*&ater radiator

pumps, po&er tools, garage door openers

etc'Brushless DC (BLDC) motor simulation

can %e simpl$ implemented &ith the

reuired control scheme using speciali4ed

simulink %uilt*in tools and %lock sets such as

simpo&er s$stems tool%o' But it reuires

po&erful processor reuirements, large

random access memor$ and long simulation

time' o oercome these dra&%acks this

paper presents a state space modelling,

simulation and control of permanent

magnet %rushless DC motor' B$ reading the

instantaneous position of the rotor as an

output, different aria%les of the motor can

%e controlled &ithout the need of an$

eternal sensors or position detection

techniues'

-n this paper, the motor is designed %ased

on state space model to get information

a%out the state of the s$stem aria%les at

some predetermined points along the flo&

of signals' B$ adopting this model, po&erful

processor reuirement, large random

access memor$ can %e aoided &ith more

design flei%ilit$ and faster results can %e

o%tained'

0. MODELING THE BRUSHLESS DC MOTOR

he modeling of %rushless dc motor

inoles soling man$ simultaneous

differential euations, each depending

upon the inputs to the motor and the

simulation constants' Simulation constants

are alues like the phase inductance that do

not change during simulation' herefore

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these parameters can %e treated as

constants during a simulation' !o&eer, the

model proides for dialogue %oes that can

%e used to ar$ the alues of these

constants' he euations for the %rushless

dc motor are listed as under' Star &ound

rotor is assumed' he core %lock for the

%rushless dc motor has %een &ritten as a

state space model' During the course of the

pro3ect, man$ approaches &ere tried and it

&as reali4ed that state space modelling

ena%led accurate and eas$ description of

the %rushless dc motor'

0.1 STATE SPACE MODELING

he coupled circuit euations of the stator

&indings in terms of motor electrical

constants are

5here6

7s6 Stator resistance per phase

-a,-%, -c6 Stator phase currents

p =is the time deriatie operator

Ea, E%, Ec represent the %ack emfs in the

respectie phases in (8)

"n6 is the neutral point node oltage gien

%$

Vn=13 Vas+ Vbs+ Vcs BEMFs

Based on euation (8), the euialent

circuit of motors can %e o%tained as sho&n

in +ig' 8'

+ig' 8' Euialent circuit for stator &indings

he induced emfs are all assumed to %e

trape4oidal, &hose peak alue is gien %$

Ep 9 (BL)0 9 0(Blr:) 9 0: 9

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represents flu linkage 9 BLr, < represents

the total flu linkage gien as the product

num%er of conductors and flu

linkage.conductor' -f there is no change in

rotor reluctance &ith angle %ecause of non*

salient rotor and assuming three s$mmetric

phases, inductances and mutual

inductances are assumed to %e s$mmetric

for all phases as in =>?' !ence (8) %ecomes

(8)

Simplif$ing (@) further &e get the follo&ing

(A)

#nd torue generated is gien %$6

()

he induced emfs can %e &ritten as

'''''''''''''''''''''''(@)

&herefa(), f%(), fc() are functions haing

same shapes as %ack emfs' he alues from

() can %e su%stituted in (>)

to o%tain the alue of torue' #lso,

'''''''''''''''''''''''(>)

&herel is the load torue, is the moment

of inertia, B is the friction coefficient'

Electrical rotor speed and position are

related %$

'''''''''''''''''''''''''''''''''''''''''''''''()

&here F is the num%er of poles in the

motor' +rom the a%oe euations, the

s$stem state euations are &ritten in the

follo&ing

&here the states are chosen as (t) 9 = -a-%-c

: ?

hus the s$stem matrices as gien %elo&,

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'''''''''''''''''''''''''''''(G)

he input ector is defined as u(t) 9 =

"a"%"cl?

&hereLl 9 L H M, L is the self inductance of

the &inding per phase, M is the mutual

inductance per phase and "a,"%, "c are the

per phase impressed oltage on the motor

&indings'

4. IDEAL BACK EMF MODEL O+ BLDC

MOTOR8

here are t&o t$pes of BLDC &ith respect to

%ack*EM+ signal of motor; sinusoidal and

trape4oidal' here are also t&o t$pes of

BLDC according to hae sensors for

detecting rotor position or not' 0ormall$

!all Effect sensors &ere %eing used for lo&

cost, lo& resolution reuirements and

optical encoder for high resolution

reuirements' Sensor signals are using to

ad3ust F5M seuence of *phase %ridge

inerter' -n sensorless control %ack*EM+

sensing, %ack* EM+ integration, flu linkage*

%ased, free&heeling diode conduction and

speed independent position function

techniues are using for electronic

commutation' -n this model, !all Effect

signals are produced according to rotor

position for commutation' #lso a *phase

inerter using M2S+Es is used as oltage

source' Different control techniues can %e

applied to the model' !ence control

techniues of BLDC are not o%3ectie of

paper; therefore proportional plus integral

(F-) controller is

used in loop control algorithm to control

speed' Schematic s$stem of BLDC motor

drie is sho&n in +ig' A'

+ig' A Schematic s$stem of BLDC motor

drie

#s sho&n in +ig' A simulation model is

consisting of three parts' Each part is

simulated separatel$ and integrated in

oerall simulation model' +or decoding !all

Effect signals in F5M generator, M#L#B

code is &ritten' M#L#B code is &ritten to

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produce -deal Back*EM+ of BLDC as function

of rotor position' Simulation result of -deal

%ack*EM+ reference &aeforms of all

phases ersus electrical angle are sho&n in

+ig' '

+ig' ' -deal Back*EM+ &aeforms

!ence it is assumed that phase 4ones are

distri%uted s$mmetricall$ to different phase

&indings; %ack*EM+ signals hae 8AI

degree phase shift &ith respect to each

other' +or conenient implementation of

euation in M#L#B . S-M/L-01, most of

references are used state space euations'

-t makes the BLDC model more simple and

conenient for arious control techniues

implementation' -deal reference %ack*EM+

signal of motor also is produced

#ccording electrical rotation of rotor in

each phase separatel$ and applied as

negatie feed%ack to phase oltage' BLDC

motor model is sho&n in +ig' @'

+ig' @ BLDC motor model

!all Effect signals of motor are produced

according to electrical degree' a%le - sho&s

!all Effect signal alues

according to electrical degree of rotor'

TABLE I8!#LL E++EC S-J0#LS

ELECTRICAL

DEGREE

HALL 1 HALL 0 HALL 4

39:3 8 I 8

:39103 I I 8

10391;3 I 8 8

1;39053 I 8 I

0539433 8 8 I

43394:3 8 I I

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5ith implementing of a *phase full %ridge

inerter and a

F- speed regulator oerall model of motor is

modelled'

2erall model of BLDC motor drie is sho&n

in +ig' >'

+ig' > 2erall model of BLDC motor drie

5. SENSORLESS CONTROL OF BLDC MOTOR

USING BACK EMF TECHNI

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chosen' #n S*+unction %lock is connected to

the state space %lock to choose the motor

specifications such as, the num%er of

conductor turns per phase, resistance per

phase, rotor dimensions etc as defined %$

the user' he S*+unction &ill read the

instantaneous position among t&ele

positions &hich are separated %$ I'

Depending on the position, the %ack e'm'f

and torue in each phase &ill %e defined'

he estimate %lock contains the F-D

controller' he %lock again is an M*file S*

+unction' his %lock calculates the

reference phase current from the speed

and reuired torue' 7euired torue is

calculated %$ actual speed and the speed

error alue' he a%oe alue &ill %e read

and used in a F-D controller' he reuired

torue is calculated as follo&s,

&here E is the angular speed error, E*8 is

the preious time step error in angular

speed, ts is the sampling time, 1p, 1i, 1d are

proportional, integral and deriatie

constants'

he reuired current is calculated from the

instantaneous reuired torue' hen it is

conerted %$ means of an approimated

Farks ransformation to three phase

currents' he approimated parks

transformation gies thecorresponding

phase current to eer$ stator phase

according to the rotors position' # hold

%lock is used to hold on %oth the reuired

and instantaneous current alues in the

open loop' 2nce the changer %lock closes

the control loop, the hold %lock &ill gie an

access to the current alues to pass to the

present controller scheme' -n this

simulation, h$steresis controller function is

chosen' /suall$, the controller is used to

fire the gates of si step inerter s&itches,

as in'

=. S+'u)t+" Re&u)t& Ad D+&*u&&+"

=.1 IDEAL BACK EMF METHOD8

Simulation results of BLDC motor under no

load and load conditions are sho&n' #s it

can %e seen in +ig' , d$namic response of

BLDC due to its permanent magnet rotor is

high' Fulsating torue of BLDC is sho&n in

+ig' G' +igure N sho&s %ack*EM+ produced in

phase # of motor' a%le -- sho&s BLDC

motor specification to inestigate

performance of adanced model' 2utput

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and -nput po&er characteristics of motor

under no load condition is sho&n in +ig' 8I

and +ig' 88' 5ith respect to stead$ state

alues of po&er, efficienc$ of s$stem is

O@'P' S$stem sho&s high efficienc$

operation of BLDC'

TABLE II8BLDC M227 SFEC-+-C#-20

DESCRIPTION VALUE UNIT

POWER 8I 15

DC VOLTAGE A@I "

PHASE RESISTANCE !R( 8 Q

PHASE INDUCTANCE !L( I'A> m*!

INERTIA !>( 8>'8Ge*

1g*mA

DAMPING RATIO !?( I'II8 0*s.m

POLES @ **

+ig' N Speed characteristics under no load

condition

+ig' O orue characteristics under no load

condition

+ig'8I Back*EM+ of phase #

+ig88 2utput po&er characteristics under

no load condition

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+ig'8A input po&er characteristics under

no load condition

+ig' 8 Speed characteristics under load

condition

+ig' 8@ Current characteristics under load

condition

Simulation also has %een done under 8I

0'm load torue' BLDC speed characteristic

is sho&n in +ig' 8A under load condition' -t

can %e seen that under load condition time

for speed to reach its final alue is

increased' Current characteristics of phase

# of motor under load condition is sho&n in

+ig' 8' Maimum alue of current is @I

amps'

=.0 SIMULATION RESULTS OF SENSORLESS

CONTROL OF BLDC MOTOR USING BACK

EMF TECHNIN seconds &ith IP oershoot' +rom

+ig' > and +ig' , the %ack emf is almost

trape4oidal &ith 8AI phase difference'

Since the three phase torues are

calculated from K currents, it gies

8AIphase difference %et&een each phases

as sho&n in +ig' G' +rom +ig' N, the rotor

position can %e anal$4ed under arious

aligned and unaligned conditions'

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#BLE ---6 Specifications of BLDC Motor

Drie6

Cu$$et 45A R"t"$ )e-t6 43*'

T"$@ue I'O 0*m 7otor radius AIcm

Se) +du*t*e

e$ #+d+-

A'GAm! 0o of turns

per phase

8II

Mutu)

+du*t*e

et#ee

#+d+-&

*8'>m! +lu densit$ I'N8G&%

M"t"$ +e$t+ I'IIIA Coulom%

friction

I'I8GN0

Rted &eed @>II 7FM Static friction I'INO0

Nu'e$ "

")e&

@ "iscous

friction

I'IIA0

Nu'e$ "

6&e&

-nput dc

oltage

8I"

W+d+-

$e&+&t*e e$

6&e

I'GQ 0o' of slots

per pole per

phase

8II

7ES/LS6

+ig8>'6 hree Fhase Back EM+

+ig8' hree Fhase Currents

+ig8G'three phase torue

+ig8N'7otor Fosition

+ig8O'speed

:. C"*)u&+"&8

-n this paper it is sho&n that BLDC motor is

a good choice in automotie industr$ due to

higher efficienc$, higher po&er densit$ and

higher speed ranges compare to other

motor t$pes' BLDC motor model &ith ideal

%ack*EM+ method and sensorless control of

BLDC motor using Back EMf echniue is

presented in this paper' he proposed

model is simulated in M#L#B . S-M/L-01'

Simulation results in first case under no

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load and load conditions are sho&ing

proper performance of model' 2utput

characteristics and simplicit$ of model

make it effectiel$ useful in design of BLDC

motor dries &ith different control

algorithms in different applications' Second

Method is implemented using State space

echniue' BLDC motor anal$sis %ased on

state space model can %e easil$ carried out

using M#L#B G' ersion' his model has

man$ adantages oer transfer function

model' he simulation stud$ using state

space model has %een alidated &ith the

results o%tained using transfer function

model' +urther using state space model, the

performance characteristics of the BLDC

motor can %e ealuated for different

machine parameters, &hich can %e easil$

aried in the simulation stud$ and useful

information can %e o%tained'

he simulation results demonstrate that the

simulated

5aeforms fit theoretical anal$sis &ell'

!o&eer, the simulation inoles soling

man$ simultaneous differential

euations and the results o%tained are

highl$ dependent upon the choice of the

s$stem soler, &here some soler gies

highl$ accurate results, %ut need longer

time to terminate' hrough the

modulari4ation design, a lot of time spent

on design can %e saed and the design

efficienc$ can %e promoted rapidl$' he

second method proposed in this paper

proides a noel and effectie tool for

anal$4ing and designing the control s$stem

of %rushless DC motor'

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