13311911 electrical drives lectures

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Electrical Drives

MEP 1422

2004/2005-02

Module 1. Introduction to drives:

Elements in electrical drives, overview of DC and AC drives.Torque equations,

Components of load torque, torque characteristics. Four-quadran

operation

Notes on Introduction to Electromechanical Energy Conversion

Module 2 Converters in electric drive systems:

Controlled rectifier, Linear scheme, Non-linear scheme,

Switched-mode converters - average model and transfer functio

Two-quadrant converters, Four-quadrant converters, Bipolar

switching, Unipolar switching,

Current-controlled converters, Fixed switching frequency contro

Hysteresis control

Example of Simulink file for 2-Q converter (switching and aver

model)

Current ripple in 4 Q converter Space Vector Modulation (SVM)

Module 3 DC motor drives

DC drives in power point format, in .pdf

Construction, modeling and transfer function, Converters for DC

drives – quadrant of operations.

MATLAB – based controller design method

– here

Linear analysis in Simulink

Large signal simulation using SIMULINK – here



Module 4. Induction motor drives

Dynamic model of induction machine

Construction and principle of operations,

Speed Control-

constant V/f, Scalar control – problems at low speed

current

Simulink example on open-loop constant V/Hz using SIMULIN

s-function for IM simulationCompiled with Borland C - here

Current controlled and voltage boost, open-loop and closed-loop

control.

Field-oriented control of IM:

Rotor flux orientation

Stator flux orientation

Simulink example on indirect FOC IM–

requires imch.dllPPoint for principles of direct torque control and in pdf

Direct Torque Control using SIMULINK and the required *.dll

for the S-function



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G.K. Dubey, “Fundamental of Electrical Drives”, Narosa, 1994.

N. Mohan, “Power Electronics: Converters, applications and design” John Wiley and Sons, 1995.



ELE CTR OME

CHANI CAL

ENER GY

C ONVER SI ON

El e c tr om e ch ani c al

en er g y

c onv e

r si on

pr o c e s s

i nv ol v e s

th r e e

f orm s

of

en er g y :

el e c tri c al ,

m a gn e ti c

f i el d

an d

m e ch ani c al .

In

r o t a ti n g

el e c tri c al

m a ch i n e s ,

en er g y i s c on ti n u o u sl y c onv er t e d f r om el e c tri c al t o m e ch ani c al , or v

i c e v er s a .

El e c tri c al

m o t or s

c onv er t s

el e

c tri c al

en er g y

t o

m e ch ani c al

en er g y

an d

i t

i s

r ev er s e d

i n

th e

c a s e

of

g en er a t or s .

In

b o th

c a s e s ,

m a gn e ti c

f i el d

a c t s

a s

a

m e d i um i n th e pr o c e s s of el e c tr om e ch ani c al en er g y c onv er si on . W e wi l

l l o ok ( or

r evi ew )

th e

pr o c e s s

of

el e c

tr om e ch ani c al

en er g y

c onv er si on

of

a

si m pl e

tr an sl a ti on al s y s t em f or a n on-l i n e ar an d l i n e ar m a gn e ti c s y s t em . W e

wi l l th en

a p pl y th i s b a si c pri n ci pl e t o a

r o t a ti n g m a ch i n e .

Ex am pl e

of

el e c tr om e ch ani c al

s y

s t em

Th e ch ar a c t eri s ti c of th e f l ux

l i nk a g e an d c urr en t ( λ -i ) of a s y s t e

m sh own i n

Fi g

1

i s

d e t ermi n e d

b y

th e

B-

H

ch ar a c t eri s ti c

of

th e

c or e

an d

th e

l en g th

of

th e ai r- g a p . Wi th sm al l ai r- g a p l en g th , g , th e λ -i ch ar a c t eri s ti c i s

d omi n a t e d

b y

th e

B-H


of

th e

c or e

wh i ch

h a s

a

n on-l i n e ar

ch ar

a c t eri s ti c

d u e

t o

th e

c or e

m a gn e ti c

s a

t ur a ti on .

Wi th

l ar g e

g ,

h ow ev er ,

t

h e

l i n e ar

m a gn e ti c


of

th e

ai r- g a p

wi l l

d omi n a t e .

Th u s

f or

l ar

g e

ai r- g a p

s y s t em

th e

λ -i

c urv e

of

th e

s y s t em

d i s pl a y s

a

l i n e ar

ch ar a c t eri s

ti c .

If

a

l i n e ar s y s t em

i s a s s um e d , al l

of th e

mmf d r o p s a p p e ar a cr o s s

th e a

i r- g a p .

In

o th er w or d s , i t i s a s s um e d th a t th e r el u c t an c e of th e c or e i s n e gl i g

i b l y sm al l

c om p ar e d t o th a t of th e ai r- g a

p’ s r el u c t an c e . Th i s a s s um p ti on i s b a

s e d on th e

f a c t th a t th e m a gn e ti c p erm e a b

i l i t y

of th e c or e i s m u ch l ar g er th a

n th e ai r-

g a p

p erm e a b i l i t y .

Th e

λ -i

c urv e s

f or

d i f f er en t

ai r- g a p

v al u e s

ar e

th er ef or e

l i n e ar .

Fi g . 1

−

−

n on-l i n e ar s y s t em

l i n e ar s y s t em

Fi g . 2

Th

e d i f f er en ti al r el a ti on

b e tw e en

th e 3

f orm s of en er g y

exi s t s i n

th e s y s t e

m

c a

n b e wri t t en a s :

d W

e = d Wf + d

Wm

( 1

)

Wh

er e d W

e – d i f f er en ti al ch an g e i n el e c t

ri c al en er g y

d Wf - d i f f er en ti al ch an g e i n f i el d

en er g y

d Wm - d i f f er en ti al ch an g e i n m e ch a

ni c al en er g y

If

th e p o si ti on of th e m ovi n g p ar t i s f

i x e d ( ai r- g a p l en g th i s f i x e d , th u s d Wm

=

0 ) an d th e c urr en t i n th e c oi l i s i n

cr e a s e d f r om 0 t o i x , th e f i el d en er g

y

wi

l l i n cr e a s e an d i s gi v en b y :

d W

e = e .i d t = d Wf

( 2

)

S u

b s ti t u ti n g e = d λ / d t ,

d Wf = i d λ

( 3

)

If

th e f l ux l i nk a g e i n cr e a s e d f r om 0 t o

λ x , th e s t or e d en er g y c an b e wri t t en a

s :

λ

λ

=

x

0

f

i d

W

( 4

)

λ x

i x

λ

c o- en er g y

en er g y

λ

λ

Fi g . 3



Th e c o- en er g y , wh i ch i s u s e d l a

t er t o c al c ul a t e th e f or c e , i n th i s p a

r ti c ul ar

ex am pl e i s d ef i n e d a s :

λ

=

i x

0

f

d i

' W

( 5 )

I t sh o ul d b e n o t e d th a t f or a l

i n e ar s y s t em , Wf = Wf ’

If th e m ovi n g p ar t i s al l ow t o

m ov e sl owl y , f r om x = x1 t o x = x2 , s u

ch th a t

th e ai r- g a p i s r e d u c e d , th e r a t

e of ch an g e of f l ux l i nk a g e wi l l b e v e

r y sm al l

d uri n g th i s m ov em en t an d h en c e

th e c urr en t c an b e a s s um e d t o b e c on s t

an t .

Fi g . 4

Th e m e ch ani c al f or c e a s s o ci a t e d

wi th th i s m ov em en t c an b e o b t ai n e d i f

th e

ch an g e i n m e ch ani c al en er g y i s

k n own . Th u s ,

d Wm = d W

e

- d Wf

( 6 )

D uri n g th e m o ti on , d W

e = e .i d t

= i d λ . H en c e

λ

λ

λ

=

2 x1

x

e

i d

W

Th e ch an g e i n th e s t or e d f i el d

en er g y c an b e o b t ai n e d b y c al c ul a ti n g

th e

d i f f er en c e i n s t or e d en er g y b e t

w e en th e tw o p o si ti on s .

I t c an b e sh own gr a ph i c al l y th a

t Wm i s gi v en b y th e sh a d e d ar e a of Fi

g .4 wh i ch

e s s en ti al l y i s th e i n cr e a s e i n

c o- en er g y . Th u s :

d Wm = d Wf ’

Si n c e d Wm = f d x , th e m e ch ani c a

l f or c e c an b e c al c ul a t e d a s :

t

t an

c on

s

i

f

m

x

) x ,i ( '

W

f

=

∂

∂

=

( 7 )

If

th e

m ov em en t

of

th e

m ov

i n g

p ar t

i s

v er y

f a s t

( i . e .

f or

th e

s am e

d i s pl a c em en t

b u t

f or

a

v er y

s

h or t

ti m e ) ,

th e

ch an g e

i n

f l ux

l i nk a g e

c an

b e

a s s um e d n e gl i gi b l e . H ow ev er , t

h e r a t e of ch an g e of th e f l ux l i nk a g e

wi th ti m e

i s

f i ni t e

an d

h en c e

c a u s e s

th

e

c urr en t

t o

d e cr e a s e

d uri n g

th i s

m o

v em en t .

I t

c an

b e

gr a ph i c al l y

sh own

th a t

th e

m e ch ani c al

en er g y

i s

gi v en

b y

th e

sh a d e d

λ

λ

ar

e a of Fi g 5 , wh i ch i s a r e d u c ti on i n f i el d en er g y . Th u s th e m e ch ani c al f or c

e

i s

gi v en b y :

t

t an

c on

s

f

m

x

) x ,i ( W

f

= λ

∂

∂ −

=

( 8

)

If

th e d i f f er en ti al m ov em en t i s sm al l , t

h e sh a d e d ar e a of Fi g 4 an d Fi g 5 i s

th

e s am e . H en c e th e f or c e c al c ul a t e d u si

n g e q u a ti on ( 7 ) an d ( 8 ) wi l l b e th e

s a

m e .

Fi g . 5

Li

n e ar

s y s t em

F o

r l i n e ar s y s t em , th e f l ux l i nk a g e i s p

r o p or ti on al t o th e c urr en t , wh er e th e

c o

n s t an t of pr o p or ti on al i t y i s th e i n d u c

t an c e of th e c oi l . Th e i n d u c t an c e

h o

w ev er d e p en d s on th e p o si ti on , x . Th u s

,

λ = L ( x ) i

( 9

)

Th

e c o- en er g y i s gi v en b y :

) x ( L

i 2 1

d i

'

W

2

i 0

f

=

λ

=

( 1 0

)

U s

i n g e q u a ti on ( 7 ) ,

d x

) x (

d L

i

2 1

x

) x ,i ( '

W

f

2

t

t an

c on

s

i

f

m

=

∂

∂

=

=

( 1 1

)

R o

t a ti n g

m a ch i n e s

Fi

g 6 sh ow s a g en er al r o t a ti n g m a ch i n e

wi th s al i en t s t a t or an d s al i en t r o t or

.

B o

th s t a t or an d r o t or ar e exi t e d ( d o u b l

y–f e d ) . W e ar e i n t er e s t e d i n o b t ai ni n

g

th

e

el e c tr om a gn e ti c

t or q u e

ex pr e s si on

of

th e

s y s t em .

W e

c an

d o

th i s

b

y

o b

t ai ni n g

th e

ex pr e s si on

f or

th e

c o– en

er g y

( or

en er g y )

an d

d i f f er en ti a t e

i

t

wi

th r e s p e c t t o x f or c on s t an t c urr en t (

or c on s t an t f l ux ) .

λ

λ



W e wi l l a s s um e th e c on tr ol si gn al

s f or th e swi t ch e s ar e o b t ai n e d a s a r

e s ul t of

c om p ari s on b e tw e en th e c on tr ol si

gn al an d a tri an g ul ar

Th e o u t p u t of th e c om p ar a t or i s o

b t ai n e d a s f ol l ow s :

wh en v

c > v

tri , u p p er swi t ch ON

( 1 )

wh en v

c < v

tri , l ow er swi t ch ON

O b vi o u sl y , th e w av ef orm of v

a wi l

l f ol l ow th a t of q . Th e i n s t an t an e o u s

v al u e of v

a i s

gi v en b y : v

a = q ( V

d c ) Th e av er a g e

v al u e of v

a wi l l d e p en d on th e d u t y r a

ti o of q an d

th e d u t y r a ti o of q i n t urn d e p en

d s on th e c on tr ol si gn al v

c . W e c an o b

t ai n th e

r el a ti on b e tw e en th e av er a g e v ol t

a g e V

a an d th e d u t y r a ti o d b y c al c ul a

ti n g th e

av er a g e v al u e of v

a i n t erm s of d

.

Wh er e d = t on / T

( 2 )

d i s i n f a c t an av er a g e v al u e of

q ov er a c y cl e an d th er ef or e h av e a r a

n g e of b e tw e en

0 an d 1 , th u s ,

( 3 )

=

0 1

q

d c

d T

0

d c

a

d V

d t

V

T 1

V

s

=

=

d t

q

T 1

d

t r i

T

t t

t r i +

=

!

If t

h e tri an g ul ar f r e q u en c y i s h i gh an d th

er ef or e i s m u ch l ar g er th an th e c on tr o

l

si gn

al , d c an b e a s s um e d c on ti n u o u s . H ow ev

er wh en s el e c ti n g th e b an d wi d th of th e

cl o s

e d -l o o p s y s t em , th e d i s cr e t e v al u e s of

d m u s t b e t ak en i n t o a c c o un t , i . e . th

e

b an d

wi d th m u s t b e l i mi t e d t o on e or tw o or

d er l ow er th an th e tri an g ul ar f r e q u en c

y .

Th e

r el a ti on b e tw e en d an d v

c i s o b t ai n e d a s f ol l ow s :

Wh en

v c = V

tri

, p , d = 1 , wh en v

c = -V

tri

, p , d

= 0 .

A s s u

mi n g d i s c on ti n u o u s , th e r el a ti on b e t

w e en d an d v

c i s o b t ai n e d a s :

( 4 )

Th e

r el a ti on b e tw e en v

c an d V

a c an b e o b t ai

n e d b y s u b s ti t u ti n g ( 4 ) i n t o ( 2 ) ,

( 5 )

If w

e w an t t o i n cl u d e th e c onv er t er i n t o o

ur cl o s e d -l o o p m o d el of a D C d ri v e s y s

t em ,

w e n

e e d t o o b t ai n th e sm al l si gn al tr an sf e

r f un c ti on b e tw e en v

c an d V

a . Th i s i s d on e

b y i

n tr o d u ci n g sm al l si gn al p er t ur b a ti on i

n V

a an d v

c .

( 6 )

S e p a

r a ti n g th e d c an d a c c om p on en t s ,

!

p ,

t r i c

V2

v

5 . 0

d

+

=

c

p ,

t r i d c

d c

a

v

V2

V

V 5 . 0

V

+

=

(

)

(

)

c

c

p ,

t r i d c

d c

a

a

v~

v

V2 V

V 5 . 0

v~

V

+

+

=

+



"

D C

:

( 7 )

A C

:

( 8 )

B y t ak i n g L a pl a c e tr an sf orm of e q

u a ti on ( 8 ) , th e sm al l si gn al tr an sf er

f un c ti on

b e tw e en v

c an d VA c an b e o b t ai n e d .

F o ur- q u a d r an t

c onv er t er

Th e m o d el d ev el o p e d f or th e tw o- q

u a d r an t c onv er t er c an b e u s e d a s a b ui

l d i n g b l o ck i n

d ev el o pi n g th e m o d el f or th e f o ur

- q u a d r an t c onv er t er . A s i l l u s tr a t e d i n

th e f i g ur e

b el ow , th e 4 - q u a d r an t c onv er t er i

s c om p o s e d of tw o l e g s , wi th e a ch l e g

si mi l ar t o

th a t of th e 2 - q u a d r an t c onv er t er .

W e wi l l c on si d er tw o swi t ch i n g s ch em e

s n orm al l y

em pl o y e d : ( 1 ) Bi p ol ar swi t ch i n g s

ch em e ( 2 ) uni p ol ar swi t ch i n g s ch em e .

Th e i n s t an t an e o u s v ol t a g e v

a c an

b e m a d e ei th er e q u al s V

d c , -V

d c or 0 .

V a = V

d c

wh e

n Q1 an d Q2 ar e ON

v a = -V

d c

wh e

n Q 3 an d Q4 ar e ON

v a = 0

wh e

n c urr en t f r e ewh e el s th r o u gh Q an d D

Th er ef or e th e o u t p u t v ol t a g e v

a c

an swi n g b e tw e en V

d c an d –V

d c , V

d c an d 0

or 0 an d V

d c ,

wh i ch i s d e t ermi n e d b y th e swi t ch

i n g s ch em e ch o s en :

c

p ,

t r i d c

d c

a

v

V2

V

V 5 . 0

V

+

=

c

p ,

t r i d c

a

v~

V2

V

v~

= p , t r i d c

V2

V

# $

# $

%

&

+

v a

–

'

'

'

'

"

(

(

Bi p o

l ar swi t ch i n g

L e g

A an d L e g B o b t ai n e d th e swi t ch i n g si g

n al s f r om th e s am e c on tr ol si gn al . Th i

s

i m pl

i e s th a t swi t ch i n g of L e g A an d L e g B

ar e al w a y s c om pl em en t s .

In a

f orw ar d b r e ak i n g m o d e wh er e th e av er a

g e v ol t a g e V

a i s p o si ti v e an d sm al l er

th an

th e

b a ck emf of th e arm a t ur e , c urr en t wi l l

f l ow th r o u gh D1 an d D2 wh en v

a = V

d c a

n d

wi l l

f l ow th r o u gh Q 3 an d Q4 wh en v

a = -V

d c

U si n

g th e c om p ari s on b e tw e en th e c on tr ol s

i gn al an d tri an g ul ar w av ef orm a s sh own

i n

Fi g u

r e 7 , th e r e s ul t an t q an d q i s a s b el o

w :

)

%

&

*

!

!



*

Fr om pr evi o u s an al y si s , th e av er a

g e v ol t a g e f or L e g A an d L e g B i s gi v e

n b y :

VA

O =

d A ( V

d c )

an d VB

O = d B ( V

d c ) = ( 1 - d A ) ( V

d c )

( 9 )

Si mi l arl y r el a ti on b e tw e en v

c an d

d A an d d B c an b e wri t t en a s :

F or L e g A

( 1 0 )

F or L e g B

( 1 1 )

W e ar e i n t er e s t e d i n th e v ol t a g e

a cr o s s th e arm a t ur e ci r c ui t , VAB

VAB = VA

O – V

B O = ( d A – ( 1 - d A ) ) V

d c = ( 2 d A -1 ) V

d c

( 1 2 )

S u b s ti t u ti n g d A f r om ( 1 0 ) i n t o ( 1

2 ) gi v e s ,

( 1 4 )

B y t ak i n g th e L a pl a c e tr an sf orm o

f th e a c c om p on en t s i n ( 1 4 ) , th e tr an s

f er f un c ti on

b e tw e en th e vAB ( s ) an d v

c ( s ) i s o b

t ai n e d :

( 1 5 )

!

+

! + ,

p ,

t r i c

A

V2

v

5 . 0

d

+

=

p ,

t r i c

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c

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t

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Th e

swi t ch i n g si gn al s f or L e g B i s o b t ai n e

d f r om th e i nv er s e of c on tr ol si gn al f

or

L e g

A . Th i s i s i l l u s tr a t e d i n Fi g ur e 1 0 . A

c c or d i n g t o o ur pr evi o u s an al y si s , th e

c on t

i n u o u s d u t y r a ti o f or L e g A , d A , i s gi v en b y :

( 1 6 )

Si n c

e L e g B u s e s th e i nv er s e c on tr ol si gn a

l , a c c or d i n gl y th e c on ti n u o u s d u t y r a

ti o

f or

L e g B i s gi v en b y :

( 1 7 )

Th i s

gi v e s an d av er a g e arm a t ur e v ol t a g e a s

,

VAB = ( d A – d B

) V d c =

( 1 8 )

Th e

tr an sf er f un c ti on o b t ai n e d f or uni p ol a

r swi t ch i n g s ch em e i s th er ef or e si mi l a

r t o

th e

b i p ol ar swi t ch i n g s ch em e .

p ,

t r i d c

V V

# $

# $

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R ef er en c e s :

N . M oh an , “ P ow er El e c tr oni c s :

C onv er t er s , a p pl i c a ti on s an d d e si gn” J

oh n Wi l e y an d

S on s , 1 9 9 5 .

N . M oh an , “ El e c tri c Dri v e s – a

n i n t e gr a ti v e a p pr o a ch ” MNPERE , 2 0 0 0 .

W . L e onh ar d , “ C on tr ol of el e c t

ri c al d ri v e s” ,

S pri n g er-V erl a g , 1 9 8 4 .

J . M . D . M ur ph y an d

F . G . T urn

b ul l , “ P ow er el e c tr oni c c on tr ol of A C

m o t or” ,

P er g am on pr e s s , 1 9 8 8 .

%

& :

2

∆

(

: 0 < 0

=

*

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=

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SPACE VECTOR MODULATION

In contrast to Sinusoidal Pulse Width Modulation (SPWM), which treats the 3-phase quantitiesseparately, in SVM, the 3-phase quantities are treated using single equation known as space vector.

Therefore in terms of microprocessor or digital implementation, SVM gives less computational

burden. The space vector of a 3-phase voltage is defined as:2 4

j j3 3

s a b c

2v v (t) v (t)e v (t)e

3

π π = + +

,

where va, vb and vc are the phase voltages.

In 3-phase VSI, there are 8 possible switch configurations, hence there are eight possible voltage

vectors that can be generated or obtained from the VSI. SVM utilized these 8 voltage vectors to

synthesize the reference voltage.

Given a location of the reference voltage in any of the sectors, the actual voltage can be synthesized,

within a sampling period, by selecting the two adjacent voltage vectors and zero voltage vectors. Forexample, if the reference voltage is located in sector 1, voltage vectors v1, v2, v0 and v7 should beselected. This is illustrated in Figure 2

vd*

vq*

Space vector

modulator

AC

Motor

+

Vd

−

Figure 1 Space vector

modulator applied to ACmotor drive



(2/3)Vd

Sector 1Sector 3

Sector 4

Sector 5

Sector 2

Sector 6

(1/ √3)Vd

[100]

[110][010]

[011]

[001] [101]

*

sv

0 0.005 0.01 0.015 0.02 0.025 0.03

-100

-50

0

50

100 a b c

sector 6 sector 1 sector 2 sector 3 sector 4 sector 5

Figure 3 Sinusoidal

reference voltage

Figure 4 Example of

modulated waveform in

sector 2

000 010 110 111 110 010 000

Phase a

Phase b

Phase c

T T

d

q

Figure 2 Voltage

vectors of a 3-phase

VSI

T0 T1 T2 T7



The interval for each voltage vector, as shown in Figure 4, is determined by equating volt-secondintegral of vs with the sum of all voltage vectors within a cycle. Thus, for example in sector 1,

772211oos TvTvTvTvTv ⋅+⋅+⋅+⋅=⋅

Note that v1 and v2 equal dV3

2. Thus in terms of d-q components this can be written as:

0T)60sin j60(cosTV3

2TV

3

20TTv

7

oo

2d1dos

⋅++⋅+⋅+⋅=⋅

Also, we need to satisfy the time constraint: T= T0 + T1 + T2 + T7

If we let T0 = T7, we can calculate all the required time intervals. If the angle between the reference

voltage and the adjacent vector (to the right of the reference voltage) equals α, it can be shown that

for any sector, the time intervals T1 and T2 are given by:

1 s

3 1T T v cos sin

2 3

= ⋅ ⋅ α − α

2 sT 3 T v sin= ⋅ ⋅ α

In the above equation, vs is the normalized reference vector. The interval for the zero voltage vector is

given by: T0 + T7 = T – (T1 +T2). The ratio between T0 and T7 essentially control the amount of

triplen harmonic components in the fundamental phase voltage.

Further readings:

PG Handley and JT Boys, “Practical real-time PWM modulators: an assessment” IEE Proceedings-B,Vol 139, No. 2 March 1992

W. Leonhard, “Control of electrical drives”, Springer-Verlag, 1984.



1

DC DRIVES

Principle of operation and con st ruct ion – a review

DC machine consists of

s tator – stationa ry – wher e th e field flux is produ ced

rotor – rotating – where the armature winding is placed.

Field flux is obtained either from permanent magnet or from field winding excitation. Field flux

interacts with current carrying conductors in armature to produce torque. Commutator in

arm atu re circui t will ensu re th at the torqu e product ion is a lways ma ximu m, regardless of rotor

position.

Modeling of DC mot or

Th e torque is produ ced as a resu lt of intera ction of field flux with cu rren t in arm atu recondu ctors an d is given b y

Te = k t Φ ia (1)

where k t is a cons tan t depending on motor wind ings an d geometry

Φ is th e flux per pole due t o th e field wind ing

For the motor with wound field, the flux can be varied to control the speed, but for permanent

ma gnet motor , the flu x is f ixed and thu s can be writ ten a s:

Te = Ktia

where Kt depends on the perman ent magnet mater ia lThe direct ion of the torque pr oduced depend s on th e direct ion of the a rma tu re curren t

When the armature rotates , the f lux l inking the armature winding wil l vary with t ime and

th erefore according to Fara da y’s law, an emf will be indu ced acros s th e win ding. Th is gen erated

emf, known as the back emf, depends on speed of rotat ion as well as on the f lux produced by

th e field an d is given by:

ea = k t Φ ω (2)

Similar ly, for perman ent m agnet , th is can be writ ten a s:



2

ea = Kt ω

Th e polarity of th e back emf depend s on th e direction of th e motor rota tion

For separa tely excited DC motor , the arm atu re circui t is sh own:

Ra – lum ped arm atu re wind ing resis tan ce

La – self ind ucta nce of the arm atu re wind ing

ea – as defin ed before, is th e back emf of th e motor

Us in g KVL,

(3)

In s teady s ta te condi t ion,

(4)

In term s of torque an d speed th e s teady s tate equat ion can b e writ ten a s:

(5)

which gives:

(6)

Thu s three methods can be us ed to control the speed: Vt , Φ a n d Ra

Speed control using armature resis tance by adding external resis tor R ex t i s seldom used,

especially for large motor due to the losses associated with Ia2Rext . Vt is normally control for

speed u p to r ated s peed. Beyond rated speed, for separa tely excited DC motor , the speed control

is achieved by flux control, Φ. When speed control by flu x control is u sed, th e ma ximu m t orque

capabi lity of the motor is redu ced s ince for a given ma ximu m arm atu re cur rent , the flu x is less

than the ra ted va lue and thus the maximum torque produced i s l ess than the maxumum

torque. Also i t should be noted that , wi th permanent magnet exci tat ion, speed control using

flu x weaken ing is not poss ible – thu s m aximu m speed of perma nen t m agnet m otor is l imited.

When designing controllers for DC motor drives used in servo or high performance applications,

a small signal model of the motor is required. A separately excited DC motor with fixed field

excitation, or a permanent magnet DC motor, is described by equations (3), (1) and (2). If a small

per turbat ion around a DC operat ing point is int roduced, these equat ions can be wri t ten as (7)-

(9). Th e ‘~’ indicates a sm all pertu rba tion, which is a dd t o the DC comp onen ts of vt, ia, ea, Te, TL

a n d ω :

+

ea

−

aa

aaat edt

diLRiv ++=

+

vt

−

Ra La

ωΦ+Φ

= tat

t k Rk

TV

aaat ERIV +=

( )a2

tt

t Rk

T

k

V

Φ

−Φ

=ω



3

(7)

(8)

(9)

Equa t ion d escribing the d ynam ic of the mecha nical system is given by:

(10)

where Tl = TL + Bω

Tl is th e load torqu e composed of workin g torque of the load, TL and torque due to friction, Bω.

Th e frictiona l torqu e depend s on t he rota tional speed, while TL depends on the n a ture of the

load being driven. Similarly, if a s ma ll pertu rba tion is intr odu ced in Te a n d TL a n d ω, equa tion

(10) can be written as :

(11)

Separa t ing th e DC and sm all pertu rbat ion or AC compon ents in (7)–(9) an d (11), the st eady st ate

an d sm al l s igna l equa t ions descr ibing the DC motor can be obtained:

The transfer functionof the DC motor is obtained by taking the Laplace transform of the small

s igna l equat ions .

Vt(s) = Ia(s)Ra + LasIa + E a(s) (12)

Te(s) = k EIa(s) (13)

E a(s) = k Eω(s) (14)

Te(s) = TL(s) + Bω(s) + sJ ω(s) (15)

( ))e~E(

dt

i~

IdLR)i

~I(v~V aa

aa

aaaatt +++

++=+

)iI(k T~

T aaEee +=+

)~(k e~E Eee ω+ω=+

dt

dJTT m

le

ω+=

dt

)~(dJ)~(BT

~TT

~T LLee

ω+ω+ω+ω++=+

aa

aaat e~

dt

i~

dLRi

~v~ ++=

)i~

(k T~

aEe =

)~(k e~ Ee ω=

aaatERIV +=

aEe Ik T =

ω= Ee k E

dt

)~(dJ~BT

~T~

Le

ω+ω+= )(BTT Le ω+=

AC components DC components



4

Thu s th e block diagram represent ing the DC motor is sh own:

Power electronic c onve rters in DC drives

The power electronic converters are used to obtain an adjustable DC voltage applied to thearmature of a DC motor. There are basically two types of converter normally employed in DC

dr ives: (i) con tr olled re ctifier (ii) switc h –mode converter.

(i) Con tr olled rect ifier

Controlled rectifier can be operated from a single phase or three phase input

Output voltage contain low frequency ripple which may require a large inductor inserted in

arm atu re circui t , in order to redu ce the arm atu re curren t r ipple. A large arma tu re curren t r ipple

is undesirable since it may be reflected in speed response if the inertia of the motor–load is not

large enough. Controlled rectifier has low bandwidth. The average output voltage response to a

control signal, which is the delay angle, is relatively slow. Therefore controlled rectifier is not

su itable for drives requ irin g fas t resp ons e, e.g. in s ervo applications .

In terms of quadrant of operations, a single phase or a three phase rectifier is only capable of

operating in first and fourth quadrants – which is not suitable for drives requiring forwardbreaking mode. To be able to operate in al l four quadrants , configurat ions using back to back

rectifiers or con tactors sh own below mu st b e employed.

Tk aa s LR

1

+

)s(Tl

)s(Te

s JB

1

+

Ek

)s(Ia )s(ω)s(Va

+-

-

+

3-phase

supply

3-phase

supply

+

Va

-

Converter

A

ω

T

Converter

B

Converter

B

Converter

A

Converter A Converter B



5

(ii) Switch –mode converter

Switch–mode converters normally operate at high frequency. As a result of this, (i) the average

output voltage response is significantly faster than the controlled rectifier, in other words the

bandwidth of a switch–mode rectifier is higher compared to the controlled rectifier, and (ii) the

armature current ripple is relatively less than the controlled rectifier circuit when the same

amount of inductance present in the armature circui t . The switch-mode converter is therefore

suitable for applications requiring position control or fast response, for example in servo

applications, robotics, etc. In terms of quadrant of operations, 3 possible configurations arepossible: s ingle qu adra nt , two–qua dran t an d four –qua dran t converters – these a re sh own below.

Reference:

N. Mohan, “Electric Drives: An integrative approach”, University of Minnesota Printing services, 2000.

N. Mohan, “Power Electronics: Converters, applications and design” John Wiley and Sons, 1995.

≡ Contactor

Single-quadrantTwo-quadrant

Four-quadrant

ω

T

F1 and F2

are closed

F1

F2

R1

R2

R1 and R2

are closed

R1 and R2

are closed

F1 and F2are closed

1

1Q2

2

3

Q3

4

1Q2

Q3 4

Q4

ω

T T

T

ω

ω

+ Va -

3–phase

supply

+va

–

+

va

–

+ va

–



D C

M O

T O R

D R

I V E S

( M

E P 1 4 2 2 )

D r . N i k

R u m z i N i k

I d r i s

D e

p a r t m e n t o

f E n e r g y C

o n v e r s i o n

F

K E ,

U T M



C o

n t e n t s

•

I n t r o d u

c t i o n

– T r e n

d s i n D C

d r i v e s

– D C m

o t o r s

•

M o d e l i n g o f C o n v e r t e r s a n d D C m

o t o r

– P h a s

e - c o n t r o l l e d R

e c t i f i e r

– D C - D

C

c o n v e r t e r ( S w i t c h - m o d e )

– M o d e l i n g o f D C

m o

t o r

•

C l o s e d - l o o p s p e e d c

o n t r o l

– C a s c

a d e C o n t r o l S

t r u c t u r e

– C l o s e d - l o o p s p e e d

c o n t r o l - a n e x

a m p l e

• T o r q u e l o o p

• S p e e d l o o p

•

S u m m a

r y



I N T R O D U C T I O N

• D C D R

I V E S : E l e c t r i c d r i v e s t h a

t u s e D C m o

t o r s

a s t h e

p r i m e m o v e r s

• D o m i n a t e s v a r i a b l e

s p e e d a p p l i c a t i o n s b e f o

r e

P E c o n

v e r t e r s w e r e i n t r o d u c e d

• D C m o

t o r : i n d u s t r y

w o r k h o r s e f o r d e c a d e s

• W i l l A C

d r i v e r e p l a c

e s D C d r i v e

?

– P r e d i c

t e d 3 0 y e a r s a

g o

– A C w i l l e v e n t u a l l y r e

p l a c e D C – a t

a s l o w r a t e

– D C s t r o n g p r e s e n c e

– e a s y c o n t r o l – h u g e n u m b e r s



I n t r o d u c t i o n

D C

M o

t o r s

•

S e v e

r a l l i m i t a t i o n

s :

•

A d v a

n t a g e : P r e c i s e t o r q u e a n

d s p e e d c o n

t r o l

w i t h o

u t s o p h i s t i c a

t e d e l e c t r o n

i c s

•

R e

g u l a r M a i n t e

n a n c e

•

E x p e n s i v e

•

H e

a v y

•

S p e e d l i m i t a

t i o n s

•

S p

a r k i n g



C u r r e n t i n

C u r r e n t o u t

S t a t o r : f i e l d

w i n d i n g s

R o t o r : a r m a t u r e

w i n d i n g s


D C

M o t o

r s

• M e c h a n i c a

l c o m m u t a t o r

• L a r g e m a c

h i n e e m p l o y s c o m p

e n s a t i o n w i n d i n g s




a

t

i

k

T e

φ

=

E l e c t r i c t o r q u e

φ ω

=

E

a

k

e

A r m a t u r e b a c k e . m

. f .

L f

R f

i f

a

a

a

a

t

e

d t

d i

L

i

R

v

+

+

=

+ e a

_

L a

R a

i a

+ V t

_

+ V f

_

d t

d i

L

i

R

v

f

f

f

f

+

=




a

a

a

t

E

I

R

V

+

=

I n s t e a d

y s t a t e ,

(

) 2

T

e

a

T t

k

T

R

k V

φ

−

φ

=

ω

T h e r e f o

r e s p e e d i s g i v e n b

y ,

T h r e e p o s s i b l e m e t h o d s o f s p e e d c o n t r o

l :

F i e l d f l u x

A r m a t u r e

v o l t a g e V t

A r m a t u r e

r e s i s t a n c e R a

a

a

a

a

t

e

d t

d i

L

i

R

V

+

+

=

A r m a t u

r e c i r c u i t :




F o r w i d e r a n

g e o f s p e e d c o n t r o

l

0 t o ω b a s e →

a r m a t u r e v o l t a g e ,

a b o v e ω b a s e

→ f i e

l d f l u x r e d u c t i o n

A r m a t u r e v o

l t a g e c o n t r o l : r e t a i n m a x i m u m t o

r q u e

c a p a b i l i t y

F i e l d f l u x c o

n t r o l ( i . e .

f l u x r e d u c

e d ) : r e d u c e m a x i m u m t o

r q u e c a p a b i l i t y

T e

ω

M a

x i m u m

T o r q u e c a p a b i l i t y

A r m a t u r e v o l t a g

e c o n t r o l

F i e l d f l u x c o n t r o

l

ω b a s e



M O D E L I N

G O F C O N

V E R T E R S

A N

D D C M O T

O R

U s e d t o o b t a i n v a r i a b

l e a r m a t u r e v o l t a g e

P O W E R

E L E C T R O N I C

S C O N V E R T E

R S

• E

f f i c i e n t

I d e a l : l o s s l e s s

• P

h a s e - c o n t r o l l e

d r e c t i f i e r s ( A C

→

D C )

• D

C - D C

s w i t c h - m

o d e c o n v e r t e

r s ( D C

→

D C )



M o d e l i n g o f C

o n v e r t e r s a n d D

C m o t o r

P h a s e - c o n t r o l l e d r e c t i f i e r ( A C – D C )

T

Q 1

Q 2

Q 3

Q 4

ω

3 - p h a s

e

s u p p l y

+ V t

−

i a



P h a s e - c o n t r o l l e d

r e c t i f i e r

Q 1

Q 2

Q 3

Q 4

ω

T

3 - p h a s e

s u p p l y

3 - p h a s

e

s u p p

l y

+ V t

−



C m o t o r




r e c t i f i e r

Q 1

Q 2

Q 3

Q 4

ω

T

F 1

F 2

R 1

R 2

+

V a

-

3 - p

h a s

e

s u p p

l y



C m o t o r



P h a s e - c o

n t r o l l e d r e c t i f i e r ( c o n t i n u o u s

c u r r e n t )

• F i r i n

g c i r c u i t – f i r i n g a n g l e c o n t r o l

→

E s t a b l i s h r e l a t i o n b e t w e e n

v c

a n d V t

f i r i n g

c i r c u i t

c u r r e n t

c o n t r o l l e r

c o n t r o l l e d

r e c t i f i e r

α

+ V t

–

v

c

i r e f

+

-



C m o t o r




r e c t i f i e r ( c o n t i n u o u s

c u r r e n t )

• F i r i n

g

a n g l e

c o n t r o

l

π =

1 8 0

v v

c o s

V

V

t c

m

a

α

=

c

t

v

1 8 0

v

1 8 0

v vt c

=

α

l i n e a r f i r i n

g a n g l e c o n t r o l

α

=

c o s

v

v

s

c C o s i n e - w a v e c r o s s i n g c o n t r o

l

s c

m

a

v v

V

V

π

=



C m o t o r



P h a s e - c o n t r o l l e d r e c t i f i e r ( c o n t i n u o u s

c u r r e n t )

• S

t e a d y s t a t e : l i n e a r g a i n a m p l i f i e r

• C o s i n e

w a v e – c r o s s i n

g m e t h o d



C m o t o r

• T

r a n s i e n t : s a m p l e r w i t h z e r o o

r d e r h o l d

T

G H

( s )

c o n v e r t e r

T

– 1 0 m s

f o r

1 - p

h a s e

5 0 H z

s y s

t e m

–

3 . 3 3

m s

f o r

3 - p

h a s e

5 0 H z s y s

t e m



0 .

3

0 .

3 1

0 .

3 2

0 .

3 3

0 .

3 4

0 .

3 5

0 .

3 6

- 4 0 0

- 2 0 0 0

2 0 0

4 0 0

0 .

3

0 .

3 1

0 .

3 2

0 .

3 3

0 .

3 4

0 .

3 5

0 .

3 6

- 1 0 - 5 0 5 1 0


c u r r e n t )

T d

T d

–

D e l a y i n a v e r a g e o u t p u t v o l t a g e g e n e r a t i o n

0 – 1 0 m s

f o r 5 0 H z s i n g l e p h a s e s y s t e m

O u t p u t

v o l t

a g e

C o s i n e - w a v e

c r o s s i n g

C o

n t r o l

s i g

n a l



C m o t o r




c u r r e n t )

•

M o

d e l s i m p l i f i e d t o l i n e a r g a i n i f b a n d w i d t h

( e .

g . c u r r e n t l o o p

) m u c h l o w e r t

h a n s a m p l i n g

f r e

q u e n c y

⇒

L o w

b a n d w i d t h – l i m i t e d a p p l i c a t i o n s

•

L o

w

f r e q u e n c y v o l t a g e r i p p l e →

h i g h c u r r e n t

r i p

p l e →

u n d e s i r a b l e



C m o t o r



S w i t c h – m

o d e c o n v e r t e r s

Q 1

Q 2

Q 3

Q 4

ω

T

+ V t

-

T 1



C m o t o r



S w i t c h – m


+ V

t

-

T 1

D 1

T 2

D 2

Q 1

Q 2

Q 3

Q 4

ω

T

Q

1 →

T 1 a n d D 2

Q

2 →

D 1 a n d T 2



C m o t o r



S w i t c h – m


Q 1

Q 2

Q 3

Q 4

ω

T

+

V t

-

T

1

D 1

T 2

D 2

D

3

D 4

T 3

T

4



C m o t o r



S w i t c h – m


• S w i t c h i n g a t h i g h

f r e q u e n c y

→

R e d u c e s

c u r r e n t r i p p l e

→

I n c r e a s e s

c o n t r o l b a n d w

i d t h

• S u i t a b l e f o r h i g h p e r f o r m a n c e a p p l i c a t i o n s



C m o t o r



S w i t c h – m o d e c o n v e r t e r s

- m o d e l i n g

+ V d c

•

V d c

v c v

t r i

q

=

0 1

q

w h e

n v c > v t r i , u p p e r s w i t c h O N

w h e n v c < v t r i , l o w e r s w i t c

h O N



C m o t o r



t r i

o n

T

t t

t r i

T t

d t

q

T 1

d

t r i

=

=

∫ +

v c

q

T t r

i

d


– a v e r a g e d m

o d e l



C m o t o r

d c

d T

0

d c

t r i

t

d V

d t

V

T 1

V

t r i

=

=

∫

V d c

V t



V t r i , p

- V t r i , p

v c

d 1 0

0 .

5

p ,

t r i

c

V 2

v

5 . 0

d

+

=

c

p ,

t r i

d c

d c

t

v

V 2

V

V 5 . 0

V

+

=


– a v e r a g e d m

o d e l



C m o t o r



D C

m o t o r

– s m a l l s i g n a l m

o d e l



C m o t o r

E x t r

a c t t h e d c a n d a c c o m p o n e n t s b y i n t r o

d u c i n g s m a l l

p e r t u r b a t i o n s i n V t ,

i a , e

a ,

T e ,

T L

a n d ω m

a

a

a

a

a

t

e

d t

d i

L

R i

v

+

+

=

T e =

k t

i a

e e =

k t ω

d t

d J

T

T

m

l

e

ω

+

=

a

a

a

a

a

t

e ~

d t i ~

d

L

R i ~

v ~

+

+

=

) i ~ (

k

T ~

a

E

e

=

) ~ (

k

e ~

E

e

ω

=

d t

) ~ ( d J

~ B

T ~

T ~

L

e

ω

+

ω

+

= a

c c o m p o n e n t s

a

a

a

t

E

R I

V

+

=

a

E

e

I k

T

=

ω

=

E

e

k

E

) ( B

T

T

L

e

ω

+

=

d c c o m p

o n e n t s



D C

m o t o r


o d e l



C m o t o r

P e r f o r m L

a p l a c e T r a n s f o

r m a t i o n o n a c c o m p o n e n t s

a

a

a

a

a

t

e ~

d t i ~

d

L

R i ~

v ~

+

+

=

) i ~ (

k

T ~

a

E

e

=

) ~ (

k

e ~

E

e

ω

=

d t

) ~ ( d J

~

B

T ~

T ~

L

e

ω

+

ω

+

=

V t ( s

) = I a ( s ) R

a

+ L

a s I a + E

a ( s )

T e

( s ) = k E I a

( s )

E a

( s ) = k E ω ( s )

T e

( s ) = T L ( s ) + B ω ( s ) + s J ω ( s

)



D C

m o t o r


o d e l



C m o t o r

T

k

a

a

s L

R

1 +

) s ( T l

) s (

T e

s J

B

1 +

E

k

) s ( I a

) s ( ω

) s (

V a

+

-

-

+



C L O S E D - L O O P S P E E D

C O N T R O L

C a s c a d e

c o n t r o l s t r u c t u

r e

•

I t

i s f l e x i b l e – o u t e r l o o p c a n b e r e a d i l y a d d e d o r r e m o v e d

d e

p e n d i n g o n t h e c o n

t r o l r e q u i r e m e n t s

•

T h

e c o n t r o l v a r i a b l e o

f i n n e r l o o p ( e . g .

t o r q u e ) c a n b e

l i m

i t e d b y l i m i t i n g i t s r e f e r e n c e v a l u e

1 / s

c o n v e r t e r

t o r q u e

c o n t r o l l e r

s p e e d

c o n t r o l l e r

p o s i t i o n

c o

n t r o l l e r

+-

+-

+-

t a c h o

M o t o r

θ *

T *

ω *

k T



C L O S E D - L O O P

S P E E D

C O N T R O L

D e s i g n p

r o c e d u r e

i n c a

s c a d e c o n t r o l s

t r u c t u r e

•

I n n e

r l o o p ( c u r r e n t o r

t o r q u e l o o p ) t h e f

a s t e s t –

l a r g e

s t b a n d w i d t h

•

T h e

o u t e r m o s t l o o p ( p o s i t i o n l o o p ) t h e

s l o w e s t –

s m a

l l e s t b a n d w i d t h

•

D e s i g n s t a r t s f r o m t o r

q u e l o o p p r o c e e d

t o w a r d s

o u t e

r l o o p s




S P E E D

C O N T R O L

C l o s e d - l o

o p s p e e d c o n

t r o l – a n e x a m

p l e

O B J E C T I V E S :

•

F a s t

r e s p o n s e – l a r g e

b a n d w i d t h

•

M i n i m u m o v e r s h o o t

g o o d

p h a s e m a r g i n ( >

6 5 o )

•

Z e r o

s t e a d y s t a t e e r r o

r – v e r y l a r g e D C

g a i n

B O D E

P L O T S

•

O b t a

i n l i n e a r s m a l l s i g

n a l m o d e l

M E T H O D

•

D e s i g n c o n t r o l l e r s b a s e d o n l i n e a r s m a

l l s

i g n a l m o d e l

•

P e r f o r m l a r g e s i g n a l s

i m u l a t i o n f o r c o n t r o l l e r s v e r i f i c a t i o n




S P E E D

C O N T R O L

R

a

= 2 Ω

L a

= 5 . 2

m H

J

= 1 5 2 x

1 0 –

6

k g . m

2

B

= 1 x 1 0 –

4

k g . m

2

/ s e c

k t

= 0 . 1 N

m / A

k e

= 0 . 1

V / ( r a d / s )

V d

= 6 0 V

V t r i = 5 V

f s = 3 3 k H z

P e r m a n e n

t m a g n e t m o t o r ’ s

p a r a m e t e r s

C l o s e

d - l o

o p s p e e

d c o n

t r o l – a n e x a m p

l e

•

P I c o n t r o l l e r s

•

S w i t c h i n g s i g n

a l s f r o m

c o m p a r i s o n o f v

c a n d t r i a n g u l a r

w a v e f o r m




S P E E D

C O N T R O L

T o r q u e c

o n t r o l l e r d e s i g

n

T c

v t r i

+ V d c

•

q

q

+

–

k t

T o r q u e

c o n t r o l l e r

T

k

a

a

s L

R

1 +

) s ( T l

) s (

T e

s J

B

1 +

E

k

) s ( I a

) s (

ω

) s (

V a

+

-

-

+

T o r q

u e

c o n t

r o l l e r

C o n v e r t e r

p e a k

,

t r i

d c

V V

) s (

T e

-

+

D C

m o t o r



B o d e D i a g r a m

F r e q u e n c y

( r a d / s e c )

- 5 0 0

5 0

1 0 0

1 5 0

F r o m : I n p u t P o i n t T o : O u t p u t P o i n t

M a g n i t u d e ( d B )

1 0

- 2

1 0

- 1

1 0

0

1 0

1

1 0

2

1

0 3

1 0

4

1 0

5

- 9 0

- 4 5 0

4 5

9 0

P h a s e ( d e g )


S P E E D

C O N T R O L

T o r q u e c

o n t r o l l e r d e s i g

n

O p e n - l o o p g a i n

c o m p e n s a t e d


k p T = 9 0

k i T = 1 8 0 0 0




S P E E D

C O N T R O L

S p e e d c o

n t r o l l e r d e s i g n

A s s u m e t o r q

u e l o o p u n i t y g a i n f o r s p e e d b a n d w i d t h

< < T o r q u e b a n d w i d t h

1

S p e e d

c o n t r o l l e r

s J

B

1 +

ω *

T *

T

ω

–

+

T o r q u e l o o p




F r e q u e n c y

( H z )

- 5 0 0 5 0 1 0 0

1 5 0

F r o

m : I n p u t P o i n t T o : O u t p u t P o i n t


1 0 - 2

1 0 - 1

1 0

0

1 0

1

1 0

2

1 0

3

1 0

4

- 1 8 0

- 1 3 5 - 9 0 - 4 5 0

P h a s e ( d e g )


S P E E D

C O N T R O L

S p e e d c o n t r o l l e r

O p e n - l o o p g a i n


k p s = 0 . 2

k i s = 0 . 1

4




C L O S E D - L O O

P

S P E E D

C O N T R O L

L a r g e S i g n a l S i m u l a t i o n r e s u l t s

0

0 .

0 5

0 .

1

0

. 1 5

0 .

2

0 .

2 5

0 .

3

0 .

3 5

0 .

4

0 .

4 5

- 4 0

- 2 0 0

2 0

4 0

0

0 .

0 5

0 .

1

0

. 1 5

0 .

2

0 .

2 5

0 .

3

0 .

3 5

0 .

4

0 .

4 5

- 2

- 1 0 1 2

S p e e d

T o r q u e



C L O S E D - L O O P S P E E D

C O N T R O L – D E S

I G N

E X A M P L E

S U M

M A R Y

P o w e r e l e c t r o n i c s c o n v e r t e r

s – t o o b t a i n v a r i a b

l e a r m a t u r e v o l t a g e

P

h a s e c o n t r o l l e d r e c t i f i e r – s m a l l b a n d w

i d t h – l a r g e r i p p l e

S

w i t c h - m o d e D C - D C

c o n v e r t e r – l a r g e

b a n d w i d t h – s m a l l r i p p l e

C o n t r o l l e

r d e s i g n b a s e d o n

l i n e a r s m a l l s i g n a l m o d e l

P

o w e r c o n v e r t e r s - a v e r a g e d m o d e l

D

C

m o t o r – s e p a r a t e l y e x c i t e d o r p e r m a n e n t m a g n e t

C l o s e d - l o o p s p e e d c o n t r o l d e s i g n b a s e d o n B o

d e p l o t s

V e r i f y w i t h l a r g e s i g

n a l s i m u l a t i o n

S p e e d c o n t r o l b y : a r m a t u r e

v o l t a g e ( 0 → ω b

) a n

d f i e l d f l u x ( ω

b ↑ )



!"#$%!&'( ( (

)* +*,-( % .

/(,0 * $%!&'/,(/(,12,123(

60

Vd Va

Tl

speed

T

Ia

SubsystemStep1

Step

PID

PID Controller1

PID

PID Controller

Output Point

Input Point

0.2

1/Vt

Bode Diagram

Frequency (Hz)

-40

-30

-20

-10

0

10

20From: Input Point To: Output Point


10-3

10-2

10-1

100

101

102

103

-90

-45

0

45

90

P h a s e ( d e g )

Pole-Zero Map

Real Axis

I m a g i n a r y A x i s

-350 -300 -250 -200 -150 -100 -50 0-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

/(,4($%!&'1.0"0.



5(516.( 7 55 16.( / #./(,058#59+#(.-33#01#12-33#(1 012-33/(-&1*.0(

Bode Diagram

Frequency (Hz)

-40

-30

-20

-10

0

10



10-3

10-2

10-1

100

101

102

103

104

-180

-135

-90

-45

0

45

90

P h a s e ( d e g )

/(-412-3312,

//(-7(01(0.-33#1 (/1:30"/(5(75(516.(

Bode Diagram

Frequency (Hz)

-20

0

20

40

60

80

100

From: Input Point To: Output Point


10-3

10-2

10-1

100

101

102

103

104

-180

-135

-90

-45

0

45

90

P h a s e (

d e g )

/(571:37(

70 ((5336.("0 7



0 ( % ;0 " <($11/(9(/(9 " ( / 7 70 (

1

torque-loop

PID

speed_controller

PID

speed controller

PID

current controller

60

Vd Va

Tl

speed

T

Ia

SubsystemStep1

0.2

1/Vt

In1Out1

1/(sJ +B)1

In1Out1

1/(sJ +B)

Bode Diagram

Frequency (Hz)

-100

-50

0

50

100

150


Magnitude(dB)

10-3

10-2

10-1

100

101

102

103

104

105

-180

-135

-90

-45

0

Phase(deg)

/(9$(7;0";7

3(8#(.70 = 7 -33 6.( " /(>(

.(

7



!

Bode Diagram

Frequency (Hz)

-50

0

50

100



10-2

10-1

100

101

102

103

104

-135

-90

-45

0

P h a s e ( d e g )

/(>

.?

1 1

7? :3 ,+333

$? 3(- 3(,9

($%!&'1/(@(% (7>6. 7,(>&(7/(@(

vc_m

To Workspace4

vc

To Workspace3

vtri

To Workspace2

torque

To Workspace1

speed

To Workspace

Out1

Subsystem1

Va

Tl

speed

T

Ia

Subsystem

Step1

SignalGenerator

Saturation1

Relay1

Relay

PID

PIDController1

PID

PID Controller

-1

Gain

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45-40

-20

0

20

40

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45-2

-1

0

1

2

/(@!$11$7



U S I N G L I N E A R

A N A L Y S I S I N

M A T L A B

F O R

D C M O T O R

D R I V E C O

N T R O L L E R

D E S I G N

O u r o b j e c t i v e i n D C d r i v

e s y s t e m a r e :

( a )

T o

o b t a i n z e r o o r s m a l l s t e a d y s t a t e

e r r o r

– m

a k i n g s u r e D C g a i n o f o p e n – l o o p p l o t i s l a r g e

( b )

T o

a c h i e v e f a s t r e s p o n s e

– m

a k i n g s u r e c r o s s o v e r f r e q u e n c y

o f o p e n – l o o p

p l o t i s l a r g e o r l a r g e c l o s e – l o o p b a n d w i d t h



E X A M

P L E i n u s i n g l i n e a r

a n a l y s i s i n

M A T L A B

) 1

s 1 . 0 ( s

1 0 0

G O L

+

=

1

0 . 1 s + 1

T r a n s f e r F c n

1 s

I n t e g r a t o r

- K -

G a i n

1 0 0

0 . 1

s + s

2

T r a n s f e r

F c n



E X A M


a n a l y s i s i n

M A T L A B



E X A M

P L E i n u s i n g l i n

e a r a n a l y s i s i n

M A T L A B

S e l e c t B o

d e a s r e s p o n s e t

y p e i n P l o t C o n f i g u r a t i o n s w i n d o w

T r y t o p l a c e i n p u t p o i n t a t s e v e r a l d i f f e r e

n t p o s i t i o n s . F o

r

e a c h p o s i t i o n , o b t a i n t h e

p l o t u s i n g t h e S i m u l i n k → g e t

l i n e a r i z e

d m o d e l

1

0 . 1 s + 1


O u t p u t P o i n t

1 s

I n

t e g r a t o r

I n p u t P o i n t

- K -

G a i n

1

0 . 1 s + 1


O u t p u

t P o i n t

1 s

I n t e

g r a t o r

I n p u t P o i n t

- K -

G a i n

1

0 . 1 s + 1



1 s

I n t e g

r a t o r

I n p u t P o i n t

- K -

G a i n



E X A M


a n a l y s i s i n

M A T L A B


F r e q u e n c y ( r a d / s e c )

- 1 0 0

- 5 0 0

5 0

1 0 0

F r o

m : I n p u t P o i n t T o : O u t p u t P o i n t


1 0

- 1

1 0

0

1 0

1

1 0

2

1 0

3

- 1 8 0

- 1 3 5

- 9 0

- 4 5 0

P h a s e ( d e g )



E X A M


a n a l y s i s i n

M A T L A B

1

0 . 1 s + 1



1 s

I n t e g r a t o r

I n p u t P o i n t

- K -

G a i n



- 1 0 0

- 5 0 0

5 0

1 0 0

F r o m : I n p u t P o i n t T o : O u t p u t P o i n t


1 0 - 1

1 0

0

1 0

1

1 0

2

1 0

3

- 1 8 0

- 1 3 5

- 9 0

- 4 5 0

P h a s e ( d e g )

C

r o s s o v e r f r e q u e n c y

a p p r o x i m a t e s c l o

s e –

l o

o p b a n d w i d t h



E X A M


a n a l y s i s i n

M A T L A B

P I c o

n t r o l l e r

s

s

1

k

p

ik

k

i

+

• C o n t a i n a z e r o a n d a p o l e a t o r i g i n

• D C g a i n c a n b e a d

j u s t e d i n d e p e n d

e n t l y f r o m

l o c a t i o n o f z e r o

T r a n

s f e r f u n c t i o n



E X A M


a n a l y s i s i n

M A T L A B

P I c o

n t r o l l e r


1 s

I n t e g r a t o r

I n p u t P o i n t

0 . 1

G a i n 1

1 G a i n



- 1 0 0

- 5 0 0

5 0

1 0 0

F r o m : I n p u t P o i n t T o : O u t p u t P o i n

t


1 0 - 1

1 0

0

1 0

1

1 0

2

1 0

3

- 9 0

- 4 5 0

P h a s e ( d e g )

k i = 1 ,

k p = 0 . 1

k i = 1 0 0 ,

k p = 1 0



Model Name "dc_m2_linear_large_torque"Version 5.0SaveDefaultBlockParams onSampleTimeColors offLibraryLinkDisplay "none"WideLines offShowLineDimensions offShowPortDataTypes offShowLoopsOnError onIgnoreBidirectionalLines offShowStorageClass off


MinMaxOverflowArchiveMode "Overwrite"BlockNameDataTip offBlockParametersDataTip offBlockDescriptionStringDataTip offToolBar onStatusBar onBrowserShowLibraryLinks offBrowserLookUnderMasks onCreated "Wed May 28 20:17:31 2003"UpdateHistory "UpdateHistoryNever"ModifiedByFormat "%<Auto>"LastModifiedBy "Nik Rumzi"ModifiedDateFormat "%<Auto>"LastModifiedDate "Mon Jul 26 11:46:55 2004"ModelVersionFormat "1.%<AutoIncrement:33>"ConfigurationManager "None"SimParamPage "Solver"LinearizationMsg "none"Profile offParamWorkspaceSource "MATLABWorkspace"AccelSystemTargetFile "accel.tlc"AccelTemplateMakefile "accel_default_tmf"AccelMakeCommand "make_rtw"TryForcingSFcnDF offExtModeMexFile "ext_comm"





ExtModeArmWhenConnect onExtModeSkipDownloadWhenConnect offExtModeLogAll onExtModeAutoUpdateStatusClock onBufferReuse onRTWExpressionDepthLimit 5SimulationMode "normal"Solver "ode5"SolverMode "Auto"StartTime "0.0"StopTime "0.45"MaxOrder 5

MaxStep "0.0001"MinStep "0.00001"MaxNumMinSteps "-1"InitialStep "0.00001"FixedStep "0.000001"RelTol "1e-3"AbsTol "auto"OutputOption "RefineOutputTimes"OutputTimes "[]"Refine "1"LoadExternalInput offExternalInput "[t, u]"LoadInitialState off

InitialState "xInitial"SaveTime onTimeSaveName "t"SaveState offStateSaveName "xout"SaveOutput onOutputSaveName "yout"SaveFinalState offFinalStateName "xFinal"SaveFormat "Array"Decimation "1"LimitDataPoints offMaxDataPoints "1000"SignalLoggingName "sigsOut"ConsistencyChecking "none"ArrayBoundsChecking "none"AlgebraicLoopMsg "warning"BlockPriorityViolationMsg "warning"MinStepSizeMsg "warning"InheritedTsInSrcMsg "warning"DiscreteInheritContinuousMsg "warning"MultiTaskRateTransMsg "error"SingleTaskRateTransMsg "none"CheckForMatrixSingularity "none"IntegerOverflowMsg "warning"


RTWInlineParameters offBlockReductionOpt on



BooleanDataType onConditionallyExecuteInputs onParameterPooling onOptimizeBlockIOStorage onZeroCross onAssertionControl "UseLocalSettings"ProdHWDeviceType "Microprocessor"ProdHWWordLengths "8,16,32,32"RTWSystemTargetFile "grt.tlc"RTWTemplateMakefile "grt_default_tmf"RTWMakeCommand "make_rtw"RTWGenerateCodeOnly off





Block BlockType ClockDisplayTime off

Block BlockType Derivative

Block BlockType FcnExpr "sin(u[1])"

Block BlockType GainGain "1"Multiplication "Element-wise(K.*u)"ShowAdditionalParam offParameterDataTypeMode "Same as input"ParameterDataType "sfix(16)"ParameterScalingMode "Best Precision: Matrix-wise"ParameterScaling "2^0"

OutDataTypeMode "Same as input"OutDataType "sfix(16)"OutScaling "2^0"LockScale offRndMeth "Floor"SaturateOnIntegerOverflow on

Block BlockType InportPort "1"PortDimensions "-1"SampleTime "-1"ShowAdditionalParam off

LatchInput offDataType "auto"



OutDataType "sfix(16)"OutScaling "2^0"SignalType "auto"SamplingMode "auto"Interpolate on

Block BlockType LookupInputValues "[-4:5]"OutputValues " rand(1,10)-0.5"ShowAdditionalParam offLookUpMeth "Interpolation-Extrapolation"

OutDataTypeMode "Same as input"OutDataType "sfix(16)"OutScaling "2^0"LockScale offRndMeth "Floor"SaturateOnIntegerOverflow on


Block BlockType RelayOnSwitchValue "eps"OffSwitchValue "eps"OnOutputValue "1"OffOutputValue "0"ShowAdditionalParam offOutputDataTypeScalingMode "All ports same datatype"OutDataType "sfix(16)"OutScaling "2^0"ConRadixGroup "Use specified scaling"ZeroCross on

Block BlockType SaturateUpperLimit "0.5"LowerLimit "-0.5"LinearizeAsGain onZeroCross on

Block BlockType "S-Function"FunctionName "system"PortCounts "[]"SFunctionModules "''"

Block BlockType SignalGeneratorWaveForm "sine"Amplitude "1"Frequency "1"Units "Hertz"VectorParams1D on

Block BlockType StepTime "1"Before "0"

After "1"SampleTime "-1"



VectorParams1D onZeroCross on

Block BlockType SubSystemShowPortLabels onPermissions "ReadWrite"RTWSystemCode "Auto"RTWFcnNameOpts "Auto"RTWFileNameOpts "Auto"SimViewingDevice offDataTypeOverride "UseLocalSettings"

MinMaxOverflowLogging "UseLocalSettings"Block BlockType SumIconShape "rectangular"Inputs "++"ShowAdditionalParam offInputSameDT onOutDataTypeMode "Same as first input"OutDataType "sfix(16)"OutScaling "2^0"LockScale offRndMeth "Floor"

SaturateOnIntegerOverflow onBlock BlockType ToWorkspaceVariableName "simulink_output"MaxDataPoints "1000"Decimation "1"SampleTime "0"

Block BlockType TransferFcnNumerator "[1]"Denominator "[1 2 1]"AbsoluteTolerance "auto"Realization "auto"

AnnotationDefaults

HorizontalAlignment "center"VerticalAlignment "middle"ForegroundColor "black"BackgroundColor "white"DropShadow offFontName "Helvetica"FontSize 10

FontWeight "normal"FontAngle "normal"LineDefaults


System

Name "dc_m2_linear_large_torque"Location [6, 82, 1018, 533]Open on

ModelBrowserVisibility offModelBrowserWidth 212



ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "92"ReportName "simulink-default.rpt"Block BlockType GainName "Gain"Position [410, 230, 440, 260]Gain "-1"

Block BlockType ReferenceName "PID Controller"Ports [1, 1]Position [335, 90, 365, 120]SourceBlock "simulink_extras/Additional\nLinear/PID Controll"

"er"SourceType "PID Controller"P "90"I "90*200"D "0"

Block BlockType ReferenceName "PID Controller1"Ports [1, 1]Position [150, 90, 180, 120]SourceBlock "simulink_extras/Additional\nLinear/PID Controll"

"er"SourceType "PID Controller"P "0.2"I "0.7*0.2"D "0"

Block BlockType RelayName "Relay"Position [500, 90, 530, 120]OnSwitchValue "0"OffSwitchValue "0"OnOutputValue "60"

Block BlockType RelayName "Relay1"Position [520, 230, 550, 260]OnSwitchValue "0"

OffSwitchValue "0"OnOutputValue "60"Block BlockType SaturateName "Saturation1"Position [225, 90, 255, 120]UpperLimit "1.5"LowerLimit "-1.5"

Block BlockType SignalGeneratorName "Signal\nGenerator"

Position [20, 90, 50, 120]WaveForm "square"



Amplitude "-30"Frequency "5"

Block BlockType StepName "Step1"Position [600, 205, 630, 235]Time "0"After "0"SampleTime "0"

Block

BlockType SubSystemName "Subsystem"Ports [2, 3]Position [700, 120, 740, 180]TreatAsAtomicUnit offMaskPromptString "Armature resistance|La|J|Kt|B"MaskStyleString "edit,edit,edit,edit,edit"MaskTunableValueString "on,on,on,on,on"MaskCallbackString "||||"MaskEnableString "on,on,on,on,on"MaskVisibilityString "on,on,on,on,on"MaskToolTipString "on,on,on,on,on"MaskVarAliasString ",,,,"

MaskVariables "Ra=@1;La=@2;J=@3;Kt=@4;B=@5;"MaskIconFrame onMaskIconOpaque onMaskIconRotate "none"MaskIconUnits "autoscale"MaskValueString "2|5.2e-3|152e-6|0.1|0.0001"System

Name "Subsystem"Location [90, 152, 644, 411]Open offModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"Block BlockType InportName "Va"Position [25, 88, 55, 102]

Block BlockType Inport

Name "Tl"Position [280, 28, 310, 42]Port "2"

Block BlockType GainName "Gain"Position [250, 80, 280, 110]Gain "Kt"

Block BlockType GainName "Gain2"

Position [270, 185, 300, 215]Orientation "left"



Gain "Kt"Block BlockType SumName "Sum"Ports [2, 1]Position [80, 85, 100, 105]ShowName offIconShape "round"Inputs "|+-"InputSameDT offOutDataTypeMode "Inherit via internal rule"

Block BlockType SumName "Sum1"Ports [2, 1]Position [310, 85, 330, 105]NamePlacement "alternate"ShowName offIconShape "round"Inputs "-+|"InputSameDT offOutDataTypeMode "Inherit via internal rule"

Block BlockType TransferFcnName "Transfer Fcn"Position [145, 77, 205, 113]Denominator "[La Ra]"

Block BlockType TransferFcnName "Transfer Fcn1"Position [375, 77, 435, 113]Denominator "[J B]"

Block BlockType OutportName "speed"Position [495, 88, 525, 102]

Block BlockType OutportName "T"Position [390, 33, 420, 47]Port "2"

Block BlockType Outport

Name "Ia"Position [240, 33, 270, 47]Port "3"

Line SrcBlock "Sum"SrcPort 1DstBlock "Transfer Fcn"DstPort 1

Line SrcBlock "Gain"SrcPort 1




Line SrcBlock "Transfer Fcn"SrcPort 1Points [10, 0]Branch DstBlock "Gain"DstPort 1

Branch Points [0, -55]DstBlock "Ia"

DstPort 1

Line SrcBlock "Sum1"SrcPort 1Points [5, 0]Branch Points [0, -55]DstBlock "T"DstPort 1

Branch

DstBlock "Transfer Fcn1"DstPort 1

Line SrcBlock "Transfer Fcn1"SrcPort 1Points [35, 0]Branch DstBlock "speed"DstPort 1

Branch Points [0, 105]DstBlock "Gain2"DstPort 1

Line SrcBlock "Tl"SrcPort 1Points [5, 0]DstBlock "Sum1"DstPort 1

Line SrcBlock "Va"SrcPort 1DstBlock "Sum"DstPort 1

Line SrcBlock "Gain2"SrcPort 1Points [-175, 0]DstBlock "Sum"DstPort 2



Block BlockType SubSystemName "Subsystem1"Ports [0, 1]Position [325, 162, 360, 198]TreatAsAtomicUnit offMaskPromptString "frekuensi|V peak"MaskStyleString "edit,edit"MaskTunableValueString "on,on"MaskCallbackString "|"MaskEnableString "on,on"MaskVisibilityString "on,on"

MaskToolTipString "on,on"MaskVarAliasString ","MaskVariables "f=@1;v1=@2;"MaskIconFrame onMaskIconOpaque onMaskIconRotate "none"MaskIconUnits "autoscale"MaskValueString "33000|5"System

Name "Subsystem1"Location [553, 276, 688, 358]Open offModelBrowserVisibility off

ModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"Block BlockType ReferenceName "Repeating\nSequence"Ports [0, 1]Position [25, 25, 55, 55]SourceBlock "simulink/Sources/Repeating\nSequence"SourceType "Repeating table"rep_seq_t "[0 1/(2*f) 1/f]"rep_seq_y "[-v1 v1 -v1]"


Line SrcBlock "Repeating\nSequence"SrcPort 1

DstBlock "Out1"DstPort 1

Block BlockType SumName "Sum"Ports [2, 1]Position [100, 95, 120, 115]ShowName offIconShape "round"Inputs "|+-"

InputSameDT offOutDataTypeMode "Inherit via internal rule"



Block BlockType SumName "Sum1"Ports [2, 1]Position [290, 95, 310, 115]ShowName offIconShape "round"Inputs "|+-"InputSameDT offOutDataTypeMode "Inherit via internal rule"


Block BlockType Sum

Name "Sum3"Ports [2, 1]Position [470, 235, 490, 255]ShowName offIconShape "round"Inputs "-+|"InputSameDT offOutDataTypeMode "Inherit via internal rule"

Block BlockType SumName "Sum4"Ports [2, 1]Position [560, 145, 580, 165]ShowName offIconShape "round"Inputs "+|-"InputSameDT offOutDataTypeMode "Inherit via internal rule"

Block BlockType ToWorkspaceName "To Workspace"Position [910, 115, 970, 145]VariableName "speed"

MaxDataPoints "inf"SampleTime "-1"SaveFormat "Array"

Block BlockType ToWorkspaceName "To Workspace1"Position [800, 75, 860, 105]VariableName "torque"MaxDataPoints "inf"SampleTime "-1"SaveFormat "Array"

Block BlockType ToWorkspace



Name "To Workspace2"Position [445, 25, 505, 55]VariableName "vtri"MaxDataPoints "inf"SampleTime "-1"SaveFormat "Array"

Block BlockType ToWorkspaceName "To Workspace3"Position [485, 290, 545, 320]VariableName "vc"

MaxDataPoints "inf"SampleTime "-1"SaveFormat "Array"

Block BlockType ToWorkspaceName "To Workspace4"Position [495, 370, 555, 400]VariableName "vc_m"MaxDataPoints "inf"SampleTime "-1"SaveFormat "Array"

Line SrcBlock "PID Controller"SrcPort 1Points [10, 0]Branch

Points [20, 0]Branch Points [-5, 0]DstBlock "Gain"DstPort 1

Branch DstBlock "Sum2"DstPort 1

Branch

Points [0, 200]DstBlock "To Workspace3"DstPort 1

Line SrcBlock "Step1"SrcPort 1

Points [50, 0]DstBlock "Subsystem"DstPort 2

Line SrcBlock "Sum2"SrcPort 1DstBlock "Relay"DstPort 1

Line SrcBlock "Subsystem1"SrcPort 1

Points [45, 0]Branch



Points [30, 0]Branch Points [40, 0]DstBlock "Sum3"DstPort 1


Branch

Points [0, -140]DstBlock "To Workspace2"DstPort 1

Line SrcBlock "Signal\nGenerator"SrcPort 1DstBlock "Sum"DstPort 1

Line SrcBlock "Sum"

SrcPort 1DstBlock "PID Controller1"DstPort 1

Line SrcBlock "PID Controller1"SrcPort 1DstBlock "Saturation1"DstPort 1

Line SrcBlock "Sum1"SrcPort 1DstBlock "PID Controller"DstPort 1

Line SrcBlock "Saturation1"SrcPort 1DstBlock "Sum1"DstPort 1

Line SrcBlock "Subsystem"SrcPort 1

Points [120, 0]Branch Points [0, 295; -755, 0]DstBlock "Sum"DstPort 2

Branch

DstBlock "To Workspace"DstPort 1

Line SrcBlock "Gain"

SrcPort 1Points [5, 0]




Branch


Line SrcBlock "Relay"

SrcPort 1Points [35, 0]DstBlock "Sum4"DstPort 1

Line SrcBlock "Sum3"SrcPort 1DstBlock "Relay1"DstPort 1

Line SrcBlock "Relay1"

SrcPort 1Points [15, 0]DstBlock "Sum4"DstPort 2

Line SrcBlock "Sum4"SrcPort 1Points [50, 0; 0, -20]DstBlock "Subsystem"DstPort 1

Line SrcBlock "Subsystem"SrcPort 2Points [30, 0]Branch


Branch

Points [0, 195; -475, 0]DstBlock "Sum1"DstPort 2



1

PEMACU MOTOR ARUHAN

Mot or aruhan ï%LQDDQGDQSULQVLSRSHUDVLUHYLVLRQ Motor aru ha n terdir i dar i s tator dan rotor

Pada s t ator terdapa t belitan 3 fasa yang disam bu ng kepada bekalan voltan 3 fasa (a , b, dan c)

Secara a m, terda pat du a jenis rotor : squirrel cage (san gkar tu pai) dan wou nd (berbeli t )

Bila vol tan s inu soidal t iga fasa seimba ng dikenaka n, ak an terbentu k flu ks m agnet pada sela

uda ra yang berputar dengan ke la jua n:

f 2p

2s π=ω r ad / s (1 )

ωs – dikena li seba gai freku ens i segerak (syn chr onou s frequ ency)

f – ialah freku ensi bekalan t iga fasa pada stator

p – ialah bi lan gan ku tu b

Flux se la udara berputar in i akan mengaruh kan dge pada pengalir ro tor . Arus akan te rhas i l

pada pengalir ro tor dan akan ber in teraks i dengan fluks se la u dara b erputar u ntu k menghasi lkan dayaki las yang akan memutarkan rotor .Oleh i tu laju rotor sent iasa kurang dari

laju segerak.

Perbezaan laju ini dikenali sebagai laju gelin ciran (slip s peed).

ωs l = ωs – ωr (2)

Nisbah laju gelinciran kepada laju segerak ialah gelinciran.

s

rssω

ω−ω= (3)

Fluks se la u dara yang berputar juga aka n mengaruh kan dge pada be lit an s ta tor yang dikena li

seba gai dge balikan (back emf) ata u voltan sela u dar a (air gap voltage).

Voltan sela u dara yang teraru h diberi oleh:

E ag = k f φa g (4)

J ika Vs ialah vol tan per-fasa yang dikena kan pada belitan stator da n Is ialah a ru s bel itan

stator , persam aan litar s ta tor ialah:

a

b

b’

c

c’

x x

x

•

• •



2

Vs = Rs Is + j(2πf)Lls + E ag (5)

d.g.e. yang teraru h pad a rotor adalah disebabkan oleh fluk s ma gnet yan g sam a tapi pada

frekuensi gelinciran dan ia boleh ditulis sebagai:

E r = k sf φag = s E ag (6)

Oleh i tu, persamaan untuk l i tar rotor ialah:

E r = s E ag = Rr Ir + js(2πf)Llr (7)

J ika kedua-dua be lah persam aan d ibaha gi dengan s ,

lrrr

a g L)f 2( jIs

RE π+=⇒ (8)

Litar setara per fasa

Rs – Rinta ngan belitan stat or

Rr – Rin tan gan pen galir rotorLls – Kearu ha n bocor belitan stator

Llr – Kearu ha n bocor belitan rotor

Lm – Kearuh an kemagnetan

s – gelincira n

Rotor t idak m empu nyai sum ber kua sa, oleh i tu ku asa yang dipindah kan dari litar s ta tor ke litar

rotor dikenali sebagai kuasa sela udara (air-gap power) dan diberi oleh:

Ku asa mekan ikal boleh di tul is da lam sebu tan dayaki las d an laju rotor sebagai:

Pm = Tem ωr

Tapi sωs = ωs - ωr ⇒ ωr = (1-s)ωs

+

Vs

–

Rs Lls Llr

Rr

s

+

E a g

–

Is Ir

Im

Lm

Hilang

p a d a Rr D it ukar kepada kua sa mekan ika l

Pm = (1- s)Pag

[ ]s1s

RI3RI3

s

RI3P r2

rr

2

rr2

rag −+==



3

∴ Pa g = Tem ωs

Oleh itus

r

2

r

s

ag

ems

RI3PT

ω=

ω=

J ika

( )lrlsr

s

sr

XX js

RR

VI

+++= , daya kilas boleh ditulis sebagai:

( )2

lrls

2

rs

2s

s

rem

XXs

RR

V

s

R3T

++

+

ω=

Bentu k lazim ciri T-ω un t uk m o to r a r uh an :

Gelinciran s emas a da ya kilas ma ksimu m d iber i oleh:

( )2

lrls

2

s

rm

XXR

Rs

++±=

Nilai dayakilas ma ksima (pu ll-out t orque):

( )

++±ω=

2

lrls

2

ss

2

s

s

m a x

XXRR

V

s

3T

0 ωra ted ωs

1 0

ωr

s

Tm,ra ted

Pull ou t

Torque

Tem



4

Kawalan laju mo to r aruhan

Terdapat beberapa kaedah kawalan la ju :

(i) Pole ch an gin g ïPHQXNDUELODQJDQNXWXE

Laju segerak bergantung kepada bi langan kutub

Dengan m enuka r sam bun gan pada be lit an , b i langan ku tub boleh d iuba h.

(ii) Var iab le volta ge, fixed frequ en cy

Magnitud voltan dikawal, freku ensi tetap, e .g. mengguna kan t ran sformer.

(iii) Var iable m agn itu de variab le frequ en cy

Magnitud voltan beka lan d ituka r berkadaran dengan frekuens i dan m erupakan kaeadah yang

pal ing popular d igunaka n da lam pemacu kawalan la ju motor a ruh an. Untuk s yang kec il dan

φa g yang tetap, boleh di tun juk kan hu bu ngan di antara dayaki las da n laju gelinciran (s lip speed)

ada lah linear

Untu k men gekalkan f lu ks sela ud ara pada ni lai kadara n, bi la voltan diubah , freku ensi juga

per lu d iuba h:

E ag = k f φag

Oleh u ntu k men ghas ilkan φa g yang malar pada n ila i kadaran , n i sbahf

E a gharu s lah m alar . J ika

ke ja tuh an voltan pada R s d a n Xls ada lah kecil dibandingkan dengan Vs ,

f

V

f

Esag ≈

Vol tan bekalan diubah secara berkadaran dengan laju atau frequensi sehingga laju kadaran.

TL

T

ωr

Lower s peed gives

h igher slip ∴ less

efficien t



5

Unt uk ω > ωra ted, ma gni tud voltan di tetapka n tapi frekuen si dina ikkan , oleh i tu torque capa bility

menguran g kerana fluks m ula menguran g

Bila laju k ecil , kejatu h an voltan oleh R s d a n Xls adalah besar j ika dibandingkn dengan Vs . Oleh

itu kebiasaa nn ya Vs dinaikkan lebih besar sedikit (boost) semasa frequens i rendah

Ciri T-ω bi la m agni tud Vs dan f d iuba h berkadaran

Bagaiman akah magni tud dan frekuens i d ikawal serentak ?

Menggu n aka n Pulse Width Modu lation (PWM) In verter

T

T,rated

TL

ωr ωr , ra ted

ωs , ra ted

Vs

ωr

Vs

f

Vs , ra ted

f ra ted



6

Example 1

400 V, 50 Hz 4ïSROH 1370 rpm

Rs = 2 Ω, Rr = 3 Ω, Xls = Xlr = 3.5 Ω

Motor is controlled by a voltage sou rce in verter with const an t V/ f.

Calculate:

(a) Sp eed for frequ en cy of 30 Hz an d 80 % of fu ll load

(b) Frequ ency for a speed of 100 0 rpm an d fu ll load torqu e

(c) Torqu e for a frequ ency of 40 Hz an d speed of 110 0 rpm

(a)

8.0,slip

rated

rated,slip

rated

N

T8.0

N

T=

Nsl ip,rated = Ns ï1r , ra ted = 1500 ïUSP

rpm104)130(8.0NT

T8.0N ra ted,slip

ra ted

ra ted8.0,slip ===∴

Pada 30 Hz, laju segerak ialah 30 x 60 = 1800/ 2 = 900 rpm

Fixed AC.

Var iable voltage

Var iable freq.

IMPWM in verter

AC–DC

(rectifier)

Control

(f and V)

50 Hz30 Hz

Tra ted

0.8 Tra ted

1500

Rated

slip

speed

Nslip,0.8



7

∴Nr = Ns ï1slip = 900 ï04 = 796 rpm

(b)

Ns = 130 + 1000 = 1130 rpm

∴ f = 37.67 Hz

(c)

∴ Ns = 1200 rp m

Nslip = 1200 ïUSP

50 Hz? Hz

Tra ted

1500

Nslip,rated

= 130

1000 Ns

Nslip,rated

= 130

1370

6 0f p

2Ns ×=

50 Hz40 Hz

Tra ted

T = ?

1500

Nslip,rated

= 130 r pm

1100 Ns

Nslip

1370

6 0f p

2Ns ×=



8

∴T = 0.76 9 Tra ted Tra ted = ?

Tra ted diperolehi da ri :

Tra ted = 38.06 Nm

∴ Dayakilas pada 40 Hz, laju 1100 rpm ialah T = 0.769 (38.06) = 29.267 Nm

Example 2

A 4–pole, 3-phase, 50 Hz IM, 1460 rpm has a rated torque of 20 Nm. It is used

to drive a load with characteristic given by TL = Kω2 , such that the speed

equals rated value at rated torque. If a constant V/Hz control method is used,

find the speed of motor at 0.5 rated torque.

If the starting torque of 1.1 times the rated is required, what should be thestarting frequency?

ωslip,r = 1500 – 1460 = 40 rpm or 4.19 rad/s

a) Load torque is given by:

TL = Kω2

1460 rpm ⇒ 152.9 rad/s

20 = K(152.9)2

100

T

130

Tra ted =

( )2lrls

2r

s

2s

s

rem

XXs

RR

V

s

R3T

++

+

ω=

TL = K ω2

TL(Nm)

ω(rad/s)

Trated

Zslip,r

Zsyn,r

Zr,r

50 Hz

0.5 Trated



9

⇒ K = 20/(152.9)2

∴ at 0.5 rated torque, the speed is 108.11 rad/s

Motor T-ω is obtained as follows:

Therefore at 0.5 Trated and speed of 108.11 rad/s

∴ ωsyn = 110.2 ⇒ f = 35 Hz

At start-up,

2

2L9.152

20T ω=

rs yn

e

r,rr,s yn

ra ted

slip

ra ted T77.4

TT

ω−ω==

ω−ω=

ω

rsy ne 77.477.4T ω−ω=

)11.108(77.477.410 s yn −ω=

TL = K ω2

TL(Nm)

ω(rad/s)

Trated

Zslip,r

Zsyn,r

Zr,r

50 Hz

1.1(Trated

)

Zslip

= Zsyn

19.4

TT1.1 r a ted

slip

rated =ω

61.4)1.1(19.4sy nsy nslip ==ω∴ω=ω



1 0

SCALAR CONTROL OF IM

We have seen that applying balanced, sinusoidal 3-phase supply to a 3-phasesinusoidally distributed winding produces a rotating mmf wave and hencerotating magnetic flux. The rotating magnetic flux will induce emf on therotor circuit, which is shorted for squirell cage rotor. Rotor current willflow and interact with the rotating flux, producing torque.

Per-phase steady state equivalent circuit

To ensure maximum torque capability at all time it is therefore necessary tomaintain the magnetic flux at its rated value at any frequency. From thesteady state equivalent circuit, this is equivalent to maintaining themagnetizing current at its rated value.

The flux can be maintained constant at its rated by maintaining the ratio Eg/f

constant. At high speed, where the induced back emf is large, the drop acrossthe stator leakage and resistance is negligibly small.- therefore E

g/f is

maintained constant by maintaining V/f constant. However at low speed, theback emf is low and the drop is significant. Thus the flux is reduced belowrated – torque capability is also reduced.

Simulation results with constant V/f

The performance can be improved by:

(i) Boosting the voltage at low frequency:

s p e e d -

r a d / s

t or q u e -

Nm

Im

Rs

Rr / s

Lrl Ls l

Lm

+

V

−

+

E g

−



1 1

To accurately boost the voltage, stator current needs to be measured. The

voltage drop drop is calculated and added to stator voltage on-line

ii) Control the stator current such that constant magnetising current ismaintained. This is achieved by using a current-controlled voltage sourceinverter.

m

rlr

r

mlr

1

1

rmlr

r

lr

m

I

s

RL j

s

R)LL( j

I

I

s

R)LL( j

s

RL j

I

+ω

++ω=⇒

++ω

+ω=

Introducing σr = rotor leakage factor, which gives, Llr = σrLm,

,I

1T1

j

1T jI

I

s

RL

1 j

s

RL j

I

m

r

r

rslip

rslip

1

m

r

r

r

r

rr

1

+

σ+

σω

+ω=

+

σ+

σω

+ω=

Where Tr= L

r/R

rand ω

slip= ω - ω

r= sω

The method depends on the rotor parameters, which vary with temperature.

Open-loop V/f control



1 2

For low cost, low performance drive, open-loop constant V/f control isnormally employed. With open-loop speed control, the rotor speed will be lessthan the synchronous speed by slip speed. In other words, the desired speed,

ω*, will differ from the actual speed by slip speed. The slip speed on theother hand, depends on load. To improve the performance or the speedregulation, slip speed can be estimated and added to the reference speed –slip compensation technique. Typical arrangement is shown below:

How is the slip speed estimated?

The slip frequency is proportional to the torque, hence it can estimated byestimating the torque. The torque is estimated from,

Te= P

ag/ω

syn

VSIRectifier3-phase

supply IM

Pulse

WidthModulator

Vboost Slip speed

calculator

ω*

+ +

+ + V

Vdc Idc

Ramp



1 3

P

agis

estimated by subtracting the input DC power with the inverter and stator

copper losses.

Closed-loop speed control

Speed regulation can be improved by employing closed-loop speed control system

with tachometer feedback, as shown below.

The reference and actual speed are compared. The error is fed to the speedcontroller which defines the inverter frequency. The current limit isactivated only when current exceeds the maximum allowable value. The signalgenerated by the current limit block will reduce the rate by which theinverter frequency is increased. This is to avoid the frequency from reachingthe breakdown frequency.

Further readings:Power Electronic Control of AC Motors – J.M.D. Murphy and F.G. Turnbull,

Pergamon Press



Modelling of 3-phase Induction Machine (IM)

The steady state model of IM, which is represented by a steady state per phase equivalecircuit introduced in the undergraduate courses, describes the steady state behaviour the IM. It is used when steady state analysis, such as efficiency, losses, steady statorque, current, fluxes need to be evaluated. The model assumes input to be a balanced, phase steady state sinusoidal voltage. If the IM is fed by power electronic converterthe steady state analysis can be performed by representing the pulse-width modulat

waveform of the inverter using Fourier series. Steady state model of IM is also used derive the control signals used for scalar control drives. Since the model only valid steady state condition, such drive normally has a poor transient performance. Applicationot requiring good transient response such as fans, blowers or compressors, normalemploy such control technique. Dynamic model on the other hand, describes the transient well as the steady state behaviour of the IM. Using the dynamic model, the transients IM, which cannot be analysed using steady state equivalent model, can be predicted studied. The model can be used to simulate the IM drives and evaluate their transieperformances, including that of using the scalar control technique. Dynamic model is alessential when developing high performance control techniques for IM drives, such vector control or direct torque control drives. A dynamic model of IM must contain effeof the magnetic coupling between stator phase circuits and the rotor phase circuits, well as coupling between phases of each circuit. This will undoubtedly result in a hunumber and complex equations, which are difficult to manage. By using space vect

equations, however, these complex equations are simplified and reduced. We will ndevelop a dynamic model of an IM using mathematical equations based on space vectors space phasors (these terms will be defined later on).

System equations

Figure 1 shows the conceptual representation of a 3-phase, 2 poles induction machine. Thmagnetic axis of each winding is represented by an inductor symbol. As usual the angles

between windings of each phase are 120o. The angle between rotor’s phase a axis and

stator’s phase a axis is given by θr. The equation describing the stator and rotorcircuits can be written as:

vabcs = Rsiabcs + d(ψ ψψ ψ abcs)/dt

vabcr = Rriabcr + d(ψ ψψ ψ abr)/dt

where,

Ψ

Ψ

Ψ

=Ψ

=

=

cs

bs

as

abcs

cs

bs

as

abcs

cs

bs

as

abcs

i

i

i

i

v

v

v

v and

Ψ

Ψ

Ψ

=Ψ

=

=

cr

br

ar

abcs

cr

br

ar

abcr

cr

br

ar

abcr

i

i

i

i

v

v

v

v

It is clear that since the displacements between various windings of all the phases arenon-quadrature, there exists magnetic coupling between them. The stator and rotor flux

linkages (ψ abcs and ψ abcs)of equations (1) and (2) are contributed by the stator and rotorcurrents. Thus:

r,abcss,abcsabcsΨ+Ψ=Ψ

s,abcrr,abcrabcr Ψ+Ψ=Ψ



ψ abcs,s and ψ abcs,r are the components of the stator flux linkage caused by stator and rotor

currents (phase a, b and c) respectively, and, ψ abcr,r and ψ abcr,s are the components of therotor flux linkage caused by rotor and stator currents (phase a, b and c) respectivelyThese flux linkages can be written in terms of the inductances and respective currents.

=Ψ

cs

bs

as

csbcsacs

bcsbsabs

acsabsas

s,abcs

i

i

i

LLL

LLL

LLL

=Ψ

cr

br

ar

cr,csbr,csar,cs

cr,bsbr,bsar,bs

cr,asbr,asar,as

r,abcs

i

ii

LLL

LLLLLL

=Ψ

cr

br

ar

crbcracr

bcrbrabr

acrabrar

r,abcr

i

i

i

LLL

LLL

LLL

stator, b

rotor, b

rotor, a

stator, a

rotor, c

stator, c

ξ = 0

θr

Figure 1



=Ψ

cs

bs

as

cs,crbs,cras,cr

cs,brbs,bras,br

cs,arbs,aras,ar

s,abcr

i

i

i

LLL

LLL

LLL

In equation (5), Las, Lbs and Lcs are the self inductances of phases a, b and crespectively. The self inductance consists of magnetising and leakage inductance.

Las = Lms + Lls. Lbs = Lms + Lls. Lcs = Lms + Lls.

Labs, Lbcs, Lacs in equation (5), are the mutual inductances between stator phases.

For symmetrical winding, which is normally the case, magnetising and leakage as well asmutual inductances for each phase are equal.

It can be shown that the magnetizing and the mutual inductances are given by:

π

µ=

4g

rlNL2

soms

2

L

8g

rlNLLL ms2

soacsbcsabs −=

π

µ−===

Thus equation (5) can be written as:

+−−

−+−

−−+

=Ψ

cs

bs

as

lsms

msms

ms

lsms

ms

msmslsms

s,abcs

i

i

i

LL2

L

2

L2

LLL

2

L2

L

2

LLL

(

The mutual inductances between the stator and rotor windings in (6) and (8) depend on th

rotor position, θr and it can be shown that they can be written as:

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

θπ−θπ+θ

π+θθπ−θ

π−θπ+θθ

=Ψ

cr

br

ar

rrr

rrr

rrr

ms

s

rr,abcs

i

i

i

cos3

2cos3

2cos

32coscos

32cos

32cos

32coscos

LN

N(

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

θπ+θπ−θ

π−θθπ+θ

π+θπ−θθ

=Ψ

cs

bs

as

rrr

rrr

rrr

ms

s

rs,abcr

i

i

i

cos3

2cos3

2cos

32coscos

32cos

32cos

32coscos

LN

N(

Space phasors representation of induction machine

Equations (1)-(8) give the complete description of the electrical characteristics of aninduction machine. There are six circuits that describe the 3-phase induction machine aneach of them coupled to one another. Although the determinations of the inductances arequite straight forward, however, the number of equations involved is large. We will nowdevelop a model of the induction machine which is based on space phasors or space vectorand valid under steady state and transient conditions. By doing so, the number ofequations is significantly reduced.



If the permeability of the core is assumed infintely large, all the mmf drops will appeaacross the airgap. Therefore, the stator airgap MMF of a sinusoidally distributed windinfor phase a can be written as:

)cos(i2

Nas

sas α−ξ=ℑ (

ξ is any angle where ξ=0 coincide with the magnetic axis of stator winding phase a. α is

the angle in which airgap mmf is maximum. ias is the stator phase a current. If α = 0 the

equation (9) can be written as:

ξ=ℑ cosi2

Nas

sas (

Phases b and c are spatially separated from phase a by 120o. Thus airgap mmf of phase band c are given by:

)3

2cos(i

2

Nbs

sbs

π−ξ=ℑ (

)3

2cos(i

2

Ncs

scs

π+ξ=ℑ (

The total airgap mmf

)3

2

cos(i2

N

)3

2

cos(i2

N

cosi2

N

cs

s

bs

s

as

s

abcs

π

+ξ+

π

−ξ+ξ=ℑ (

Using Euler’s identity and with some mathematical manupulation, it can be shown that:

( ) ( ) ξ−ξ +++++=ℑ jcs

2bsas

jcsbs

2as

sabcs eiaaiieaiiai

4

N(

where a = ej(2π/3)

This can be further reduced or written as:

ξξ− +=ℑ j*s

js

sabcs eiei

4

N

2

3(

The term si is defined as the space phasor or complex space vector of the stator curren

It is given by:

( )cs2

bsass iaaii3

2i ++= (

The physical current can be obtained from the space phasor by separating the space phasointo its real and imaginary part. In most cases we can assume that ias + ibs + ics = 0.

( )

−+=

−++−=

++++=

)ii(3

1ji

)ii(2

3j)ii(

2

1i

3

2

)240sinj240(cosi)120sinj120(cosii3

2i

csbsas

csbscsbsas

csbsass

Thus

[ ]sasiRei = (

Similarly it can be shown that



= and = (

Similar definitions can be made to the stator voltage, rotor current, stator flux androtor flux. Equations (1) and (2) therefore can be written as:

Ψ+= (

dt

diRv rrrr

Ψ+= (

Ψ is composed of components caused by stator and rotor currents as given by (3). In

space phasors, (3) can be written as:

Ψ+Ψ=Ψ (

Ψ is obtained by multiplying second and third rows of (5) with a and a2 respectively.

Similarly, Ψ can be obtained from (6). With some mathematical manipulations, it can b

shown that:

rj'

rmssseiLiL

θ+=Ψ (

Where Ls = Lls + Lm , Lm = 3/2Lms and r

s

r'

r iN

Ni =

Similarly, it can be shown that the rotor flux linkage can be written as:

rj

sm

'

rr

'

reiLiL

θ−+=Ψ (

Note that the rotor current in (26) (i.e.'

ri ) , is the space vector referred to t

rotating rotor reference frame. However, the d and q components ofrj'

rei

θare expressed

the stator stationary reference frame. This is illustrated in Figure 2. Therefore we c

define the rotor current referred to the stator stationary frame as

rj'

r

s

reii

θ= (

Equation (26) can be written in stationary stator reference frame as:

s

rm

s

ss

s

siLiL +=Ψ (

Where the superscript ‘s’ referred to the stator reference frame.

rj'

r

'

reii

ξ=

)rr(j'

r

s

reii

θ+ξ=

θr

ωr

dr

qr qs

ds

isdr

isqr

ξr

'ri

Figure 2



Similarly the termrj

sei

θ−in (27) is the stator current referred to rotating rotor frame

This is illustrated in Figure 3.

Re-writing equations (23),(24),(26) and (27), the space vector equations to describe thesquirrel cage IM written in stationary stator frame can be written as follows:

dt

diRv

s

ss

ss

s

s

ψ += (3

s

rr

s

rs

rrj

dt

diR0 ψ ω−

ψ += (3

s

rm

s

ss

s

siLiL +=ψ (3

s

sm

s

rr

s

riLiL +=ψ (3

In a general reference frame rotating at angular speed of ω, these equations can bewritten as:

g

sg

g

sg

ss

g

s

jdt

diRv ψ ω+

ψ += (3

g

rrg

g

rg

rr)(j

dt

diR0 ψ ω−ω+

ψ += (3

g

rm

g

ss

g

siLiL +=ψ (3

g

sm

g

rr

g

riLiL +=ψ (3

Torque equation

The product of the stator voltage and conjugate stator current space vectors is given by

( ) ( )csbs

2

ascs

2

bsas

*

ssaiiai

3

2vaavv

3

2iv ++++= (

After some mathematical manipulations, with the three phase currents sum to zero, it canbe shown that:

[ ] ( )cscsbsbsasas

*

ss iviviv3

2ivRe ++= (

θr

ωr

dr

qr qs

dsirds

irqsξs

si

sj

sseii

ξ=

)rs(j

s

r

seii

θ−ξ=Figure 3



For a three phase induction machine without a neutral return, the power into the machinecan be written as:

[ ]( ) [ ]( )*'

r

'

r

*

sse ivRe2

3ivRe

2

3P += (

Replacing the voltage vectors expressed in rotating general reference frame, it can beshown that equation (36) can be expressed as:

[ ]

+

+ω−ω+++ω+

+++++=

'*

rsm

2'

rmlsr

*

srm

2

smls

2'

rsm

2'

r

'

lr2

s

ls2

'

rr

2

sse

iiLi)LL()(jiiLi)LL(jRe2

3

iiLi2

Li

2

Lp

2

3ir

2

3ir

2

3P

(

Equation (37) can be divided into three terms:

(i) Power dissipated in stator and rotor resistances(ii) Time rate of change of stored energy(iii) Power conversion from electrical to mechanical – responsible for torque

production

[ ]

++ω−ω+++ω= '*

rsm

2'

rmlsr

*

srm

2

smlsmechiiLi)LL()(jiiLi)LL(jRe

2

3P (

The first and third terms of (38) have only imaginary components. Thus,

[ ] [ ] '*

rsmr

'*

rsm

*

srm

'*

rsmr

*

srmmechiiLjiiLiiL(jRe

2

3iiL)(jiiL(jRe

2

3P ω−+ω=ω−ω+ω= (

Since the term'*

rsm

*

srmiiLiiL + has no imaginary part, the mechanical power reduces to:

'*rsmrmech iiLjRe

23P ω−= (

Which can also be written as:

'*

rsmrmech iiLIm2

3P ω= (

OR

[ ]'

qrds

'

drqsmrmechiiiiL

2

3P −ω= (

The mechanical power is the product of torque and speed, and the mechanical rotor speed

related to the rotor speed as ωr = (p/2)ωrm , thus from (42)

[ ]'

qrds

'

drqsme iiiiL2

p

2

3T −= (



Simulation of induction machine (IM) with MATLAB/SIMULINK

For the purpose of simulation and microprocessor implementation, the space vectorepresentation of the induction machine is converted to its equivalent d-q axis forTransforming equations (30)–(33) to their equivalent d-q axis forms in stationa

reference frame (ωg = 0), and re-arranging them into matrix form, the following obtained:

⋅

+ω−ω−

ω+ω

+

+

=

rq

rd

sq

sd

rrrrmmr

rrrrmrm

mss

mss

rq

rd

sq

sd

i

i

i

i

sLRLsLL

LsLRLsL

sL0sLR0

0sL0sLR

v

v

v

v

(

‘s’in (44) represents the derivative operator d/dt. The space vectors equations can albe put into state space forms with the choice of flux linkages or currents as stavariables. If the stator and rotor currents are chosen as the state variables, rarranging (44) the IM equation can be written as:

⋅

−

−+

⋅

ω−−ω−

ωω−

−ωω

ω−−ω−

−=

sq

sd

m

m

r

r

sr

2

m

rq

rd

sq

sd

srsrrmssmr

srrsrsmrms

mrrmrrs

2

mr

rmrmrsq2mrrs

sr

2

m

rq

rd

sq

sd

v

v

L0

0L

L0

0L

LLL

1

i

i

i

i

LRLLLRLL

LLLRLLLR

LRLLLRL

LLLRiLLR

LLL

1

i

i

i

i

(45

Equations (43),(45) along with the mechanical torque equation, can be used to simulate tIM using SIMULINK. The SIMULINK blocks used to simulate the IM is shown in Figure 4.

q

8

Te

7

Vq

6

irq

5

Vd

4

speed

3

ird

2

isq

1isd

Sum

Mux

Mux

1/s

Integrator

I n1 Out 1

IM1

-K-

Gain2

-K-

Gain1

Demux

Demux

Tload

Constant

3to2

-K-

1/J1

-K-

1/J

3

Vc

2

Vb

1

Va

Figure 4



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BlockType OutportName "out_1"Position [185, 55, 205, 75]InitialOutput "0"

Line


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SrcBlock "in_1"

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Block BlockType Integrator



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Points [0, 235]Branch Points [35, 0]Branch Points [0, -85]DstBlock "Gain3"DstPort 1

Branch DstBlock "Gain2"DstPort 1

Branch Points [0, 160; 25, 0]




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Block BlockType SubSystemName "Induction Machine"Ports [3, 8]

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Block


Block


Block

BlockType SumName "Ib"Ports [2, 1]Position [240, 255, 260, 275]

Block

BlockType SumName "Ib1"Ports [3, 1]Position [260, 87, 280, 123]Inputs "+++"

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BlockType OutportName "q"



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Branch Points [0, 105]




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SrcBlock "Ib"SrcPort 1DstBlock "q"DstPort 1

Block BlockType Constant

Name "Constant"Position [630, 306, 670, 324]Orientation "left"Value "Tload"

Block BlockType DemuxName "Demux"Ports [1, 5]Position [420, 91, 460, 149]Outputs "5"

Block BlockType GainName "Gain1"Position [150, 407, 175, 433]Orientation "left"Gain "2/pole"

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BlockType InportName "In1"



Position [25, 33, 55, 47]Block

BlockType "S-Function"Name "S-Function"Ports [1, 1]Position [80, 25, 140, 55]FunctionName "imch"Parameters "Rs, Rr, Ls,Lr,Lm,pole"

Block

BlockType Outport

Name "Out1"Position [165, 33, 195, 47]InitialOutput "0"

Line

SrcBlock "In1"SrcPort 1DstBlock "S-Function"DstPort 1

Line

SrcBlock "S-Function"SrcPort 1


Block BlockType IntegratorName "Integrator"Ports [1, 1]Position [360, 295, 380, 315]Orientation "left"

Block BlockType MuxName "Mux"Ports [3, 1]Position [260, 104, 290, 136]Inputs "3"

Block BlockType SumName "Sum"Ports [3, 1]Position [440, 287, 460, 323]Orientation "left"

Inputs "+--"Block BlockType GainName "load_C"Position [375, 367, 400, 393]Gain "load_C"SaturateOnIntegerOverflow off

Block BlockType OutportName "isd"Position [630, 25, 650, 45]

InitialOutput "0"



Block BlockType OutportName "isq"Position [625, 70, 645, 90]Port "2"InitialOutput "0"

Block BlockType OutportName "ird"Position [600, 140, 620, 160]Port "3"

InitialOutput "0"Block BlockType OutportName "speed"Position [90, 410, 110, 430]Orientation "left"Port "4"InitialOutput "0"

Block BlockType OutportName "Vd"


Block BlockType OutportName "irq"Position [595, 185, 615, 205]Port "6"InitialOutput "0"

Block BlockType OutportName "Vq"Position [90, 285, 110, 305]Orientation "left"Port "7"InitialOutput "0"

Block BlockType OutportName "Te"Position [715, 230, 735, 250]Port "8"InitialOutput "0"

Line SrcBlock "Demux"SrcPort 1Points [60, 0; 0, -20]DstBlock "isq"DstPort 1

Line SrcBlock "Demux"SrcPort 2Points [65, 0; 0, -75]DstBlock "isd"

DstPort 1



Line SrcBlock "3to2"SrcPort 2Points [0, 0]Branch Points [0, 170]DstBlock "Vq"DstPort 1

Branch Points [55, 0; 0, -15]DstBlock "Mux"

DstPort 1

Line SrcBlock "3to2"SrcPort 1Points [0, 0; 25, 0]Branch Points [0, -35]DstBlock "Vd"DstPort 1

Branch

Points [30, 0; 0, 25]DstBlock "Mux"DstPort 2

Line SrcBlock "Demux"SrcPort 5Points [45, 0; 0, 145]Branch Points [0, 15; -35, 0]DstBlock "Sum"DstPort 1

Branch Points [70, 0; 0, -45]DstBlock "Te"DstPort 1

Line SrcBlock "Vc"SrcPort 1Points [20, 0; 0, -120]DstBlock "3to2"

DstPort 3Line SrcBlock "Vb"SrcPort 1Points [20, 0; 0, -20]DstBlock "3to2"DstPort 2

Line SrcBlock "Va"SrcPort 1Points [20, 0; 0, 40]

DstBlock "3to2"DstPort 1



Line SrcBlock "1/J"SrcPort 1Points [0, 0; -25, 0]Branch Points [0, -175]DstBlock "Mux"DstPort 3

Branch Points [-15, 0; 0, 75]


Branch

DstBlock "load_C"DstPort 1

Line SrcBlock "Mux"

SrcPort 1DstBlock "IM1"DstPort 1

Line SrcBlock "IM1"SrcPort 1DstBlock "Demux"DstPort 1

Line SrcBlock "Sum"SrcPort 1DstBlock "Integrator"DstPort 1

Line SrcBlock "Integrator"SrcPort 1DstBlock "1/J"DstPort 1

Line SrcBlock "Demux"SrcPort 3

Points [30, 0; 0, 75]DstBlock "irq"DstPort 1

Line SrcBlock "Demux"SrcPort 4Points [25, 0; 0, 20]DstBlock "ird"DstPort 1

Line SrcBlock "Gain1"




DstBlock "speed"DstPort 1

Line SrcBlock "load_C"SrcPort 1Points [145, 0; 0, -75]DstBlock "Sum"DstPort 2

Line SrcBlock "Constant"

SrcPort 1DstBlock "Sum"DstPort 3

Annotation Name "q"Position [482, 87]VerticalAlignment "top"

Block BlockType Reference

Name "Manual Switch"Ports [2, 1]Position [150, 232, 180, 268]SourceBlock "simulink/Signal\nRouting/Manual Switch"SourceType "Manual Switch"sw "0"action "0"

Block BlockType MuxName "Mux"Ports [2, 1]Position [660, 41, 665, 79]ShowName offInputs "2"DisplayOption "bar"

Block BlockType RateLimiterName "Rate Limiter"Position [170, 115, 200, 145]RisingSlewLimit "50"FallingSlewLimit "-50"

Block

BlockType ScopeName "Scope"Ports [3]Position [735, 104, 765, 136]Location [357, 69, 795, 439]Open onNumInputPorts "3"List

ListType AxesTitlesaxes1 "%<SignalLabel>"axes2 "%<SignalLabel>"axes3 "%<SignalLabel>"

List ListType SelectedSignals



axes1 ""axes2 ""axes3 ""

TimeRange "1.5"YMin "-10~-20~-50"YMax "80~20~50"DataFormat "StructureWithTime"

Block BlockType ScopeName "Scope1"

Ports [4]Position [455, 271, 490, 364]Location [6, 204, 444, 564]Open onNumInputPorts "4"List

ListType AxesTitlesaxes1 "%<SignalLabel>"axes2 "%<SignalLabel>"axes3 "%<SignalLabel>"axes4 "%<SignalLabel>"

List

ListType SelectedSignalsaxes1 ""axes2 ""axes3 ""axes4 ""

TimeRange "1.5"YMin "-400~-400~-400~-5"YMax "400~400~400~60"SaveName "ScopeData1"DataFormat "StructureWithTime"

Block BlockType ReferenceName "Slider\nGain1"Ports [1, 1]Position [100, 115, 130, 145]SourceBlock "simulink/Math\nOperations/Slider\nGain"SourceType "Slider Gain"low "0"gain "0.07"high "1"

Line SrcBlock "Induction Machine"

SrcPort 8Points [55, 0; 0, -60]DstBlock "Scope"DstPort 2

Line SrcBlock "Induction Machine"SrcPort 2Points [190, 0]DstBlock "Scope"DstPort 3

Line

SrcBlock "Slider\nGain1"SrcPort 1



DstBlock "Rate Limiter"DstPort 1

Line SrcBlock "Constant"SrcPort 1DstBlock "Slider\nGain1"DstPort 1

Line SrcBlock "Constant V/Hz"SrcPort 2

Points [0, 0; 70, 0]Branch

DstBlock "Induction Machine"DstPort 2

Branch

Points [0, 175]DstBlock "Scope1"DstPort 2

Line SrcBlock "Constant V/Hz"

SrcPort 1Points [55, 0; 0, -20; 35, 0]Branch

DstBlock "Induction Machine"DstPort 1

Branch


Line SrcBlock "Constant V/Hz"SrcPort 3Points [0, 0; 40, 0]Branch

Points [15, 0; 0, 20]DstBlock "Induction Machine"DstPort 3

Branch


Line SrcBlock "Rate Limiter"SrcPort 1Points [0, 0; 10, 0]Branch


Branch

Points [25, 0]




DstBlock "Constant V/Hz"DstPort 1

Branch Points [0, -80]DstBlock "Gain"DstPort 1

Line SrcBlock "Constant1"

SrcPort 1Points [0, -30]DstBlock "Manual Switch"DstPort 2

Line SrcBlock "Constant2"SrcPort 1DstBlock "Manual Switch"DstPort 1

Line SrcBlock "Manual Switch"

SrcPort 1Points [70, 0]DstBlock "Constant V/Hz"DstPort 2

Line SrcBlock "Mux"SrcPort 1Points [50, 0]DstBlock "Scope"DstPort 1

Line SrcBlock "Induction Machine"SrcPort 4Points [115, 0]DstBlock "Mux"DstPort 2

Line SrcBlock "Gain"SrcPort 1DstBlock "Mux"DstPort 1



/** sfuntmpl.c: Template C S-function source file.** -------------------------------------------------------------------------* | See matlabroot/simulink/src/sfuntmpl.doc for a more detailed template |* -------------------------------------------------------------------------** Copyright (c) 1990-97, by The MathWorks, Inc.* All Rights Reserved* $Revision 1.1 $*/

/** You must specify the S_FUNCTION_NAME as the name of your S-function.*/

#define S_FUNCTION_NAME imch

/* Input Arguments */

/** Need to include simstruc.h for the definition of the SimStruct and* its associated macro definitions.

*//* #include "tmwtypes.h" */#include "tmwtypes.h"#include "simstruc.h"

#define Rs ssGetArg(S,0)#define Rr ssGetArg(S,1)#define Ls ssGetArg(S,2)#define Lr ssGetArg(S,3)#define Lm ssGetArg(S,4)#define pole ssGetArg(S,5)

/*====================** S-function methods **====================*/

/* Function: mdlInitializeSizes ===============================================* Abstract:** The sizes information is used by SIMULINK to determine the S-function* block's characteristics (number of inputs, outputs, states, etc.).**/static void mdlInitializeSizes(SimStruct *S)

ssSetNumContStates( S, 4); /* number of continuous states */ssSetNumDiscStates( S, 0); /* number of discrete states */ssSetNumInputs( S, 3); /* number of inputs */ssSetNumOutputs( S, 5); /* number of outputs */ssSetDirectFeedThrough(S, 0); /* direct feedthrough flag */ssSetNumSampleTimes( S, 1); /* number of sample times */ssSetNumInputArgs( S, 6);ssSetNumRWork( S, 0); /* number of real work vector elements */ssSetNumIWork( S, 0); /* number of integer work vector elements*/ssSetNumPWork( S, 0); /* number of pointer work vector elements*/ssSetNumModes( S, 0); /* number of mode work vector elements */ssSetNumNonsampledZCs( S, 0); /* number of nonsampled zero crossings */

ssSetOptions( S, 0); /* general options (SS_OPTION_xx) */



/* Function: mdlInitializeSampleTimes =========================================*/static void mdlInitializeSampleTimes(SimStruct *S)

ssSetSampleTime(S, 0, CONTINUOUS_SAMPLE_TIME);ssSetOffsetTime(S, 0, 0.0);

/* Function: mdlInitializeConditions ==========================================* Abstract:** In this function, you should initialize the continuous and discrete* states for your S-function block. The initial states are placed* in the x0 variable. You can also perform any other initialization* activities that your S-function may require.*/static void mdlInitializeConditions(real_T *x0, SimStruct *S)

int i;for (i=0; i<4; i++)

*x0++ = 0.0;

/* Function: mdlOutputs =======================================================* Abstract:** In this function, you compute the outputs of your S-function* block. The outputs are placed in the y variable.*/static void mdlOutputs(real_T *y, const real_T *x, const real_T *u,

SimStruct *S, int_T tid)double lm;double pl;lm = mxGetPr(Lm)[0];pl = mxGetPr(pole)[0];

y[0]=x[0];y[1]=x[1];y[2]=x[2];y[3]=x[3];y[4]=1.5*(pl/2)*lm*((x[0]*x[3])-(x[1]*x[2]));

static void mdlUpdate(real_T *x, const real_T *u, SimStruct *S, int_T tid)

/* Function: mdlDerivatives ===================================================* Abstract:** In this function, you compute the S-function block's derivatives.* The derivatives are placed in the dx variable.*/static void mdlDerivatives(real_T *dx, const real_T *x, const real_T *u,



SimStruct *S, int_tid)

/* x0=iq x1=id x2= iqr x3= idr u0=vq u1=vd u2=w */double lr,ls,rr,rs,lm,a;

lm = mxGetPr(Lm)[0];lr = mxGetPr(Lr)[0];ls = mxGetPr(Ls)[0];rr = mxGetPr(Rr)[0];rs = mxGetPr(Rs)[0];

a=1/(lm*lm-lr*ls);

dx[0]=(u[2]*lm*lm*x[1]+rs*lr*x[0]+u[2]*lr*lm*x[3]-rr*lm*x[2]-lr*u[0])*a;

dx[1]=(rs*lr*x[1]-u[2]*lm*lm*x[0]-rr*lm*x[3]-u[2]*lr*lm*x[2]-lr*u[1])*a;

dx[2]=-(u[2]*lm*ls*x[1]+rs*lm*x[0]+u[2]*lr*ls*x[3]-rr*ls*x[2]-lm*u[0])*a;

dx[3]=-(rs*lm*x[1]-u[2]*lm*ls*x[0]-rr*ls*x[3]-u[2]*lr*ls*x[2]-lm*u[1])*a;

/* Function: mdlTerminate =====================================================* Abstract:** In this function, you should perform any actions that are necessary* at the termination of a simulation. For example, if memory was allocated* in mdlInitializeConditions, this is the place to free it.*/static void mdlTerminate(SimStruct *S)

/** YOUR CODE GOES HERE*/

/*======================================================** See sfuntmpl.doc for the optional S-function methods **======================================================*/

/*=============================** Required S-function trailer **=============================*/

#ifdef MATLAB_MEX_FILE /* Is this file being compiled as a MEX-file? */#include "simulink.c" /* MEX-file interface mechanism */#else

#include "cg_sfun.h" /* Code generation registration function */#endif



! "## !

$

( )%

!

% ++= π &

%'! %& $

( += %

%&

[ ] ( )

−−=

++==

%

%&

%&

!%

!%) )

[ ] ( ) ( )

%

!

&

!

% −=

++== *

$

( )%

!

% ++= +

$

( θ

= ,

-ω$



( )%

!

% ++= .

/$

( θ

= 0

1& # #

1&

( ) ( )α+θ+α+θ=rrrr

s

rsinjicosii

αθ= jj

r

s

reeii r

α=∴ ( 234$

( ) ( )α−θ+α−θ=rsrs

r

ssinjicosii

α−θ= ( (

&5

α−=∴ (

&&

α ( α− ( 4

!

$

(

) ψ ω+

ψ += &%

θ

θ

ω

α



(

)5 ψ ω−ω+

ψ += &!

3 3 +=ψ &*

3 3 +=ψ &+

( )%

!% ++=

-

ψ

ψ 67

ω85$

)

ψ += &,

(

)5 ψ ω−

ψ += &.

3 3 +=ψ &0

3 3 +=ψ &2

&,&2"!!"#

$

%

%

! ×ψ = %5

94$

( ) 3 3 %

%

!

%

%

! ×+=×ψ = %&

:$

3 %

%

! −= %%

$

3

3

%

%

! ×ψ = %!

#%!%*

3

3

%

%

!

ψ −ψ = %*



;%*#1"<%* # 1%=

ψ ψ =ψ

5 =ψ ψ

%*$

3

3

%

%

! ψ

ψ = %+

1%

%+><%+

84 %+>< - 1"<

ψ

%+ 1 4

1"<$1"<1&!

(

)5 ψ ω−ω+

ψ +=

-&+

ψ

ψ

ψ

ψ

ψ



(

3

)3

3

)5 ψ ω−ω+

ψ +−ψ = %,

ψ ψ =ψ 5

=ψ ψ %,$

( )

(

(

3

)3

3

)5 ψ ω+

ψ ++−ψ =

ψ ψ %.

-$

3

)3

3

)5

ψ +−ψ =

ψ %0

3

)3 5 ψ ω+−=

ψ %2

11"< / >1"<1"<4 ?

%,@

1!1"<



1*#?>:3/&220AB/<C"DE?F4BE&225AB</<C"DE?F4G>1H&20.AE;</<CEE"



STATOR FLUX FOC

In stator flux FOC, the frame chosen is aligned to the synchronously rotating frame

such that the d–axis coincide with stator flux space phasor.

Figure 1

The torque equation in general reference frame is given by:

(1)

(2)

In the chosen reference frame, ψ =ψ and =ψ , hence (2) reduces to:

(3)

To implement the stator flux FOC using current–controlled VSI, we need to

i) derive the d and q components of the stator current reference values,

ii) obtain the stator flux position in order to transform the rotating frame

to stationary frame..

From (3), given Te* and ψ s

*,the q component of the stator current in this reference

frame can be easily obtained. To look at the relation between isd and ψ s we need to

examine the IM equations.

The induction machine in general reference frame is given by equations (4)–(7):

ψ ω+

ψ +=

ψ ω−ω+

ψ +=

+=ψ

+=ψ (7)

Ψ

ψ

ψ

ψ

ψ

×ψ =

( )

ψ −ψ =

( )

ψ =



Substitute (7) into (5)

(8)

The stator flux is obtained by substituting the rotor current (which in practice,

normally unavailable) from (6), into (8)

With mathematical manipulations and recognizing that in the reference frame where

only the d axis component of the stator flux exists, it can be shown that by

separating the real and imaginary terms and after substituting rotor current,

equation (8) is given by:

(9)

(10)

From (10), it can be seen that ψ s is proportional to isd and isq. There exists a

coupling between ψ s and isq. Varying isq to control the torque will result in ψ s to

vary too hence the torque will not react immediately to isq.

Figure 2

To overcome this problem, a de–coupler to compensate the effect of the isq component from the output of the PI controller is can be designed [1].

[1] X. Xu, R. K. Doncker, D.W. Novotny, “A stator flux oriented Induction machine

drive”, IEEE-PESC, 1988.

( )

+ω−ω+

++=

( ) ( )

=σ−ψ τω−στ+ψ ψ

( ) ( )

=στω−στ+=ψ τ+ψ ψ

→

θ

Ψ

!

"

""

−

Ψ

θ

#ψ #

!$!$

%&' '(



Model Name "foc"Version 5.0SaveDefaultBlockParams onSampleTimeColors offLibraryLinkDisplay "none"WideLines offShowLineDimensions offShowPortDataTypes offShowLoopsOnError onIgnoreBidirectionalLines offShowStorageClass off


MinMaxOverflowArchiveMode "Overwrite"BlockNameDataTip offBlockParametersDataTip offBlockDescriptionStringDataTip offToolBar onStatusBar onBrowserShowLibraryLinks offBrowserLookUnderMasks offCreated "Tue Oct 01 11:07:25 2002"UpdateHistory "UpdateHistoryNever"ModifiedByFormat "%<Auto>"LastModifiedBy "Administrator"ModifiedDateFormat "%<Auto>"LastModifiedDate "Sun Sep 12 00:33:10 2004"ModelVersionFormat "1.%<AutoIncrement:22>"ConfigurationManager "none"SimParamPage "WorkspaceI/O"LinearizationMsg "none"Profile offParamWorkspaceSource "MATLABWorkspace"AccelSystemTargetFile "accel.tlc"AccelTemplateMakefile "accel_default_tmf"AccelMakeCommand "make_rtw"TryForcingSFcnDF offExtModeMexFile "ext_comm"





ExtModeArmWhenConnect onExtModeSkipDownloadWhenConnect offExtModeLogAll onExtModeAutoUpdateStatusClock onBufferReuse onRTWExpressionDepthLimit 5SimulationMode "normal"Solver "ode5"SolverMode "Auto"StartTime "0.0"StopTime "1000"MaxOrder 5

MaxStep "0.0001"MinStep "0.00001"MaxNumMinSteps "-1"InitialStep "0.00001"FixedStep "5e-6"RelTol "1e-3"AbsTol "auto"OutputOption "RefineOutputTimes"OutputTimes "[]"Refine "1"LoadExternalInput offExternalInput "[t, u]"LoadInitialState off

InitialState "xInitial"SaveTime offTimeSaveName "t"SaveState offStateSaveName "xout"SaveOutput offOutputSaveName "yout"SaveFinalState offFinalStateName "xFinal"SaveFormat "Array"Decimation "1"LimitDataPoints offMaxDataPoints "10000000"SignalLoggingName "sigsOut"ConsistencyChecking "none"ArrayBoundsChecking "none"AlgebraicLoopMsg "warning"BlockPriorityViolationMsg "warning"MinStepSizeMsg "warning"InheritedTsInSrcMsg "warning"DiscreteInheritContinuousMsg "warning"MultiTaskRateTransMsg "error"SingleTaskRateTransMsg "none"CheckForMatrixSingularity "none"IntegerOverflowMsg "warning"


RTWInlineParameters offBlockReductionOpt off



BooleanDataType offConditionallyExecuteInputs onParameterPooling onOptimizeBlockIOStorage onZeroCross onAssertionControl "UseLocalSettings"ProdHWDeviceType "Microprocessor"ProdHWWordLengths "8,16,32,32"RTWSystemTargetFile "grt.tlc"RTWTemplateMakefile "grt_default_tmf"RTWMakeCommand "make_rtw"RTWGenerateCodeOnly off







Block BlockType Derivative

Block

BlockType FcnExpr "sin(u[1])"Block BlockType GainGain "1"Multiplication "Element-wise(K.*u)"ShowAdditionalParam offParameterDataTypeMode "Same as input"ParameterDataType "sfix(16)"ParameterScalingMode "Best Precision: Matrix-wise"ParameterScaling "2^0"OutDataTypeMode "Same as input"

OutDataType "sfix(16)"OutScaling "2^0"



LockScale offRndMeth "Floor"SaturateOnIntegerOverflow on

Block BlockType InportPort "1"PortDimensions "-1"SampleTime "-1"ShowAdditionalParam offLatchInput offDataType "auto"

OutDataType "sfix(16)"OutScaling "2^0"SignalType "auto"SamplingMode "auto"Interpolate on

Block BlockType IntegratorExternalReset "none"InitialConditionSource "internal"InitialCondition "0"LimitOutput offUpperSaturationLimit "inf"

LowerSaturationLimit "-inf"ShowSaturationPort offShowStatePort offAbsoluteTolerance "auto"ZeroCross on

Block BlockType MathOperator "exp"OutputSignalType "auto"

Block BlockType MuxInputs "4"DisplayOption "none"


Block BlockType RelayOnSwitchValue "eps"

OffSwitchValue "eps"OnOutputValue "1"OffOutputValue "0"ShowAdditionalParam offOutputDataTypeScalingMode "All ports same datatype"OutDataType "sfix(16)"OutScaling "2^0"ConRadixGroup "Use specified scaling"ZeroCross on

Block BlockType ScopeFloating off

ModelBased offTickLabels "OneTimeTick"



ZoomMode "on"Grid "on"TimeRange "auto"YMin "-5"YMax "5"SaveToWorkspace offSaveName "ScopeData"LimitDataPoints onMaxDataPoints "5000"Decimation "1"SampleInput offSampleTime "0"

Block BlockType "S-Function"FunctionName "system"PortCounts "[]"SFunctionModules "''"

Block BlockType SignalGeneratorWaveForm "sine"Amplitude "1"Frequency "1"Units "Hertz"

VectorParams1D onBlock BlockType SubSystemShowPortLabels onPermissions "ReadWrite"RTWSystemCode "Auto"RTWFcnNameOpts "Auto"RTWFileNameOpts "Auto"SimViewingDevice offDataTypeOverride "UseLocalSettings"MinMaxOverflowLogging "UseLocalSettings"

Block BlockType SumIconShape "rectangular"Inputs "++"ShowAdditionalParam offInputSameDT onOutDataTypeMode "Same as first input"OutDataType "sfix(16)"OutScaling "2^0"LockScale offRndMeth "Floor"SaturateOnIntegerOverflow on

Block BlockType TrigonometryOperator "sin"OutputSignalType "auto"

AnnotationDefaults

HorizontalAlignment "center"VerticalAlignment "middle"ForegroundColor "black"BackgroundColor "white"DropShadow off

FontName "Helvetica"FontSize 10



FontWeight "normal"FontAngle "normal"

LineDefaults


System

Name "foc"Location [26, 100, 942, 425]

Open onModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "91"ReportName "simulink-default.rpt"Block BlockType GainName "Gain3"


Block BlockType SubSystemName "Induction Machine"Ports [3, 8]Position [645, 13, 700, 142]TreatAsAtomicUnit offMaskPromptString "Stator resistance (ohm)|Rotor resistance (ohm)|"

"Stator self inductance (H)|Rotor self inductance (H)|Mutual Inductance (H)|No"" of poles|Moment of inertia (kg.m^2)|Load torque (Nm)"

MaskStyleString "edit,edit,edit,edit,edit,edit,edit,edit"MaskTunableValueString "on,on,on,on,on,on,on,on"MaskCallbackString "|||||||"MaskEnableString "on,on,on,on,on,on,on,on"MaskVisibilityString "on,on,on,on,on,on,on,on"MaskToolTipString "on,on,on,on,on,on,on,on"MaskVarAliasString ",,,,,,,"MaskVariables "Rs=@1;Rr=@2;Ls=@3;Lr=@4;Lm=@5;pole=@6;J=@7;Tloa"

"d=@8;"MaskIconFrame onMaskIconOpaque onMaskIconRotate "none"MaskIconUnits "autoscale"

MaskValueString "5.5|4.51|306.5e-3|306.5e-3|291.9e-3|4|0.02|0"System Name "Induction Machine"Location [4, 74, 764, 534]Open offModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"




Name "Va"Position [25, 40, 45, 60]

Block BlockType InportName "Vb"Position [25, 120, 45, 140]Port "2"

Block BlockType InportName "Vc"

Position [25, 240, 45, 260]Port "3"

Block BlockType GainName "1/J"Position [260, 292, 285, 318]Orientation "left"Gain "1/J"SaturateOnIntegerOverflow off


Name "1/J1"Position [375, 367, 400, 393]Gain "0.01"SaturateOnIntegerOverflow off

Block BlockType SubSystemName "3to2"Ports [3, 2]Position [105, 81, 135, 139]ShowPortLabels offTreatAsAtomicUnit offSystem Name "3to2"Location [323, 87, 947, 513]Open offModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"Block


Block

BlockType InportName "b"Position [15, 115, 35, 135]Port "2"

Block

BlockType InportName "c"

Position [15, 180, 35, 200]Port "3"



Block


Block


Block


Block


Block BlockType GainName "Gain7"Position [135, 63, 175, 87]Gain "0.66666"

Block


Block


Block


Block BlockType OutportName "q"Position [310, 250, 330, 270]Port "2"InitialOutput "0"

Line

SrcBlock "Ib1"SrcPort 1DstBlock "d"DstPort 1

Line SrcBlock "Gain7"



SrcPort 1Points [30, 0; 0, -15]DstBlock "Ib1"DstPort 1

Line

SrcBlock "in_1"SrcPort 1Points [40, 0; 0, 15]DstBlock "Gain7"DstPort 1


Line


Line

SrcBlock "c"SrcPort 1Points [40, 0; 0, 5]Branch DstBlock "Gain6"DstPort 1


Line

SrcBlock "b"SrcPort 1Points [20, 0; 0, 30]Branch DstBlock "Gain5"DstPort 1



Line


Line


Points [30, 0; 0, -40]DstBlock "Ib"



DstPort 2Line

SrcBlock "Ib"SrcPort 1DstBlock "q"DstPort 1

Block BlockType Constant

Name "Constant"Position [630, 306, 670, 324]Orientation "left"Value "Tload"


Block

BlockType GainName "Gain1"Position [150, 407, 175, 433]Orientation "left"Gain "2/pole"

Block BlockType SubSystemName "IM1"Ports [1, 1]Position [320, 106, 380, 134]TreatAsAtomicUnit offSystem Name "IM1"Location [248, 340, 468, 422]Open offModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"Block

BlockType InportName "In1"Position [25, 33, 55, 47]

Block


Block

BlockType OutportName "Out1"



Position [165, 33, 195, 47]InitialOutput "0"

Line


Line

SrcBlock "S-Function"SrcPort 1



Block

BlockType MuxName "Mux"Ports [3, 1]Position [260, 104, 290, 136]Inputs "3"

Block BlockType SumName "Sum"Ports [3, 1]Position [440, 287, 460, 323]Orientation "left"Inputs "+--"

Block BlockType OutportName "isd"Position [630, 25, 650, 45]InitialOutput "0"

Block BlockType OutportName "isq"Position [625, 70, 645, 90]Port "2"

InitialOutput "0"Block BlockType OutportName "ird"Position [600, 140, 620, 160]Port "3"InitialOutput "0"

Block BlockType OutportName "speed"Position [90, 410, 110, 430]

Orientation "left"Port "4"



InitialOutput "0"Block BlockType OutportName "Vd"Position [265, 50, 285, 70]Port "5"InitialOutput "0"

Block BlockType OutportName "irq"



Block

BlockType OutportName "Te"Position [715, 230, 735, 250]Port "8"InitialOutput "0"


Line SrcBlock "Demux"SrcPort 2Points [65, 0; 0, -75]DstBlock "isd"DstPort 1

Line SrcBlock "3to2"SrcPort 2Points [0, 0]Branch

Points [0, 170]DstBlock "Vq"DstPort 1

Branch Points [55, 0; 0, -15]DstBlock "Mux"DstPort 1

Line SrcBlock "3to2"SrcPort 1

Points [0, 0; 25, 0]Branch



Points [0, -35]DstBlock "Vd"DstPort 1

Branch Points [30, 0; 0, 25]DstBlock "Mux"DstPort 2

Line SrcBlock "Demux"

SrcPort 5Points [45, 0; 0, 145]Branch Points [0, 15; -35, 0]DstBlock "Sum"DstPort 1


Line SrcBlock "Vc"SrcPort 1Points [20, 0; 0, -120]DstBlock "3to2"DstPort 3

Line SrcBlock "Vb"SrcPort 1Points [20, 0; 0, -20]DstBlock "3to2"DstPort 2

Line SrcBlock "Va"SrcPort 1Points [20, 0; 0, 40]DstBlock "3to2"DstPort 1

Line SrcBlock "1/J"SrcPort 1Points [0, 0; -25, 0]

Branch Points [0, -175]DstBlock "Mux"DstPort 3

Branch Points [-15, 0; 0, 75]Branch


Branch

DstBlock "1/J1"DstPort 1



Line SrcBlock "Mux"SrcPort 1DstBlock "IM1"DstPort 1

Line SrcBlock "IM1"SrcPort 1

DstBlock "Demux"DstPort 1

Line SrcBlock "Sum"SrcPort 1DstBlock "Integrator"DstPort 1

Line SrcBlock "Integrator"SrcPort 1DstBlock "1/J"

DstPort 1Line SrcBlock "Demux"SrcPort 3Points [30, 0; 0, 75]DstBlock "irq"DstPort 1

Line SrcBlock "Demux"SrcPort 4Points [25, 0; 0, 20]DstBlock "ird"DstPort 1

Line SrcBlock "Gain1"SrcPort 1Points [0, 0]DstBlock "speed"DstPort 1

Line SrcBlock "1/J1"

SrcPort 1Points [145, 0; 0, -75]DstBlock "Sum"DstPort 2

Line SrcBlock "Constant"SrcPort 1DstBlock "Sum"DstPort 3

Annotation Name "q"

Position [482, 87]VerticalAlignment "top"




Block BlockType IntegratorName "Integrator2"

Ports [1, 1]Position [390, 305, 420, 335]Orientation "left"

Block BlockType RelayName "Relay"Position [540, 30, 570, 60]OnSwitchValue "0.2"OffSwitchValue "-0.2"OnOutputValue "300"OffOutputValue "-300"

Block BlockType RelayName "Relay1"Position [545, 65, 575, 95]OnSwitchValue "0.2"OffSwitchValue "-0.2"OnOutputValue "300"OffOutputValue "-300"

Block BlockType RelayName "Relay2"Position [545, 115, 575, 145]OnSwitchValue "0.2"OffSwitchValue "-0.2"OnOutputValue "300"OffOutputValue "-300"

Block BlockType ConstantName "Rotor Flux"Position [20, 134, 40, 156]Value "1.2*(291.9e-3/306.5e-3)"

Block

BlockType ScopeName "Scope"Ports [2]Position [835, 205, 865, 240]Location [581, 461, 905, 736]Open onNumInputPorts "2"ZoomMode "yonly"List

ListType AxesTitlesaxes1 "%<SignalLabel>"axes2 "%<SignalLabel>"

List ListType SelectedSignals



axes1 ""axes2 ""

TimeRange "0.1"YMin "-25~-30"YMax "25~30"DataFormat "StructureWithTime"

Block BlockType SignalGeneratorName "Signal\nGenerator"Position [25, 50, 55, 80]

WaveForm "square"Amplitude "-20"Frequency "20"

Block BlockType SubSystemName "Subsystem"Ports [4, 4]Position [895, 21, 945, 124]TreatAsAtomicUnit offSystem

Name "Subsystem"Location [596, 100, 1004, 348]

Open offModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"Block BlockType InportName "ird"Position [25, 33, 55, 47]

Block BlockType InportName "isd"Position [25, 78, 55, 92]Port "2"

Block BlockType InportName "irq"Position [25, 128, 55, 142]Port "3"

Block BlockType InportName "isq"Position [25, 173, 55, 187]Port "4"

Block BlockType ReferenceName "Cartesian to\nPolar"Ports [2, 2]Position [255, 87, 285, 118]SourceBlock "simulink_extras/Transformations/Cartesian t"

"o\nPolar"SourceType "Cart2Polar"



Block BlockType GainName "Gain"Position [80, 25, 110, 55]Gain "306.5e-3"

Block BlockType GainName "Gain1"Position [80, 70, 110, 100]Gain "291.9e-3"



Block BlockType SumName "Sum"Ports [2, 1]Position [175, 55, 195, 75]ShowName offIconShape "round"Inputs "+|+"InputSameDT offOutDataTypeMode "Inherit via internal rule"

Block BlockType SumName "Sum1"Ports [2, 1]Position [175, 150, 195, 170]ShowName offIconShape "round"Inputs "+|+"InputSameDT offOutDataTypeMode "Inherit via internal rule"

Block BlockType OutportName "Fm"

Position [355, 88, 385, 102]Block BlockType OutportName "F_the"Position [310, 103, 340, 117]Port "2"

Block BlockType OutportName "Fd"Position [310, 33, 340, 47]Port "3"

Block



BlockType OutportName "Fq"Position [305, 153, 335, 167]Port "4"

Line SrcBlock "Gain"SrcPort 1Points [40, 0]DstBlock "Sum"DstPort 1

Line SrcBlock "Gain1"SrcPort 1Points [70, 0]DstBlock "Sum"DstPort 2

Line SrcBlock "Sum"SrcPort 1Points [25, 0]Branch Points [15, 0]

DstBlock "Cartesian to\nPolar"DstPort 1

Branch Points [0, -25]DstBlock "Fd"DstPort 1

Line SrcBlock "Gain2"SrcPort 1Points [40, 0]DstBlock "Sum1"DstPort 1


Line SrcBlock "Sum1"

SrcPort 1Points [40, 0; 0, -5]Branch DstBlock "Cartesian to\nPolar"DstPort 2

Branch Points [0, 5]DstBlock "Fq"DstPort 1

Line

SrcBlock "ird"SrcPort 1



DstBlock "Gain"DstPort 1

Line SrcBlock "isd"SrcPort 1DstBlock "Gain1"DstPort 1

Line SrcBlock "Cartesian to\nPolar"SrcPort 1

DstBlock "Fm"DstPort 1

Line SrcBlock "Cartesian to\nPolar"SrcPort 2DstBlock "F_the"DstPort 1

Line SrcBlock "irq"SrcPort 1DstBlock "Gain2"

DstPort 1Line SrcBlock "isq"SrcPort 1DstBlock "Gain3"DstPort 1

Block BlockType SubSystemName "Subsystem1"Ports [2, 3]Position [95, 50, 135, 110]TreatAsAtomicUnit offMaskPromptString "Lm|Lr|Rr|p"MaskStyleString "edit,edit,edit,edit"MaskTunableValueString "on,on,on,on"MaskCallbackString "|||"MaskEnableString "on,on,on,on"MaskVisibilityString "on,on,on,on"MaskToolTipString "on,on,on,on"MaskVarAliasString ",,,"MaskVariables "Lm=@1;Lr=@2;Rr=@3;p=@4;"

MaskIconFrame onMaskIconOpaque onMaskIconRotate "none"MaskIconUnits "autoscale"MaskValueString "291.9e-3|306.5e-3|4.51|4"System

Name "Subsystem1"Location [2, 74, 1014, 724]Open offModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"

PaperPositionMode "auto"PaperType "usletter"



PaperUnits "inches"ZoomFactor "100"Block BlockType InportName "T"Position [90, 33, 120, 47]

Block BlockType InportName "Flux"Position [35, 118, 65, 132]Port "2"

Block BlockType ConstantName "Constant1"Position [140, 279, 210, 301]Value "1/Lm"

Block BlockType DerivativeName "Derivative"Position [165, 180, 195, 210]

Block

BlockType ReferenceName "Dot Product"Ports [2, 1]Position [230, 26, 260, 59]SourceBlock "simulink/Math\nOperations/Dot Product"SourceType "Dot Product"

Block BlockType ReferenceName "Dot Product1"Ports [2, 1]Position [292, 115, 323, 150]Orientation "down"NamePlacement "alternate"SourceBlock "simulink/Math\nOperations/Dot Product"SourceType "Dot Product"

Block BlockType ReferenceName "Dot Product2"Ports [2, 1]Position [390, 205, 425, 240]NamePlacement "alternate"SourceBlock "simulink/Math\nOperations/Dot Product"SourceType "Dot Product"

Block BlockType GainName "Gain"Position [145, 25, 175, 55]Gain "(4*Lr)/(3*p*Lm)"

Block BlockType GainName "Gain1"Position [230, 85, 260, 115]Gain "(Lm*Rr)/Lr"




Name "Gain2"Position [115, 180, 145, 210]Gain "Lr/Rr"

Block BlockType MathName "Math\nFunction"Ports [1, 1]Position [145, 110, 175, 140]Operator "reciprocal"

Block

BlockType SumName "Sum2"Ports [2, 1]Position [255, 185, 275, 205]ShowName offIconShape "round"Inputs "|++"InputSameDT offOutDataTypeMode "Inherit via internal rule"

Block BlockType OutportName "isq"

Position [340, 38, 370, 52]Block BlockType OutportName "slip"Position [295, 175, 325, 190]Orientation "down"Port "2"

Block BlockType OutportName "isd"Position [510, 218, 540, 232]Port "3"

Line SrcBlock "Flux"SrcPort 1Points [25, 0]Branch DstBlock "Math\nFunction"DstPort 1



Branch

Points [0, 40; 170, 0]DstBlock "Sum2"DstPort 2

Line SrcBlock "Math\nFunction"

SrcPort 1Points [25, 0; 0, -25]



Branch Points [0, -50]DstBlock "Dot Product"DstPort 2


Line SrcBlock "Gain"

SrcPort 1Points [35, 0]DstBlock "Dot Product"DstPort 1

Line SrcBlock "Dot Product"SrcPort 1Points [0, 0; 55, 0]Branch Points [-5, 0]DstBlock "Dot Product1"DstPort 2

Branch DstBlock "isq"DstPort 1

Line SrcBlock "Gain1"SrcPort 1DstBlock "Dot Product1"DstPort 1

Line SrcBlock "T"SrcPort 1DstBlock "Gain"DstPort 1

Line SrcBlock "Dot Product1"SrcPort 1DstBlock "slip"DstPort 1

Line

SrcBlock "Gain2"SrcPort 1DstBlock "Derivative"DstPort 1

Line SrcBlock "Derivative"SrcPort 1DstBlock "Sum2"DstPort 1

Line SrcBlock "Dot Product2"

SrcPort 1DstBlock "isd"



DstPort 1Line SrcBlock "Sum2"SrcPort 1Points [45, 0; 0, 20]DstBlock "Dot Product2"DstPort 1

Line SrcBlock "Constant1"SrcPort 1

Points [85, 0; 0, -60]DstBlock "Dot Product2"DstPort 2

Block BlockType SubSystemName "Subsystem3"Ports [2, 3]Position [605, 185, 645, 245]Orientation "left"TreatAsAtomicUnit off

System Name "Subsystem3"Location [436, 127, 909, 413]Open offModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"Block BlockType InportName "In1"Position [80, 38, 110, 52]

Block BlockType InportName "In2"Position [115, 143, 145, 157]Port "2"


Name "Gain1"Position [215, 28, 255, 52]Gain "1.0001"


Block BlockType GainName "Gain2"

Position [215, 83, 255, 107]Gain "-0.5"





Block BlockType SumName "Ib2"Ports [2, 1]Position [375, 102, 395, 138]





Line SrcBlock "In1"SrcPort 1Points [0, 0; 15, 0]Branch Points [70, 0]DstBlock "Gain1"DstPort 1

Branch Points [0, 50]Branch


Branch


Line



SrcBlock "In2"SrcPort 1Points [0, 0; 15, 0]Branch DstBlock "Gain8"DstPort 1


Line SrcBlock "Gain2"SrcPort 1Points [50, 0; 0, 15]DstBlock "Ib2"DstPort 1

Line SrcBlock "Gain8"SrcPort 1Points [50, 0; 0, -20]DstBlock "Ib2"

DstPort 2Line SrcBlock "Gain9"SrcPort 1Points [50, 0; 0, -5]DstBlock "Ib3"DstPort 1


Line SrcBlock "Gain1"SrcPort 1DstBlock "Out1"DstPort 1

Line SrcBlock "Ib2"SrcPort 1

DstBlock "Out2"DstPort 1Line SrcBlock "Ib3"SrcPort 1DstBlock "Out3"DstPort 1


Name "Subsystem4"Ports [2, 3]



Position [345, 50, 385, 110]TreatAsAtomicUnit offSystem

Name "Subsystem4"Location [436, 127, 909, 413]Open offModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"

PaperUnits "inches"ZoomFactor "100"Block BlockType InportName "In1"Position [80, 38, 110, 52]

Block BlockType InportName "In2"Position [115, 143, 145, 157]Port "2"





Block



Block BlockType Sum

Name "Ib3"Ports [2, 1]



Position [375, 187, 395, 223]Block BlockType OutportName "Out1"Position [280, 33, 310, 47]



Line SrcBlock "In1"SrcPort 1Points [0, 0; 15, 0]Branch Points [70, 0]


Branch Points [0, 50]Branch


Branch


Line SrcBlock "In2"SrcPort 1Points [0, 0; 15, 0]Branch DstBlock "Gain8"DstPort 1

Branch


Line SrcBlock "Gain2"SrcPort 1Points [50, 0; 0, 15]DstBlock "Ib2"DstPort 1

Line




Points [50, 0; 0, -20]DstBlock "Ib2"DstPort 2


Line


Line SrcBlock "Gain1"SrcPort 1DstBlock "Out1"DstPort 1

Line

SrcBlock "Ib2"SrcPort 1DstBlock "Out2"DstPort 1

Line SrcBlock "Ib3"SrcPort 1DstBlock "Out3"DstPort 1

Block BlockType SubSystemName "Subsystem5"Ports [3, 2]Position [240, 48, 280, 112]TreatAsAtomicUnit offSystem

Name "Subsystem5"Location [468, 82, 922, 447]Open offModelBrowserVisibility offModelBrowserWidth 200

ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"Block BlockType InportName "iq"Position [25, 113, 55, 127]


Name "id"Position [25, 23, 55, 37]



Port "2"Block BlockType InportName "fp"Position [25, 243, 55, 257]Port "3"

Block BlockType ReferenceName "Dot Product"Ports [2, 1]

Position [245, 46, 275, 79]SourceBlock "simulink/Math\nOperations/Dot Product"SourceType "Dot Product"

Block BlockType ReferenceName "Dot Product1"Ports [2, 1]Position [245, 136, 275, 169]SourceBlock "simulink/Math\nOperations/Dot Product"SourceType "Dot Product"

Block

BlockType ReferenceName "Dot Product2"Ports [2, 1]Position [260, 201, 290, 234]SourceBlock "simulink/Math\nOperations/Dot Product"SourceType "Dot Product"

Block BlockType ReferenceName "Dot Product3"Ports [2, 1]Position [260, 251, 290, 284]SourceBlock "simulink/Math\nOperations/Dot Product"SourceType "Dot Product"


Block BlockType SumName "Sum2"Ports [2, 1]Position [350, 210, 370, 230]ShowName offIconShape "round"Inputs "|++"InputSameDT offOutDataTypeMode "Inherit via internal rule"

Block

BlockType TrigonometryName "Trigonometric\nFunction"



Ports [1, 1]Position [165, 145, 195, 175]

Block BlockType TrigonometryName "Trigonometric\nFunction1"Ports [1, 1]Position [170, 55, 200, 85]Operator "cos"


Name "Out1"Position [395, 98, 425, 112]


Line SrcBlock "fp"SrcPort 1Points [5, 0; 0, 5; 25, 0; 0, -95]

Branch DstBlock "Trigonometric\nFunction"DstPort 1

Branch Points [0, -90]DstBlock "Trigonometric\nFunction1"DstPort 1

Line SrcBlock "id"SrcPort 1Points [0, 0; 80, 0]Branch Points [0, 230]DstBlock "Dot Product3"DstPort 1

Branch Points [90, 0]DstBlock "Dot Product"DstPort 1

Line SrcBlock "iq"SrcPort 1Points [0, 0; 70, 0]Branch Points [0, 105]DstBlock "Dot Product2"DstPort 2

Branch Points [90, 0; 0, 25]DstBlock "Dot Product1"DstPort 1



Line SrcBlock "Dot Product3"SrcPort 1Points [65, 0]DstBlock "Sum2"DstPort 2

Line SrcBlock "Dot Product2"SrcPort 1DstBlock "Sum2"DstPort 1

Line SrcBlock "Dot Product1"SrcPort 1Points [80, 0]DstBlock "Sum1"DstPort 2

Line SrcBlock "Trigonometric\nFunction"SrcPort 1Points [0, 0; 5, 0]Branch

DstBlock "Dot Product1"DstPort 2

Branch Points [0, 115]DstBlock "Dot Product3"DstPort 2

Line SrcBlock "Dot Product"SrcPort 1Points [55, 0]DstBlock "Sum1"DstPort 1

Line SrcBlock "Trigonometric\nFunction1"SrcPort 1Points [0, 0; 15, 0]Branch DstBlock "Dot Product"DstPort 2

Branch

Points [0, 140]DstBlock "Dot Product2"DstPort 1

Line SrcBlock "Sum1"SrcPort 1DstBlock "Out1"DstPort 1


SrcPort 1DstBlock "Out2"



DstPort 1

Block BlockType SumName "Sum"Ports [2, 1]Position [235, 305, 265, 335]Orientation "up"ShowName offIconShape "round"

Inputs "+|+"InputSameDT offOutDataTypeMode "Inherit via internal rule"

Block BlockType SumName "Sum1"Ports [2, 1]Position [460, 35, 480, 55]ShowName offIconShape "round"Inputs "|+-"InputSameDT off

OutDataTypeMode "Inherit via internal rule"Block BlockType SumName "Sum2"Ports [2, 1]Position [480, 70, 500, 90]ShowName offIconShape "round"Inputs "|+-"InputSameDT offOutDataTypeMode "Inherit via internal rule"


Line

SrcBlock "Induction Machine"SrcPort 4Points [0, 0; 15, 0]Branch

Points [20, 0; 0, 250]DstBlock "Gain3"DstPort 1

Branch

Points [0, 145]DstBlock "Scope"DstPort 1

Line



SrcBlock "Subsystem1"SrcPort 2Points [20, 0; 0, 240]DstBlock "Integrator1"DstPort 1

Line SrcBlock "Signal\nGenerator"SrcPort 1DstBlock "Subsystem1"DstPort 1

Line SrcBlock "Rotor Flux"SrcPort 1Points [15, 0; 0, -50]DstBlock "Subsystem1"DstPort 2

Line SrcBlock "Subsystem4"SrcPort 1Points [15, 0; 0, -15]DstBlock "Sum1"DstPort 1

Line SrcBlock "Sum1"SrcPort 1DstBlock "Relay"DstPort 1

Line SrcBlock "Relay"SrcPort 1Points [55, 0]DstBlock "Induction Machine"DstPort 1

Line SrcBlock "Subsystem4"SrcPort 2DstBlock "Sum2"DstPort 1



Line SrcBlock "Subsystem4"SrcPort 3Points [20, 0; 0, 30]DstBlock "Sum3"DstPort 1

Line



SrcBlock "Gain3"SrcPort 1DstBlock "Integrator2"DstPort 1

Line SrcBlock "Induction Machine"SrcPort 1Points [90, 0; 0, 35; 5, 0]Branch

DstBlock "Subsystem"DstPort 2

Branch

Points [0, 140]DstBlock "Subsystem3"DstPort 1

Line SrcBlock "Induction Machine"SrcPort 2Points [0, 10; 75, 0]Branch

Points [30, 0; 0, 60]

DstBlock "Subsystem"DstPort 4

Branch

Points [0, 180]DstBlock "Subsystem3"DstPort 2

Line SrcBlock "Induction Machine"SrcPort 3Points [175, 0]DstBlock "Subsystem"DstPort 1

Line SrcBlock "Induction Machine"SrcPort 6Points [175, 0]DstBlock "Subsystem"DstPort 3

Line SrcBlock "Relay1"

SrcPort 1DstBlock "Induction Machine"DstPort 2

Line SrcBlock "Relay2"SrcPort 1Points [35, 0; 0, -10; 15, 0]DstBlock "Induction Machine"DstPort 3

Line SrcBlock "Integrator1"

SrcPort 1DstBlock "Sum"



DstPort 1Line SrcBlock "Integrator2"SrcPort 1DstBlock "Sum"DstPort 2

Line SrcBlock "Subsystem3"SrcPort 1Points [-130, 0]


Line SrcBlock "Subsystem3"SrcPort 2Points [-110, 0]DstBlock "Sum2"DstPort 2

Line SrcBlock "Subsystem3"SrcPort 3

Points [-85, 0]DstBlock "Sum3"DstPort 2

Line SrcBlock "Subsystem1"SrcPort 3Points [50, 0; 0, -20]DstBlock "Subsystem5"DstPort 2

Line SrcBlock "Subsystem5"SrcPort 1DstBlock "Subsystem4"DstPort 1

Line SrcBlock "Subsystem5"SrcPort 2DstBlock "Subsystem4"DstPort 2

Line SrcBlock "Subsystem1"

SrcPort 1DstBlock "Subsystem5"DstPort 1

Line SrcBlock "Sum"SrcPort 1Points [0, -120; -25, 0]DstBlock "Subsystem5"DstPort 3

Line SrcBlock "Induction Machine"

SrcPort 8Points [20, 0; 0, 100]



DstBlock "Scope"DstPort 2



DIRECT TORQUE CONTROL OF IM

If a three phase VSI is connected to an IM, there can be eight possible

configurations of six switching devices within the inverter. As a result, there are

eight possible input voltage vectors to the IM. The eight voltage vectors, two of

which are zero vectors, are shown in Fig 1.

DTC utilises the eight possible stator voltage vectors, to control the stator

flux and torque to follow the reference values within the hysteresis bands. The

voltage space vector of a three-phase system is given by:

( ) π=++=

(1)

vsA, vsB, and vsC are the instantaneous phase voltages.

For the switching VSI, it can be shown that for a DC link voltage of Vd, the

voltage space vector is given by:

( ) π=++=

(2)

Sa(t), Sb(t) and Sc(t) are the switching functions of each leg of the VSI, such that

Swhen upper switch is on

whenlower switch is oni =

1

0

Figure 1. Voltage vectors for 3-phase VSI

Direct Flux Control

The IM stator voltage equation is given by:

ψ += (3)

Where v i ands s s, , ψ are the stator voltage, current and stator flux space vectors

respectively. According to equation (3), if the stator resistance is small and can

be neglected, the change in stator flux, ∆ψ s , will follow the stator voltage, i.e.

∆ ∆ψ s sv t= (4)



This simply means that the tip of the stator flux will follow that of the stator

voltage space vector multiplied by the small change in time. Hence if the stator

flux space vector (magnitude and angle) is known, its locus can be controlled by

selecting appropriate stator voltage vectors. In DTC the stator flux space vector

is obtained by calculation utilizing the motor terminal variables (stator voltages

and currents). The stator flux is forced to follow the reference value within a

hysteresis band by selecting the appropriate stator voltage vector using the

hysteresis comparator and selection table.

Direct Torque Control

As shown by Takahashi and Noguchi [1], under a condition of a constant mechanical

frequency and stator flux magnitude, when a step increase in the stator angular

frequency is applied at t=0, the rate of change of torque at time t=0 is

proportional to the slip frequency of the stator flux . Thus,

dT

dt tsl t

==

00

α ω (5)

where ωsl is the instantaneous angular slip frequency

If the torque and stator flux is kept within their hysteresis bands by selecting

appropriate voltage vectors, an independent control over the torque and stator flux

is accomplished. If the stator flux space vector plane is divided into six sectors

or segments (Figure 2), a set of table or rules of which voltage vector should be

chosen in a particular sector (either to increase stator flux or to reduce stator

flux and either to increase torque or to reduce torque) can be constructed; such

table is given by Table 1.

Figure 2 Six sectors of stator flux plane



vs,3

vs,3

vs,3

vs,2

vs,4

vs,4

vs,3

vs,2

vs,6

vs,5

vs,4

vs,1

Table 1 Voltage vectors look-up table.

! "

" ""

"

""

! "

" ""

"

""

Figure 3 Flux control within the hysteresis band

Figure 4 Basic DTC

#$ %&'&%()*+,'-.)*-//0))*0)/)1))2)-()3.45678

Sector I

Sector II

ψ ψψ ψ

θθθθψ ψψ ψ

ψ ψψ ψ



Model Name "DTC_hysteresis"Version 5.0SaveDefaultBlockParams onSampleTimeColors offLibraryLinkDisplay "none"WideLines offShowLineDimensions offShowPortDataTypes offShowLoopsOnError onIgnoreBidirectionalLines offShowStorageClass off


MinMaxOverflowArchiveMode "Overwrite"BlockNameDataTip offBlockParametersDataTip offBlockDescriptionStringDataTip offToolBar onStatusBar onBrowserShowLibraryLinks offBrowserLookUnderMasks offCreated "Tue Oct 01 11:07:25 2002"UpdateHistory "UpdateHistoryNever"ModifiedByFormat "%<Auto>"LastModifiedBy "Administrator"ModifiedDateFormat "%<Auto>"LastModifiedDate "Mon Aug 09 11:36:28 2004"ModelVersionFormat "1.%<AutoIncrement:16>"ConfigurationManager "none"SimParamPage "Solver"LinearizationMsg "none"Profile offParamWorkspaceSource "MATLABWorkspace"AccelSystemTargetFile "accel.tlc"AccelTemplateMakefile "accel_default_tmf"AccelMakeCommand "make_rtw"TryForcingSFcnDF offExtModeMexFile "ext_comm"





ExtModeArmWhenConnect onExtModeSkipDownloadWhenConnect offExtModeLogAll onExtModeAutoUpdateStatusClock onBufferReuse onRTWExpressionDepthLimit 5SimulationMode "normal"Solver "ode5"SolverMode "Auto"StartTime "0.0"StopTime "1000"MaxOrder 5

MaxStep "0.0001"MinStep "0.00001"MaxNumMinSteps "-1"InitialStep "0.00001"FixedStep "1e-6"RelTol "1e-3"AbsTol "auto"OutputOption "RefineOutputTimes"OutputTimes "[]"Refine "1"LoadExternalInput offExternalInput "[t, u]"LoadInitialState off

InitialState "xInitial"SaveTime onTimeSaveName "t"SaveState offStateSaveName "xout"SaveOutput onOutputSaveName "yout"SaveFinalState offFinalStateName "xFinal"SaveFormat "Array"Decimation "1"LimitDataPoints onMaxDataPoints "10000000"SignalLoggingName "sigsOut"ConsistencyChecking "none"ArrayBoundsChecking "none"AlgebraicLoopMsg "warning"BlockPriorityViolationMsg "warning"MinStepSizeMsg "warning"InheritedTsInSrcMsg "warning"DiscreteInheritContinuousMsg "warning"MultiTaskRateTransMsg "error"SingleTaskRateTransMsg "none"CheckForMatrixSingularity "none"IntegerOverflowMsg "warning"


RTWInlineParameters offBlockReductionOpt off



BooleanDataType offConditionallyExecuteInputs onParameterPooling onOptimizeBlockIOStorage onZeroCross onAssertionControl "UseLocalSettings"ProdHWDeviceType "Microprocessor"ProdHWWordLengths "8,16,32,32"RTWSystemTargetFile "grt.tlc"RTWTemplateMakefile "grt_default_tmf"RTWMakeCommand "make_rtw"RTWGenerateCodeOnly off






Block BlockType FcnExpr "sin(u[1])"

Block BlockType GainGain "1"Multiplication "Element-wise(K.*u)"ShowAdditionalParam offParameterDataTypeMode "Same as input"ParameterDataType "sfix(16)"ParameterScalingMode "Best Precision: Matrix-wise"ParameterScaling "2^0"OutDataTypeMode "Same as input"

OutDataType "sfix(16)"OutScaling "2^0"LockScale offRndMeth "Floor"SaturateOnIntegerOverflow on

Block BlockType InportPort "1"PortDimensions "-1"SampleTime "-1"ShowAdditionalParam offLatchInput off

DataType "auto"OutDataType "sfix(16)"



OutScaling "2^0"SignalType "auto"SamplingMode "auto"Interpolate on

Block BlockType IntegratorExternalReset "none"InitialConditionSource "internal"InitialCondition "0"LimitOutput offUpperSaturationLimit "inf"

LowerSaturationLimit "-inf"ShowSaturationPort offShowStatePort offAbsoluteTolerance "auto"ZeroCross on

Block BlockType MuxInputs "4"DisplayOption "none"


Port "1"OutputWhenDisabled "held"InitialOutput "[]"

Block BlockType RelayOnSwitchValue "eps"OffSwitchValue "eps"OnOutputValue "1"OffOutputValue "0"ShowAdditionalParam offOutputDataTypeScalingMode "All ports same datatype"OutDataType "sfix(16)"OutScaling "2^0"ConRadixGroup "Use specified scaling"ZeroCross on

Block BlockType ScopeFloating offModelBased offTickLabels "OneTimeTick"ZoomMode "on"Grid "on"TimeRange "auto"

YMin "-5"YMax "5"SaveToWorkspace offSaveName "ScopeData"LimitDataPoints onMaxDataPoints "5000"Decimation "1"SampleInput offSampleTime "0"

Block BlockType "S-Function"FunctionName "system"

PortCounts "[]"SFunctionModules "''"



Block BlockType SignalGeneratorWaveForm "sine"Amplitude "1"Frequency "1"Units "Hertz"VectorParams1D on

Block BlockType StepTime "1"

Before "0"After "1"SampleTime "-1"VectorParams1D onZeroCross on

Block BlockType SubSystemShowPortLabels onPermissions "ReadWrite"RTWSystemCode "Auto"RTWFcnNameOpts "Auto"RTWFileNameOpts "Auto"

SimViewingDevice offDataTypeOverride "UseLocalSettings"MinMaxOverflowLogging "UseLocalSettings"

Block BlockType SumIconShape "rectangular"Inputs "++"ShowAdditionalParam offInputSameDT onOutDataTypeMode "Same as first input"OutDataType "sfix(16)"OutScaling "2^0"LockScale offRndMeth "Floor"SaturateOnIntegerOverflow on

AnnotationDefaults

HorizontalAlignment "center"VerticalAlignment "middle"ForegroundColor "black"BackgroundColor "white"DropShadow offFontName "Helvetica"

FontSize 10FontWeight "normal"FontAngle "normal"

LineDefaults


System

Name "DTC_hysteresis"Location [2, 74, 1014, 724]

Open onModelBrowserVisibility off



ModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"ReportName "simulink-default.rpt"Block BlockType SubSystemName "Induction Machine"Ports [3, 8]

Position [160, 63, 215, 192]TreatAsAtomicUnit offMaskPromptString "Stator resistance (ohm)|Rotor resistance (ohm)|"

"Stator self inductance (H)|Rotor self inductance (H)|Mutual Inductance (H)|No"" of poles|Moment of inertia (kg.m^2)|Load torque (Nm)"

MaskStyleString "edit,edit,edit,edit,edit,edit,edit,edit"MaskTunableValueString "on,on,on,on,on,on,on,on"MaskCallbackString "|||||||"MaskEnableString "on,on,on,on,on,on,on,on"MaskVisibilityString "on,on,on,on,on,on,on,on"MaskToolTipString "on,on,on,on,on,on,on,on"MaskVarAliasString ",,,,,,,"MaskVariables "Rs=@1;Rr=@2;Ls=@3;Lr=@4;Lm=@5;pole=@6;J=@7;Tloa"

"d=@8;"MaskIconFrame onMaskIconOpaque onMaskIconRotate "none"MaskIconUnits "autoscale"MaskValueString "5.5|4.51|306.5e-3|306.5e-3|291.9e-3|4|0.03|1"System

Name "Induction Machine"Location [175, 176, 935, 636]Open offModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"Block BlockType InportName "Va"Position [25, 40, 45, 60]


Name "Vb"Position [25, 120, 45, 140]Port "2"

Block BlockType InportName "Vc"Position [25, 240, 45, 260]Port "3"

Block BlockType GainName "1/J"




Gain "1/J"SaturateOnIntegerOverflow off

Block BlockType GainName "1/J1"Position [295, 347, 320, 373]Gain "0.05"SaturateOnIntegerOverflow off


Name "3to2"Ports [3, 2]Position [105, 81, 135, 139]ShowPortLabels offTreatAsAtomicUnit offSystem Name "3to2"Location [4, 42, 628, 468]Open offModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"

PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"Block


Block


Block


Block

BlockType GainName "Gain3"Position [120, 248, 160, 272]

Gain "0.577"Block


Block


Block




Block


Block


Block


Block


Block

BlockType OutportName "q"Position [310, 250, 330, 270]Port "2"InitialOutput "0"

Line

SrcBlock "Ib1"SrcPort 1Points [15, 0; 0, -35]DstBlock "d"DstPort 1

Line

SrcBlock "Gain7"SrcPort 1Points [30, 0; 0, 20]DstBlock "Ib1"DstPort 1

Line SrcBlock "in_1"SrcPort 1Points [40, 0; 0, 15]DstBlock "Gain7"DstPort 1

Line

SrcBlock "Gain6"SrcPort 1Points [30, 0; 0, -90]DstBlock "Ib1"

DstPort 2




Line

SrcBlock "in_3"SrcPort 1Points [40, 0; 0, 5]Branch



Line

SrcBlock "in_2"SrcPort 1Points [20, 0; 0, 30]



Line


Line

SrcBlock "Gain4"SrcPort 1Points [30, 0; 0, -40]DstBlock "Ib"DstPort 2

Line

SrcBlock "Ib"

SrcPort 1DstBlock "q"DstPort 1





Name "Gain1"Position [150, 407, 175, 433]Orientation "left"Gain "2/pole"

Block BlockType SubSystemName "IM1"Ports [1, 1]Position [320, 106, 380, 134]TreatAsAtomicUnit offSystem

Name "IM1"Location [248, 340, 468, 422]Open offModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"Block

BlockType Inport

Name "In1"Position [25, 33, 55, 47]

Block


Block

BlockType OutportName "Out1"Position [165, 33, 195, 47]InitialOutput "0"

Line


Line

SrcBlock "S-Function"

SrcPort 1DstBlock "Out1"DstPort 1


Block BlockType Mux



Name "Mux"Ports [3, 1]Position [260, 104, 290, 136]Inputs "3"

Block BlockType SumName "Sum"Ports [2, 1]Position [440, 287, 460, 323]Orientation "left"Inputs "+-"

Block BlockType OutportName "isd"Position [630, 25, 650, 45]InitialOutput "0"

Block BlockType OutportName "isq"Position [625, 70, 645, 90]Port "2"InitialOutput "0"

Block BlockType OutportName "ird"Position [600, 140, 620, 160]Port "3"InitialOutput "0"

Block BlockType OutportName "speed"Position [90, 410, 110, 430]Orientation "left"Port "4"InitialOutput "0"

Block BlockType OutportName "Vd"Position [265, 50, 285, 70]Port "5"InitialOutput "0"


Name "irq"Position [595, 185, 615, 205]Port "6"InitialOutput "0"





Name "Te"Position [715, 230, 735, 250]Port "8"InitialOutput "0"


Line SrcBlock "Demux"SrcPort 2Points [65, 0; 0, -75]DstBlock "isd"DstPort 1

Line SrcBlock "3to2"SrcPort 2Points [0, 0]Branch Points [0, 170]

DstBlock "Vq"DstPort 1

Branch Points [55, 0; 0, -15]DstBlock "Mux"DstPort 1

Line SrcBlock "3to2"SrcPort 1Points [0, 0; 25, 0]Branch Points [0, -35]DstBlock "Vd"DstPort 1

Branch Points [30, 0; 0, 25]DstBlock "Mux"DstPort 2

Line

SrcBlock "Demux"SrcPort 5Points [45, 0; 0, 145]Branch Points [0, 15; -35, 0]DstBlock "Sum"DstPort 1


Line



SrcBlock "Vc"SrcPort 1Points [20, 0; 0, -120]DstBlock "3to2"DstPort 3

Line SrcBlock "Vb"SrcPort 1Points [20, 0; 0, -20]DstBlock "3to2"DstPort 2

Line SrcBlock "Va"SrcPort 1Points [20, 0; 0, 40]DstBlock "3to2"DstPort 1

Line SrcBlock "1/J"SrcPort 1Points [0, 0; -25, 0]Branch

Points [0, -175]DstBlock "Mux"DstPort 3

Branch Points [-15, 0; 0, 115]DstBlock "Gain1"DstPort 1

Line SrcBlock "Mux"SrcPort 1DstBlock "IM1"DstPort 1

Line SrcBlock "IM1"SrcPort 1DstBlock "Demux"DstPort 1

Line SrcBlock "Sum"SrcPort 1

DstBlock "Integrator"DstPort 1Line SrcBlock "Integrator"SrcPort 1DstBlock "1/J"DstPort 1

Line SrcBlock "1/J1"SrcPort 1Points [190, 0; 0, -45]

DstBlock "Sum"DstPort 2



Line SrcBlock "Demux"SrcPort 3Points [30, 0; 0, 75]DstBlock "irq"DstPort 1

Line SrcBlock "Demux"SrcPort 4Points [25, 0; 0, 20]

DstBlock "ird"DstPort 1

Line SrcBlock "Gain1"SrcPort 1Points [0, 0; -10, 0]Branch DstBlock "speed"DstPort 1

Branch Points [0, -60]

DstBlock "1/J1"DstPort 1

Annotation Name "q"Position [482, 87]VerticalAlignment "top"

Block BlockType "S-Function"Name "S-Function2"Ports [1, 1]Position [220, 355, 270, 375]Orientation "left"FunctionName "flxp2"

Block BlockType ScopeName "Scope"Ports [3]Position [560, 214, 590, 246]Location [249, 259, 660, 649]

Open onNumInputPorts "3"ZoomMode "yonly"List

ListType AxesTitlesaxes1 "%<SignalLabel>"axes2 "%<SignalLabel>"axes3 "%<SignalLabel>"

List

ListType SelectedSignalsaxes1 ""axes2 ""

axes3 ""



TimeRange "0.1"YMin "-0.1~-20~-15"YMax "2~20~15"DataFormat "StructureWithTime"

Block BlockType ScopeName "Scope1"Ports [1]Position [560, 144, 590, 176]Location [667, 408, 991, 647]Open on

NumInputPorts "1"ZoomMode "yonly"List

ListType AxesTitlesaxes1 "%<SignalLabel>"

List

ListType SelectedSignalsaxes1 ""

TimeRange "0.01"YMin "-0.1"YMax "2"

SaveName "ScopeData1"DataFormat "StructureWithTime"

Block BlockType ScopeName "Scope2"Ports [1]Position [325, 184, 355, 216]Location [667, 110, 991, 349]Open onNumInputPorts "1"ZoomMode "yonly"List

ListType AxesTitlesaxes1 "%<SignalLabel>"

List

ListType SelectedSignalsaxes1 ""

TimeRange "0.01"YMin "-20"YMax "20"SaveName "ScopeData2"DataFormat "StructureWithTime"

Block BlockType SignalGeneratorName "Signal\nGenerator"Position [640, 320, 670, 350]Orientation "left"WaveForm "square"Amplitude "-15"Frequency "15"

Block BlockType StepName "Step"




Time "0.001"After "1.2"

Block BlockType SubSystemName "Subsystem"Ports [3, 3]Position [110, 286, 160, 384]Orientation "left"TreatAsAtomicUnit offSystem

Name "Subsystem"

Location [230, 305, 670, 522]Open offModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"Block BlockType InportName "T,err"

Position [25, 35, 45, 55]Block BlockType InportName "Flx,err"Position [25, 105, 45, 125]Port "2"

Block BlockType InportName "Flx ang"Position [25, 160, 45, 180]Port "3"


Block BlockType MuxName "Mux"Ports [3, 1]

Position [100, 99, 130, 131]Inputs "3"Block BlockType "S-Function"Name "S-Function1"Ports [1, 1]Position [180, 105, 230, 125]FunctionName "select2"

Block BlockType OutportName "Sa"

Position [375, 25, 395, 45]InitialOutput "0"



Block BlockType OutportName "Sb"Position [395, 105, 415, 125]Port "2"InitialOutput "0"

Block BlockType OutportName "Sc"Position [350, 170, 370, 190]

Port "3"InitialOutput "0"

Line SrcBlock "Flx ang"SrcPort 1DstBlock "Mux"DstPort 3

Line SrcBlock "Demux"SrcPort 3Points [0, 55]

DstBlock "Sc"DstPort 1

Line SrcBlock "Flx,err"SrcPort 1DstBlock "Mux"DstPort 2

Line SrcBlock "Demux"SrcPort 2DstBlock "Sb"DstPort 1

Line SrcBlock "T,err"SrcPort 1DstBlock "Mux"DstPort 1

Line SrcBlock "Demux"SrcPort 1Points [0, -70]

DstBlock "Sa"DstPort 1Line SrcBlock "Mux"SrcPort 1DstBlock "S-Function1"DstPort 1

Line SrcBlock "S-Function1"SrcPort 1DstBlock "Demux"

DstPort 1



Block BlockType SumName "Sum2"Ports [2, 1]Position [510, 307, 530, 343]Orientation "left"Inputs "-+"

Block BlockType Sum

Name "Sum4"Ports [2, 1]Position [435, 380, 455, 400]Orientation "left"Inputs "+-"

Block BlockType SubSystemName "Voltage-controlled\nPWM-VSI1"Ports [3, 3]Position [70, 96, 100, 164]ShowPortLabels offTreatAsAtomicUnit off

System Name "Voltage-controlled\nPWM-VSI1"Location [-23, 85, 764, 579]Open offModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"Block BlockType InportName "in_5"Position [370, 60, 390, 80]Orientation "left"

Block BlockType InportName "in_6"Position [390, 155, 410, 175]Orientation "left"Port "2"

Block BlockType InportName "in_7"Position [395, 225, 415, 245]Orientation "left"Port "3"

Block BlockType GainName "Gain1"Position [290, 152, 315, 178]Orientation "left"Gain "240"

Block



BlockType GainName "Gain2"Position [295, 222, 320, 248]Orientation "left"Gain "240"

Block BlockType GainName "Gain3"Position [285, 57, 310, 83]Orientation "left"Gain "240"

Block BlockType OutportName "out_1"Position [160, 60, 180, 80]Orientation "left"InitialOutput "0"

Block BlockType OutportName "out_2"Position [165, 155, 185, 175]Orientation "left"

Port "2"InitialOutput "0"

Block BlockType OutportName "out_3"Position [175, 225, 195, 245]Orientation "left"Port "3"InitialOutput "0"

Line SrcBlock "in_5"SrcPort 1DstBlock "Gain3"DstPort 1

Line SrcBlock "in_6"SrcPort 1DstBlock "Gain1"DstPort 1

Line SrcBlock "in_7"

SrcPort 1DstBlock "Gain2"DstPort 1

Line SrcBlock "Gain3"SrcPort 1DstBlock "out_1"DstPort 1

Line SrcBlock "Gain1"SrcPort 1

DstBlock "out_2"DstPort 1



Line SrcBlock "Gain2"SrcPort 1DstBlock "out_3"DstPort 1

Block BlockType RelayName "flux\nhysterisis"

Position [335, 378, 365, 402]Orientation "left"OnSwitchValue "0.01"OffSwitchValue "-0.01"

Block BlockType SubSystemName "stator flux - voltage model"Ports [4, 4]Position [345, 15, 415, 145]TreatAsAtomicUnit offMaskPromptString "Stator resistance"MaskStyleString "edit"

MaskTunableValueString "on"MaskEnableString "on"MaskVisibilityString "on"MaskToolTipString "on"MaskVariables "Rs=@1;"MaskIconFrame onMaskIconOpaque onMaskIconRotate "none"MaskIconUnits "autoscale"MaskValueString "5.5"System

Name "stator flux - voltage model"Location [160, 288, 765, 529]Open offModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"Block BlockType InportName "vd"

Position [50, 33, 80, 47]Block BlockType InportName "id"Position [40, 98, 70, 112]Port "2"

Block BlockType InportName "vq"Position [60, 143, 90, 157]Port "3"

Block



BlockType InportName "iq"Position [25, 193, 55, 207]Port "4"

Block BlockType SubSystemName "Cartesian to Polar"Ports [2, 2]Position [420, 92, 455, 143]ShowPortLabels offTreatAsAtomicUnit off

MaskType "[x,y]->[r,theta]"MaskDescription "Tranformation from cartesian to polar\ncoor"

"dinates.\nr=sqrt(x^2+y^2), theta=atan(y/x)"MaskHelp "Unmask this block for more help."MaskDisplay "plot(0,0,100,100,[24,20,15,20,20],[85,95,85"

",95,20],[80,20,95,85,95,85],[70,20,20,15,20,24],[56,56,55,52,50,46],[20,26,31"",35,38,42])"

MaskIconFrame onMaskIconOpaque onMaskIconRotate "none"MaskIconUnits "autoscale"System Name "Cartesian to Polar"

Location [0, 0, 359, 206]Open offModelBrowserVisibility offModelBrowserWidth 200ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"Block

BlockType InportName "x"Position [20, 70, 40, 90]

Block

BlockType InportName "y"Position [20, 129, 40, 151]Port "2"

Block

BlockType MuxName "Mux"Ports [2, 1]

Position [75, 96, 105, 129]Inputs "2"Block

BlockType FcnName "x->r"Position [155, 72, 260, 98]Expr "hypot(u[1],u[2])"

Block

BlockType FcnName "x->theta"Position [160, 129, 265, 151]

Expr "atan2(u[2],u[1])"



Block BlockType OutportName "r"Position [295, 75, 315, 95]InitialOutput "0"

Block

BlockType OutportName "theta"Position [295, 130, 315, 150]Port "2"InitialOutput "0"

Line

SrcBlock "x->theta"SrcPort 1DstBlock "theta"DstPort 1

Line

SrcBlock "y"SrcPort 1DstBlock "Mux"DstPort 2

Line SrcBlock "x"SrcPort 1DstBlock "Mux"DstPort 1

Line

SrcBlock "x->r"SrcPort 1DstBlock "r"DstPort 1

Line

SrcBlock "Mux"SrcPort 1Points [15, 0]Branch Points [0, 25]DstBlock "x->theta"DstPort 1

Branch Points [0, -30]DstBlock "x->r"DstPort 1

Annotation

Name "Cartesian to Polar"Position [167, 37]VerticalAlignment "top"

Block BlockType GainName "Gain2"Position [170, 167, 195, 193]

Gain "Rs"



Block BlockType GainName "Gain3"Position [170, 112, 195, 138]Gain "Rs"

Block BlockType IntegratorName "Integrator"Ports [1, 1]Position [315, 85, 345, 115]


Block BlockType SumName "Sum6"Ports [2, 1]Position [240, 90, 260, 110]Inputs "+-"

Block BlockType SumName "Sum7"Ports [2, 1]Position [240, 145, 260, 165]Inputs "+-"

Block BlockType OutportName "flxsdv"Position [500, 28, 530, 42]

Block BlockType OutportName "flxsv"Position [550, 88, 580, 102]Port "2"InitialOutput "0"

Block BlockType OutportName "angflxsv"Position [480, 123, 510, 137]Port "3"InitialOutput "0"

Block BlockType OutportName "flxsqv"Position [435, 203, 465, 217]Port "4"

Line SrcBlock "Sum6"SrcPort 1DstBlock "Integrator"DstPort 1




SrcPort 1DstBlock "Integrator1"DstPort 1


Line

SrcBlock "Gain2"SrcPort 1Points [0, -10]DstBlock "Sum7"DstPort 2

Line SrcBlock "vd"SrcPort 1Points [60, 0; 0, 55]DstBlock "Sum6"DstPort 1

Line SrcBlock "Integrator"SrcPort 1Points [0, 5; 25, 0]Branch DstBlock "Cartesian to Polar"DstPort 1

Branch Points [0, -70]DstBlock "flxsdv"DstPort 1

Line SrcBlock "Integrator1"SrcPort 1Points [50, 0]Branch Points [0, -50]DstBlock "Cartesian to Polar"DstPort 2


DstBlock "flxsqv"DstPort 1

Line SrcBlock "Cartesian to Polar"SrcPort 1Points [75, 0]DstBlock "flxsv"DstPort 1

Line SrcBlock "id"





Line SrcBlock "Cartesian to Polar"SrcPort 2DstBlock "angflxsv"DstPort 1

Line SrcBlock "vq"SrcPort 1


Line SrcBlock "iq"SrcPort 1Points [0, -20]DstBlock "Gain2"DstPort 1

Block

BlockType SubSystemName "torquehys"Ports [1, 1]Position [365, 300, 395, 350]Orientation "left"ShowPortLabels offTreatAsAtomicUnit offMaskPromptString "Hyst band"MaskStyleString "edit"MaskTunableValueString "on"MaskEnableString "on"MaskVisibilityString "on"MaskToolTipString "on"MaskVariables "Th=@1;"MaskIconFrame onMaskIconOpaque onMaskIconRotate "none"MaskIconUnits "autoscale"MaskValueString "2"System

Name "torquehys"Location [50, 122, 340, 345]Open offModelBrowserVisibility offModelBrowserWidth 200

ScreenColor "white"PaperOrientation "landscape"PaperPositionMode "auto"PaperType "usletter"PaperUnits "inches"ZoomFactor "100"Block BlockType InportName "in_1"Position [275, 95, 295, 115]Orientation "left"

Block

BlockType RelayName "Relay"



Position [185, 58, 215, 82]Orientation "left"OnSwitchValue "Th/2"OffSwitchValue "0"

Block BlockType RelayName "Relay1"Position [185, 123, 215, 147]Orientation "left"OnSwitchValue "0"OffSwitchValue "-Th/2"

OnOutputValue "0"OffOutputValue "-1"

Block BlockType SumName "Sum3"Ports [2, 1]Position [55, 105, 75, 125]Orientation "left"

Block BlockType OutportName "out_1"

Position [15, 105, 35, 125]Orientation "left"InitialOutput "0"

Line SrcBlock "Sum3"SrcPort 1DstBlock "out_1"DstPort 1

Line SrcBlock "Relay1"SrcPort 1Points [-75, 0]DstBlock "Sum3"DstPort 2

Line SrcBlock "Relay"SrcPort 1Points [-65, 0]DstBlock "Sum3"DstPort 1

Line

SrcBlock "in_1"SrcPort 1Points [-20, 0]Branch Points [0, 30]DstBlock "Relay1"DstPort 1

Branch Points [-5, 0]DstBlock "Relay"DstPort 1



Line SrcBlock "Induction Machine"SrcPort 5Points [30, 0; 0, -100]DstBlock "stator flux - voltage model"DstPort 1

Line SrcBlock "Induction Machine"SrcPort 1Points [110, 0]

DstBlock "stator flux - voltage model"DstPort 2

Line SrcBlock "Induction Machine"SrcPort 2Points [70, 0; 0, 35]DstBlock "stator flux - voltage model"DstPort 4

Line SrcBlock "Induction Machine"SrcPort 7

Points [15, 0; 0, -70]DstBlock "stator flux - voltage model"DstPort 3

Line SrcBlock "stator flux - voltage model"SrcPort 3Points [40, 0; 0, 270]DstBlock "S-Function2"DstPort 1

Line SrcBlock "Induction Machine"SrcPort 8Points [20, 0; 0, 20]Branch

Points [0, 90; 140, 0]Branch Points [165, 0]DstBlock "Sum2"DstPort 1

Branch Points [0, -60]DstBlock "Scope"

DstPort 2Branch

DstBlock "Scope2"DstPort 1

Line SrcBlock "stator flux - voltage model"SrcPort 2Points [65, 0; 0, 95]Branch

Points [0, 60]Branch



Points [0, 165]DstBlock "Sum4"DstPort 1

Branch DstBlock "Scope"DstPort 1

Branch

DstBlock "Scope1"DstPort 1

Line SrcBlock "Voltage-controlled\nPWM-VSI1"SrcPort 1Points [20, 0; 0, -25]DstBlock "Induction Machine"DstPort 1

Line SrcBlock "Voltage-controlled\nPWM-VSI1"SrcPort 2DstBlock "Induction Machine"

DstPort 2Line SrcBlock "Voltage-controlled\nPWM-VSI1"SrcPort 3Points [20, 0; 0, 25]DstBlock "Induction Machine"DstPort 3

Line SrcBlock "Subsystem"SrcPort 1Points [-80, 0; 0, -195]DstBlock "Voltage-controlled\nPWM-VSI1"DstPort 1

Line SrcBlock "Subsystem"SrcPort 2Points [-70, 0; 0, -205]DstBlock "Voltage-controlled\nPWM-VSI1"DstPort 2

Line SrcBlock "Subsystem"

SrcPort 3Points [-60, 0; 0, -215]DstBlock "Voltage-controlled\nPWM-VSI1"DstPort 3

Line SrcBlock "flux\nhysterisis"SrcPort 1Points [-40, 0; 0, -55]DstBlock "Subsystem"DstPort 2

Line

SrcBlock "Sum4"SrcPort 1



DstBlock "flux\nhysterisis"DstPort 1

Line SrcBlock "Step"SrcPort 1DstBlock "Sum4"DstPort 2

Line SrcBlock "torquehys"SrcPort 1

Points [-60, 0; 0, -20]DstBlock "Subsystem"DstPort 1

Line SrcBlock "Sum2"SrcPort 1DstBlock "torquehys"DstPort 1

Line SrcBlock "Signal\nGenerator"SrcPort 1


Line SrcBlock "S-Function2"SrcPort 1DstBlock "Subsystem"DstPort 3

Line SrcBlock "Induction Machine"SrcPort 4Points [45, 0; 0, 120]DstBlock "Scope"DstPort 3

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