RBT Lab Manuval 11E608 CE

8/15/2019 RBT Lab Manuval 11E608 CE

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BANNARI AMMAN INSTITUTE OF TECHNOLOGY

(An Autonomous Institution Affiliated to Anna University-Chennai

Approved by AICTE - Accredited by NBA and NAAC with A! "rade#

SATHYAMANGALAM – 638 401 Erode Di!ri"! T#$i% N#d&

DE'ARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

LAB MANU(AL

11E608)CONTROL ENGINEERING LABORATORY

$% B&E& E'ECTICA' AN) E'ECT*NIC$ EN"INEEIN"

Ye#r o* Re%e#e +01,


2/106

BANNARI AMMAN INSTITUTE OF TECHNOLOGY

(An Autonomous Institution Affiliated to Anna University-Chennai

Approved by AICTE - Accredited by NBA and NAAC with A! "rade#SATHYAMANGALAM – 638 401 Erode Di!ri"! T#$i% N#d&

DE'ARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

LAB MANU(AL

11E608)CONTROL ENGINEERING LABORATORY

$% B&E& E'ECTICA' AN) E'ECT*NIC$ EN"INEEIN"

're-#red ./ A--roed ./

+&$enthilnathan )r&&$enthil,umar &'a,shmanan .*)/EEE

Ye#r o* Re%e#e +01,


3/106

R +011 11E608 Co2!ro% E2i2eeri2 L#.or#!or/

'ist of E0periments as per the syllabus

S%No N#$e o* !5e E-eri$e2!

1)etermination of transfer function of armature controlled )C motor&

2)etermination of transfer function of field controlled )C motor&

3 )etermination of transfer function of AC servo motor

4& )esi5n and simulation of $I$* transfer function with non linearity

6

)esi5n and simulation of transfer function of Type 7 8 and Type 7 1 systems for different

input si5nals

%)esi5n and simulate time response of a linear system

9

)esi5n and simulate fre:uency response of a lead networ,&

;


4/106

S%No N#$e o* !5e E-eri$e2! '#e No

1)etermination of transfer function of armature controlled )C

motor&

2 )etermination of transfer function of field controlled )C motor&

3 )etermination of transfer function of AC servo motor

4&)esi5n and simulation of $I$* transfer function with non-

linearity

6)esi5n and simulation of transfer function of Type 7 8 and Type

7 1 systems for different input si5nals

%)esi5n and simulate time response of a linear system whose

dampin5 ratio must be between 8&4 and 8&;

9 )esi5n and simulate fre:uency response of a lead networ,&

;


5/106

easurement of a@

DETERMINATION OF TRANSFER FUNCTION OF ARMATURE CONTROLLED DC

MOTOR


6/106

E- No 1 D#!e

AIM To find the Transfer function of )C otor with the control si5nal applied to Armature&

GENERAL OB7ECTI(ETo assess the )C motor performance usin5 transfer function

S'ECIFIC OB7ECTI(ES

1& Understand the two types of speed control&

2& ind the speed in terms of current&

3& )etermine the transfer functionA''ARATUS REUIRED

SNO A''ARATUS RANGE9 TY'E UANTITY

1 )C shunt motor - 12 ?oltmeter 8-388? /C 1

3 Ammeter 8-18A /C 1

4 Tachometer )i5ital 1

THEORY A )C machine can run as a motor= when a )C supply is 5iven to its field windin5

to produce ma5netic flu0 while the same )C source is used to supply current to the armature&

Now the armature becomes a current carryin5 conductor and as it is ,ept in a ma5netic field= it

develops mechanical force& The direction of the force is 5iven by lemin5s 'eft .and ule& )C

motor in control applications is used for deliverin5 mechanical power to control elements while

ta,in5 electrical control si5nal as input& Electrical input to )C motor is called control si5nal

and that can be applied in two ways& In one method= the control si5nal is applied to the field

windin5 while fi0ed volta5e is applied to armature windin5& This method is called ield

controlled motor& In another method= control si5nal is applied to armature windin5 and constant

volta5e is applied to field windin5& This method is called Armature controlled motor& .ere the

transfer function of armature controlled motor is to be found out&

easurement of 'a@


7/106

odel "raph@

DERI(ATION OF TRANSFER FUNCTION


8/106

Accordin5 to +irchhoffs ?olta5e 'aw (+?'#=

e' i? ba

aaadt

di++= a (1# The e0pression for bac, emf is

n/AC


9/106

)etermination of + a@

$l&No ?olta5e Across

armature = ?a

Armature

Current= Ia

$peed in

pm= N

w= rad/sec E b ? - Ia a

1& 194 8&9 1494 164&3% 1%6&3%

2& 163 8&9 131; 13;&82 161&2;

3& 144 8&9 1269 131&%3 139&2;

4& 138 8&9 1138 11;&3 123&2;

6& 128 8&9 1849 18>&%4 113&2;

To find Armature esistance= a@

$l&No Armature

Current=Ia(A#

Armature

?olta5e=?a(?#

Armature

esistance=

a ?a/ Ia (#

1&1&6 9&6 6

2& 2 18 6

3& 2&3 12 6&2

4& 2&4 14 6&;3

a6&26 ohm


10/106

s+ + #s'Bs#( (Hs

+

(s#?

(s#

baaa2

a

a +++=

θ

FB

+ +

s#

'

s#(1B

H

BsG(1

+

a

ba

a

a

a

a

+++

=

F

B

+ + #sT#(1sTsG(1

B

+

a

baam

a

a

+++

=

where 'a/ a Armature Time Constant= Ta

H/B echanical Time Constant = Tm

'REREUISITE :NO;LEDGE

• )erivation of transfer function= speed control of )C shunt motor

'ROCEDURE

1& De!er$i2#!io2 o* : #


11/106


12/106

The connections are made as shown in the circuit dia5ram 1 for the determination of bac,

emf of the d&c motor for different speeds& Initially 188 ohms resistance is connected in

series with the armature& ield windin5 rheostat is ,ept at its minimum& Dhen supply for

the motor is 5iven= there will be tendency for the armature current to increase to a hi5h

value as bac, emf is Jero at startin5& But the current is limited by the 188 ohms armature

rheostat& Dhen the motor has started the armature resistance is 5radually cut down

completely to increase the motor speed& urther to brin5 the motor speed to rated value=

resistance in field rheostat is increased so that motor reaches rated speed& This e0citation

is called rated or normal e0citation and it is not disturbed&

*nce a5ain the armature resistance is included to the ma0imum 188 ohms while

,eepin5 the field e0citation undisturbed& Now the slow speed at full armature resistance is

noted and correspondin5ly the volta5e across the armature is noted down& The speed is

increased in steps by cuttin5 the armature resistance each time notin5 the speed and

volta5e across the armature& By measurin5 the armature resistance bac, emf for each

speed can be calculated& The readin5s are tabulated as in Table 1&

"raph@ Bac, emf = e b vs an5ular speed= w rad/sec

Me#&re$e2! o* R# Connections are made as per the circuit dia5ram 2 where

armature of the d&c motor is connected in series with low resistive load havin5 current

capacity e:ual to full load current of the armature& A voltmeter is connected across the

armature and an ammeter is connected in series with the armature& irst ,eepin5 the

ma0imum resistance in the armature supply is 5iven& The voltmeter readin5 and ammeter

readin5 are noted down& Then armature resistance is decreased so that the armature

current becomes half the rated value& The readin5s are ta,en& A5ain the armature

resistance is further decreased so that the armature current is rated value& A5ain the

readin5s are ta,en and tabulated&

3& Me#&re$e2! o* Ti$e "o2!#2! o* !5e $o!or< T$

The connections are made as shown in the circuit dia5ram 1& The e0periment is no

load test on the motor& The armature of the d&c motor is ,ept at ma0imum resistance by

connectin5 a 188


13/106


14/106

*hms rheostat in series with the armature& The field rheostat is ,ept in its minimum

position& The motor is started and armature resistance is cut slowly so that the motor is

allowed to pic, up speed& After fully cuttin5 the armature resistance= motor field resistance is

increased to a position so that motor reaches rated speed& The field current of the motor at

this position is called rated e0citation& This field rheostat position is maintained for rated

e0citation&

Before startin5 the e0periment= once a5ain armature resistance of the motor is brou5ht to

the ma0imum value of 188 ohms without disturbin5 the rated field e0citation& Now the supply

for the motor is 5iven and sufficient time is allowed so that the motor reaches a steady speed= N s

whose value is noted& rom this steady speed= 8&%32 times of the steady speed is calculated

which is e:ual to 8&%32 N s& 'et the mechanical Time constant of the motor with 188 ohms

armature resistance be Tmh& The Time constant Tmh is the time ta,en for the motor to reach 8&%32

Ns from startin5& To find out Tmh the supply is disconnected and the motor is restarted with

switchin5 on a stop watch& The time ta,en by the motor to reach 8&%32 N s is Tmh& The actual

motor time constant Tm without the e0ternal resistance of 188 ohms will be much lower and it is

calculated as follows&

T amK

T e0amhK +

T

T

e0a

a

mh

m

+=

#(

TT e0a

amhm +=

(9#

The actual Time constant= Tm of the motor will be a fraction of a second and difficult to

measure& .ence the hi5her Time constant with 188 ohms included in the armature= T mh is

measured & rom which Tm is found out by e:uation (9#


15/106


16/106

4 De!er$i2#!io2 o* L#

The connections are made similar to the circuit dia5ram 2 e0cept 238? ac is applied instead

of dc& The voltmeter and ammeter are ac meters of appropriate ran5e& The e0periment is repeated

as was done for measurement of armature resistance&

Armature time constant = Ta 'a/ a

For$#!ie Ae$e2!

1 A "o2!ro% /!e$ i2 =5i"5 "o2!ro% #"!io2 i o$e5o= de-e2de2! o2 o&!-&! i >2o=2

#

a# open loop system

b# closed loop system

c# semi closed system

d# automatic control system

2& Dhich of the followin5 activities may be included in a real-time software desi5n processL

a#


17/106

2& Dhat is meant by Time constantL


18/106

3& )efine armature Time constant&

4& )efine echanical Time constant&

6& & Drite the formula for electrical time constant&

18& Drite the formula for the mechanical time constant&

Si$&%#!i2 &e!io2

1& Dhy are you determinin5 armature Time constantL

2& Dhy are you determinin5 echanical Time constantL

3& )raw the e:uivalent circuit of armature controlled )C motor&


19/106

Fie%d Co2!ro%%ed DC Mo!or

De!er$i2#!io2 o* R #


20/106

DETERMINATION OF TRANSFER FUNCTION OF FIELD CONTROLLED DCMOTOR

E- No + D#!e

AIM

To find the Transfer function of )C otor with the control si5nal applied to ield&

GENERAL OB7ECTI(E

To assess the )C motor performance usin5 transfer function

S'ECIFIC OB7ECTI(ES

1& Understand the two types of speed control&




1 )C shunt motor - 1

2 ?oltmeter 8-388? /C 1

3 Ammeter 8-1A /C 1

4 Ammeter 8-18A /C 1

6 Tachometer )i5ital 1

THEORY

A )C machine can run as a motor= when a )C supply is 5iven to its field windin5 to

produce ma5netic flu0 while the same )C source is used to supply current to the armature& Now

the armature becomes a current carryin5 conductor and as it is ,ept in a ma5netic field= it

develops mechanical force and the direction of the force is 5iven by lemin5s 'eft .and ule&

)C motor in control applications is used for deliverin5 mechanical power to control elements for

electrical control si5nal as input&


21/106

Electrical input to )C motor is called control si5nal and that can be applied in two ways&

In one method= the control si5nal is applied to the field windin5 while fi0ed volta5e is applied to

armature windin5 and hence mechanical power is developed and that depends totally on the

ma5nitude of the

)etermination of 'f@

)etermination of f@


22/106

control si5nal applied to field& This method is called ield controlled motor& In another method=

control si5nal is applied to armature windin5 and constant volta5e is applied to field windin5&

The mechanical power developed here depends on the control si5nal that 5oes to armature& This

method is called Armature controlled motor&

DERI(ATION OF TRANSFER FUNCTION@

Accordin5 to +irchoff ?olta5e 'aw(+?'#

t#(dt

di t#( ?'I f

f

f f f =+

(s#?Fs'(s#G I f f f f =+

(1#

(t#T(t# if ∝

(t#T(t# i+ f f =


23/106

(s#T(s# i+ f f = (2#

T(t#dt

dB

2dt

2dH =+

θ θ

T(s#(s#Bs#2(Hs =+ θ (3#

ultiplyin5 e:n&(1# by + f

s#(FsG(s# ?+ ' i+ f f f f f f =+ (4#

odel "raph@


24/106

substitutin5 (s#Bs#2(Hs(s#I+ f f θ += in e:n&(4#=

(s#?+ Fs'G (s#Bs#2(Hs f f f f =++ θ

( )f f

f

f s' Bs#2(Hs

+

(s#?

(s#

++

=

θ

M(s#/?f(s#( )( )f f

f

s' BHss

+

++

=

s##

'(s#(1#

B

H(s(1

B

+

f

f

f

f

++

=

#sT#(1sTs(1

+

f m

m

++

=

where + m otor "ain Constant

Tf ield Time Constant


25/106

Tm echanical Time Constant

)etermination of + f @

$l&No $upply

?olta5e=

?(?olts#

Armature

Current= Ia

A#

$peed in

pm= N

An5ular

?elocity=

w(rad/sec#

Bac, emf=

Eb(?#

1& 9% 1&1 %68 %;&8% 92&>2

2& ;8 1&16 %92 98&39 9%&9;

3& 182 1&2 ;%8 >8&>6 >;&>%

4& 11; 1&3 >;1 182&93 114&3%

6& 13% 1&36 1142 11>&6; 132&22

%& 144 1&4 128; 12%&68 148&8;

$teady state speed =N8&%32Nm18&%32 O 1688>4;

echanical time constant =Tmh 1; sec

To find field inductance= 'f@


26/106

$l&No field

Current=If(A#

ield

?olta5e=?f(?#

Armature esistance=

f ?f / If (#

1& 6 42 ;&4

2& 6&1 %2 12&16

3& ; >8 11&26

4& > >% 18&%%

ean f 18&%2ohm

'ROCEDURE

Me#&re$e2! o* Ti$e "o2!#2! o* !5e $o!or< T$

The connections are made as shown in the circuit dia5ram& The e0periment is no

load test on the motor& The armature of the d&c motor is ,ept at ma0imum resistance by

connectin5 a 188 ohms rheostat in series with the armature& The field rheostat is ,ept in

its minimum position& The motor is started and armature resistance is cut slowly so thatthe motor is allowed to pic, up speed& After fully cuttin5 the armature resistance= motor

field resistance is increased to a position so that motor reaches rated speed& The field

current of the motor at this position is called rated e0citation& This field rheostat position

is maintained for rated e0citation&

Before startin5 the e0periment= once a5ain armature resistance of the motor is

brou5ht to the ma0imum value of 188 ohms without disturbin5 the rated field e0citation&

Now the supply for the motor is 5iven and sufficient time is

allowed so that the motor reaches a steady speed= Ns whose value is noted& rom this steady

speed= 8&%32 times of the steady speed is calculated which is e:ual to 8&%32 N s& 'et

the mechanical Time constant of the motor with 188 ohms armature resistance be T mh& The Time

constant Tmh is the time ta,en for the motor to reach 8&%32 N s from startin5& To find out Tmh the


27/106

supply is disconnected and the motor is restarted with switchin5 on a stop watch& The time

ta,en by the motor to reach 8&%32 N s is Tmh& The actual motor time constant Tm without the

e0ternal resistance of 188 ohms will be much lower and it is calculated as follows&

T amK

T e0amhK +

T

T

e0a

a

mh

m

+=


28/106

#(

TTe0a

amhm+

= (6#

The actual Time constant= Tm of the motor will be a fraction of a second and difficult to

measure& .ence the hi5her Time constant with 188 ohms included in the armature= T mh is

measured & rom which Tm is found out by e:uation (6#

+ De!er$i2#!io2 O* Fie%d Rei!#2"e o* !5e Mo!or< R *

The motor field resistance is measured by passin5 ,nown current throu5h the field

windin5& The volta5e across the field windin5 is measured usin5 a appropriate voltmeter& The

connections are made as shown in circuit dia5ram 2& Normally resistance of the field windin5 of

d&c machine will be around 288 ohms& .ence an e0ternal variable resistance of 368 ohms/1&1

amps rheostat shall be connected in series with the field windin5 of the motor& The rated 228

volts d&c shall be applied to the field windin5 of the motor in series with the 368 ohms/1&1 amps

rheostat ,ept at its ma0imum resistance& An ammeter is connected in series with the field

windin5 to measure the current and a voltmeter across the windin5 to measure the volta5e drop

in the windin5&

+eepin5 the resistance of the 368 ohms/1&1 amps rheostat in its ma0imum value= the ammeter

and voltmeter readin5s are noted& The resistance of the rheostat is reduced in steps each time


29/106

notin5 the ammeter and voltmeter readin5s& Three sets of readin5s are ta,en and the avera5e of

the three resistances measured is the motor field resistance&

3 De!er$i2#!io2 o* Fie%d =i2di2 i2d&"!#2"e< L*

The connections are made as shown in circuit 3 which is almost similar to circuit2 e0cept

a&c volta5e is applied instead of d&c volta5e& The ammeter and voltmeters are also a&c meters of

appropriate ran5e& Three sets of readin5s are ta,en & The ratio of volta5e to current 5ives the

impedance= f & The avera5e of the impedances measured 5ives the impedance of the field

windin5= f & 2 f 2 P Of 2

Of (2 - f 2#1/2

'f (2 - f 2#1/2 / 2Q


30/106

4 De!er$i2#!io2 o* : *

T(t# + a Ia(t#

+ f If (t#

+ b Ia + f If

Tor:ue + f If + a Ia (rated#

+ f + a Ia (rated# / If (rated#

Re&%!

For$#!ie Ae$e2!

1& Dhich of the followin5 is an open loop control systemL


31/106

a# Dard 'eonard control

b# ield controlled dc motor

c# etadyne

d# $troboscope

2& Dhich of the followin5 activities may be included in a real-time software desi5n processLa# inductance b# Char5e

c# Current

d# resistance

A--%i"#!io2

1& To analysis the performance of )C motor

(i# &e!io2

1& Dhat is meant by field controlled )C motorL

2& Dhat is meant by Time constant of a deviceL


32/106

3& )efine field Time constant of the motor&

4& )efine echanical Time constant of the motor&

6& Drite the formula for electrical time constant&

%& Drite the formula for the mechanical time constant&

9& )efine transfer function&

;& Dhat is meant by otor time constantL

>& )raw the bloc, dia5ram for field controlled )C otor&

18& )efine moment of inertia&

Si$&%#!i2 &e!io2

1& .ow echanical Time constant is determinedL

2& Dhy hi5h resistance is included in the armature to determine the mechanical Time constantL


33/106

$ymbolic epresentation of AC $ervomotor@

Circuit )ia5ram@


34/106

Bloc, )ia5ram of AC $ervo otor Transfer unction@

DETERMINATION OF TRANSFER FUNCTION OF AC SER(O MOTOR

E- No 3 D#!e

AIM

To derive the transfer function of the 5iven AC servo motor and e0perimentallydetermine the transfer function parameters of field controlled )C motor&

GENERAL OB7ECTI(E

To assess the AC servo motor performance usin5 transfer function

S'ECIFIC OB7ECTI(ES1& Understand the two types AC motor&




35/106


1

Two phase AC $ervo otor

$peed Control and Transfer

unction $tudy Trainer +it

- 1

2 -pin )-Connector is connected to bac,side of the trainer&6& $peed indicator switch is ,ept in


36/106

R#di& r@068$ Co2!ro% (o%!#e (C1 @ 10 (

S%No

S-eed

N i2 r-$

A2&%#r

(e%o"i!/

i2 r#d9e"

Lo#d

S i2 r#$

Tor?&e

T @ 81rS10)3 N$

1& 1486 149&86 8 8

2& 1143 11>&%34 13&6 8&8>

3& ;8> ;4&%; 29 8&1;

4& 611 63&4> 48&6 8&29

6& 2% 2&92 63 8&3%

%& The voltmeter is connected across the control windin5 C1 S C2&9& 238 ? AC $upply is switched on at which the runnin5 windin5 is applied with rated volta5e&;& & ated volta5e is applied (12 ?# to the control phase windin5 by usin5 control volta5e (C&?# pot&18& The motor is loaded with ,nown wei5hts in steps&

11& or each step= the speed N in rpm is observed and an5ular speed ω in rad/sec

2πN/%8 is calculated&12& The procedure is continued till the motor reaches 8 rpm&13& All the loads are removed and the control volta5e pot is adusted to 3/4th of the rated volta5e&14& The same procedure is repeated and the readin5s are observed and tabulated&16& or each load= tor:ue is calculated usin5 the formula

T >&;1r$18-3 (in Nm#

where r is the radius of the shaft in m

$ is the applied volta5e in ,5

1%& The 5raph An5ular $peed=ω (rad/sec# ?s Tor:ue= T (Nm# is plotted for the two control

volta5es&


37/106

19& The slope of any one of the characteristicsU

T

∂

∂ 5ives the motor constant + m&

;& + c can be found from the characteristics as follows@

• A vertical line to represent constant ω is drawn from ω a0is to meet the characteristics

of both control volta5es&

• rom the intersectin5 points of the characteristics by the vertical a0is for two ,nowncontrol volta5es= a horiJontal line towards the tor:ue a0is is drawn&

• The ratio of chan5e in tor:ue to the chan5e in control volta5ec?

T

∂

∂ is calculated

which 5ives the value of + c&

TABULATION +

Co2!ro% (o%!#e (C+ @ (

S%NoS-eed

N i2 r-$

A2&%#r

(e%o"i!/

i2 r#d9e"

Lo#d

S i2 r#$

Tor?&e

T @ 81rS10)3 N$

1 1806 180+ 0 0

+ 163 1134 13 0013

3 146 1,36 13 + 018+

4 1146 11, 13 3 0+41

, 404 4++ 13 4 036,,

6 18 18 13 , 04,6


38/106

Deri#!io2 o* Tr#2*er F&2"!io2

As we ,now=

T(t# U(t#U

T(t#?

?

T

?cUc

c

∂

∂+

∂

∂

T(t# + c?c(t# P + mU(t#

The developed tor:ue used to rotate the load on the shaft with inertia H and friction coefficient B=

with an an5ular speed of #(t ω is 5iven by

T(t# (t#Bdt

#(dH ω

ω +

t

Ta,in5 'aplace Transformation for e:uations (4# and (6# and e:uatin5 them

+ c?c(s# P + m #( sω (Hs P B# #( sω

The input to the motor is control si5nal ?c(s# and the resultin5 mechanical output is #( sω & e-

arran5in5 the above e:uation(Hs P B - + m# #( sω + c?c(s# Transfer function

m

c

+ -BHs

+

#(

U(s#

+

=

sV c


39/106

MODEL CALCULATIONS

oment of Inertia H 628 O 18-4 ,5/cm2

riction Coefficient B 8&81;9 Nm/rad/sec

For Co2!ro% (o%!#e (C1 @ 10 (

$peed N 1143 rpm

An5ular ?elocity ω 2πN/%8 11>&%34 rad/sec

'oad $ 13&6 5rams

Tor:ue T >&;1r$18-3 Nm


40/106

rom the charactersitics=

+ C c?

T

∂

∂ 8&8% Nm/rad/sec

otor Constant + m U

T

∂

∂

3 O 18-3 Nm/rad/sec

Therefore= Transfer function of AC servo motor

m

c

+ -BHs

+

#(

U(s#

+

=

sV c

echancial Time Constant T #+ -(B

H

m 3&31 seconds

RESULT

(i# &e!io2

1& Dhat type of motor is used as AC servomotorL DhyL2& Dhat improvements are made in the servomotor characteristicsL3& .ow volta5e constant + c and speed constant + m are determinedL4& )oes the ne5ative value of speed constant affect stability of the elementL6& .ow two phase AC volta5e is obtained from three phase ACL%& )oes the motor run when control windin5 volta5e is JeroL

A--%i"#!io2

1& To analysis the performance of AC servo motor

S!i$&%#!i2 &e!io2

1&


41/106

For$#!ie Ae$e2!

1& Dhich speed control method preferred for constant tor:ue driveLa# ield controlled

b# Armature controlc# echanical controld# Tor:ue control2&The synchronous speed for the seventh space harmonic mmf wave of ; pole= 68 .Jinduction machine will bea# 189&14 rpm forward direction b# 189&14 rpm reverse directionc# 6268 rpm forward directiod# 6268 rpm forward directio

No2 Li2e#r S/!e$ E#$-%e 1

No2 Li2e#r S/!e$ E#$-%e +


42/106

DESIGN AND SIMULATION OF SISO TRANSFER FUNCTION ;ITH NON

LINEARITY

E- No 4 D#!e

AIM To di5itally simulate the time response characteristics of a linear system with simple non-linearities li,e saturation and dead Jone&

GENERAL OB7ECTI(E

To determine the time response characteristics of a linear system with simple non-linearities li,e

saturation and dead Jone&

S'ECIFIC OB7ECTI(ES

1& )efine saturation and dead Jone

2& Understand the time response characteristics of linear system&

3& )etermine the time response of linear system with simple non-linearities &onA''ARATUS REUIRED


1 'C =i!5 MATLAB o*!=#re ) 1


43/106

'RE)REUISITE CONCE'TS

)erivation of transfer function= linear and nonlinear system

'ROCEDURE

1. )erivation of transfer function of the 5iven $I$* linear system@

• Apply +irchhoffs volta5e law or +irchhoffs current law to form the

differential e:uations describin5 electrical circuits comprisin5 of resistors=capacitors= and inductors&

• Apply Newtons 'aws to form the e:uations of motion for lumped parameter

mechanical systems (Translational and rotational# comprisin5 of masses=sprin5s= and dampers&

• orm transfer functions from the describin5 differential e:uations&

2. )i5ital simulation of time response characteristics of the above system@

• Drite AT'AB script and build the bloc, dia5ram for the above system usin5

$IU'IN+ bloc,s&


44/106

•


45/106


46/106

RESULT

A--%i"#!io2


47/106

To analysis the performance of $I$* linear system

(i# (oi"e &e!io2

1&)efine )ead Jone&

2&)efine saturation &

3& Dhat are non-linear systemsL

4& "ive some e0amples of non-linearities

6& Dhy ne5ative feedbac, is invariably preferred in a closed loop systemL Hustify&

S!i$&%#!i2 &e!io29Ide#9A--%i"#!io2

1& .ow to analyse non-linear systemsL

2& Dhat is AT'ABL )iscuss its si5nificance over other simulation softwares&


48/106

For$#!ie Ae$e2!

1& In case of an open loop control system which of followin5 statement is trueL

a# output is dependant on the control unit

b# output is independant on the control unit

c# output is dependant on the input and control

d# output is independant on the input and control

2&The synchronous speed for the seventh space harmonic mmf wave of ; pole= 68 .J

induction machine will be

a# 189&14 rpm forward direction b# 189&14 rpm reverse direction

c# 6268 rpm forward directio

d# 6268 rpm forward directio


49/106

TY'E )0 S/!e$

TY'E )1 S/!e$


50/106

DESIGN AND SIMULATION OF TRANSFER FUNCTION OF TY'E – 0 AND TY'E – 1

SYSTEMS FOR DIFFERENT IN'UT SIGNALS

E- No , D#!e

AIM

To di5itally simulate the time response characteristics of first and second order linear system for

different input si5nals

GENERAL OB7ECTI(E

To )rive and simulate the time response of first and second order system&

S'ECIFIC OB7ECTI(ES

$tudents will be able to

1& )efine tye number


51/106

2& )raw the time response of first order system

3& )raw the time response of second order system

A''ARATUS 9 INSTRUMENTS USED

SNO ITEM UANTITY

1


52/106

T/-e ) 0 /!e$ i$-&%e i2-&!

nuw G8 28 8FV

denG8 28 68FV

atf(nuw=den#V

impulse(a#


53/106

'ROGRAM

T/-e ) 1 /!e$ !e- i2-&!

nuw G1FV

denG8&; % 1FV

atf(nuw=den#V

step(a#


54/106

T/-e ) 1 /!e$ i$-&%e i2-&!

nuw G1FV

denG8&; % 1FV

atf(nuw=den#V

impulse(a#

RESULT

T/-e ) 0 /!e$ !e- i2-&!

T/-e ) 0 /!e$ i$-&%e i2-&!


55/106

T/-e ) 1 /!e$ !e- i2-&!

T/-e ) 1 /!e$ i$-&%e i2-&!


56/106

A''LICATIONS

To find the time domain specification&

(I(A (OICE UESTIONS

1& Dhat is analo5 simulationL2& Brief di5ital simulation&3& Dhat do u mean by type and order of the systemL4& Brief the effect on stability of a system when increasin5 S/ decreasin5 the type S/ order

of the system& 6&Dhat is dampin5 ratioL Brief its si5nificance w&r&t stability&


57/106

STIMULATING UESTIONS

1& "ive a practical e0ample for the type 8 and type 1 system&2& Dhat are the time domain specifications and what do u infer from themL

FORMATI(E ASSESMENT

1& Time ta,en for the response to raise from Jero to 188 W for very first time is called

a# rise time

b# pea, time

c# settlin5 time

d# delay time

2&An open loop= represented by the transfer function " ( s # ( s - 1 # / ( s P 2 #( s P 3 #= is a# stable and of non-minimum phase type b# stable and of minimum phase type

c# unstable and of nonminimum phase type

d# unstable and of minimum phase type

Se"o2d Order /!e$


58/106

DESIGN AND SIMULATE TIME RES'ONSE OF A LINEAR SYSTEM

E- No 6 D#!e

AIM

To di5itally simulate the time response characteristics of a linear system&GENERAL OB7ECTI(E

To )rive and simulate the time response characteristics of a linear system&

S'ECIFIC OB7ECTI(ES


59/106

S!&de2! =i%% .e #.%e !o

1& )efine different time domain specification&

2& )raw the time response characteristics of a linear system

3& Analysis the linear system&


SNO ITEM UANTITY

1


60/106

Comments on Time )omain $pecifications@

E0cept for certain applications where oscillations cannot be tolerated= it is desirable that

the !r#2ie2! re-o2e be &**i"ie2!%/ *#! S &**i"ie2!%/ d#$-ed

Thus= for a desirable transient response of a second-order system= the d#$-i2 r#!io

$&! .e .e!=ee2 04 #2d 08

($mall values of ζ (ζX8&4# yield e0cessive overshoot

'ar5e values of ζ (ζY8&;# responds slu55ishly#

'ROCEDURE

1&)erivation of transfer function of the 5iven $I$* linear system@

• Apply +irchhoffs volta5e law or +irchhoffs current law to form the

differential e:uations describin5 electrical circuits comprisin5 of resistors=capacitors= and inductors&


61/106

• Apply Newtons 'aws to form the e:uations of motion for lumped parameter mechanical systems (Translational and rotational# comprisin5 of masses=sprin5s= and dampers&

• orm transfer functions from the describin5 differential e:uations&

2&)i5ital simulation of time response characteristics of the above system@

• Drite AT'AB script and build the bloc, dia5ram for the above system usin5$IU'IN+ bloc,s&

•


62/106

A''LICATIONS

To find the time domain specification of different system&

(I(A (OICE UESTIONS

1& Dhy do u 5o for time response analysisL2& $tate newtons law& Dhat is its si5nificance in transfer function derivation&3& rom where do u 5et the bloc,s for analysis of a system in a matlab softwareL4& Dhat does an analo5ous system meanL6& 'ist the time domain specifications& "ive their usa5e in determinin5 condition of a

system&


63/106


1& Dhat does an analo5ous system meanL

2& Dhat do u infer from the e0perimentL

FORMATI(E ASSESMENT

1& 'aplace transform of step function

a# 1/s

b# s

c# 1

d# 2s

2&An open loop= represented by the transfer function " ( s # ( s - 1 # / ( s P 2 #( s P 3 #= isa# stable and of non-minimum phase type b# stable and of minimum phase type




64/106

DESIGN AND SIMULATE FREUENCY RES'ONSE OF A LEAD NET;OR:

E'NO D#!e

AIM

To determine the fre:uency response of a system with a 5iven specifications usin5 lead

networ, GENERAL OB7ECTI(E

To determine and simulate the fre:uency response of lead networ,&

S'ECIFIC OB7ECTI(ES

S!&de2! =i%% .e #.%e !o


65/106

1& )efine lead compensator&

2& )raw the fre:uency response of un compensator system&

3& )esi5n lead compensator and simulate&


1&


66/106

RESULT


67/106

(I(A UESTIONS

1& Dhat the advanta5es are of bode plotL

2& )efine phase mar5inL

3& )efine 5ain mar5inL

4& Dhat is phase and 5ain cross-over fre:uencyL

6& Dhat is bode plotL

A''LICATIONS

To find the time domain specification of different system&


1&Dhat does an analo5ous system meanL

2&Dhat do u infer from the e0perimentL


68/106

FORMATI(E ASSESMENT

1& 'aplace transform of step function


69/106

a# 1/s

b# s

c# 1

d# 2s

3& An open loop= represented by the transfer function " ( s # ( s - 1 # / ( s P 2 #( s P 3 #= isa# stable and of non-minimum phase type b# stable and of minimum phase type




70/106

'ERFORMANCE E(ALUATION OF '


71/106

AIM To performance evaluation of


72/106

numG2 8FV

denG1 3 2FV

5tf(num=den#V

step(5#

'I Co2!ro%%er

numG2 1FV

denG1 3 2FV

5tf(num=den#V

step(5#

'ID Co2!ro%%er

numG3 2 1FV

denG1 3 2FV

5tf(num=den#V

step(5#

If error is Jero= the output is constant and e:ual to


73/106

INTEGRAL CONTROLLER

In this mode= there will be a infinite si5nal chan5e in the rate of controller output with

infinitesimal chan5e in the error& This mode is often referred to as reset action&

dp/dt +i ep

dp/dt rate of controller output chan5e

+i constant relatin5 the rate of the error

The inverse of +i is called the inte5ral time Ti(1/+i#& If we inte5rate the above e:uation=

we can find the actual controller output at any time as where


74/106

'RO'ORTIONAL –INTEGRAL)DERI(ATI(E CONTROLLER


75/106

*ne the most powerful but comple0 controller mode operation combines the

proportional= inte5ral and derivative modes& This system can be used for virtually any process

conditions& This mode eliminates the offset of the proportional mode and still provides fast

response&

'ROCEDURE

1& Connections are 5iven as per circuit dia5ram&

2& Before the controller can be used= the parameters must be pro5rammed& The pro5ram mode is

selected with the ,ey operated switch&

3& )


76/106


77/106

RESULT


78/106

A''LICATIONS

1& To find the correct time domain specification of different system&

(I(A (OICE UESTIONS

Dhat is the effect of


79/106

FORMATI(E ASSESMENT

1& $teady state stability limit is

a) E:ual to transient stability limit&

b) "reater than transient stability limit&

c) 'esser than transient stability limit&

d) None of these&

2&The steady-state stability limit of a synchronous 5enerator can be increased by

a# an increase in the e0citation of the /C&

b# an increase in its reactance&

c# a decrease in the moment of inertia of the machine&

d# an increase in the moment of inertia of the machine&


80/106

STUDY OF SYNCHROS

ENo # DATE

AIM

To study the characteristics of synchros as error detector&

GENERAL OB7ECTI(E

To understand the construction and wor,in5 of synchros error detector&

S'ECIFIC OB7ECTI(E

1 )efine synchros &

+ E0plain the construction of synchros


SNO ITEM UANTITY


81/106

1 $ynchronous

Transmitter and

eceiver

1 $et

2


82/106

The rotor windin5 is applied with an AC supply volta5e throu5h slip rin5s and this rotor

is held fi0ed in a desired an5ular position say Mr (i&e& input or reference#&

'et the AC volta5e applied to the rotor of the transmitter be

Ei(t# Em sin (2Q f t# -------------Y (1#

This volta5e causes a flow of ma5netiJin5 current in the rotor coil which produces a

sinusoidally time varyin5 flu0 directed alon5 its a0is and distributed nearly sinusoidally in the air

5ap alon5 stator periphery& Because of transformer action= volta5es are induced in each of the

stator coils& As the air 5ap flu0 is sinusoidally distributed= the flu0 lin,in5 any stator coil is

proportional to the cosine of the an5le between rotor and stator coil a0is and so is the volta5e

induced in each stator coil&


83/106

the stator coil volta5es are of course in time phase with each other& Thus the synchro

transmitter acts li,e a sin5le phase transformer in which rotor coil is the primary and the stator

coil form three secondaries&

'et e1n= e2n and e3n be the volta5es induced in the stator coils $1= $2 and $3

respectively with respect to neutral& Then for the rotor position of the synchro transmitter shownin fi5ure= the rotor a0is ma,es an an5le 8 with the a0is of the stator coil $1& Thus for Mr 8o= the

correspondin5 volta5e induced by transformer section across the stator windin5 1n is 5iven by=

e1n + Em sin (2Q f t# cos Mr + Em sin (2Q f t# cos 8

+ Em sin (2Q f t# ---------------------Y (2#

where + is the constant of proportionality& As the stator windin5s 2n and 3n are 248Z and 128Z

apart (an5le measured as positive in anti-cloc,wise direction# with respect to the windin5 1n= the

volta5es induced across them are=

e2n + Em sin (2Q f t# cos (Mr P 248Z#

+ Em sin (2Q f t# cos (8 P 248Z#

+ Em sin (2Q f t# cos (248Z#

-8&6 + Em sin (2Q f t# ---------------------------(3#

e3n + Em sin (2Q f t# cos(128Z#

+ Em sin (2Q f t# cos(Mr P 128Z#

+ Em sin (2Q f t# cos(128Z#

-8&6 + Em sin (2Q f t# -------------------------(4#

TABULATION

S%No A2&%#r Di-%#"e$e2! o* Ro!or i2 deree O&!-&!(o%!#e

i2 (o%!

! r "

1 38 32 2 4;&4

2 %8 %2 2 4;&6


84/106

3 >8 >2 2 4;&6

4 128 122 2 4;&4

6 168 162 2 4;&6

% 1;8 1;8 8 4;&4

9 218 218 8 4;&3

; 248 242 2 4;&3

> 298 293 3 4;&3

18 388 383 3 4;&3

11 338 333 3 4;&;

12 3%8 3%8 3 4;&;

E:uations (2#= (3# and (4# indicate that three volta5es e1n= e2n and e3n are sin5le phase volta5esof same fre:uency and have same phase but their ma5nitudes depend on rotor position&

Now= if the rotor of the synchro transmitter shifts in anti-cloc,wise direction throu5h an an5le M=

the volta5es in the stator coils are=

e1n + Em sin (2Q f t# cos Mr ---------------------------------(6#

e2n + Em sin (2Q f t# cos(248Z - Mr# -----------------------(%#

e3n + Em sin (2Q f t# cos(128Z - Mr# -------------------------(9#

E:uations (6#= (%# and (9# reveal that ma5nitudes of the volta5es e1n= e2n and e3n vary

sinusoidally with respect to Mr as shown in fi5ure &

It is seen that when Mr 8o= the ma0imum volta5e is induced in the stator coil $1& This

position of rotor is defined as electrical Jero of the transmitter and is used as reference for


85/106

specifyin5 the an5ular position of the rotor& .ence it is inferred that the synchro transmitter is the

an5ular position of its rotor shaft and the output is a set of three sin5le phase volta5es& The

ma5nitude of these volta5es are functions of a shaft position&

The classical synchro system consists of two units@

1& $ynchro Transmitter

2& $ynchro eceiver

The synchro receiver is havin5 almost the same constructional features& The two units are

connected as shown in the fi5ure 2& & The locations of transmitter and receiver can be away from

each other& The rotor of synchro transmitter is salient pole type and that of synchro receiver is

cylindrical type&

The rotor of the synchro receiver is coupled to the output shaft of the control system& If

the position of the output shaft is indicated as Mo this results in an an5ular error Me (Mr - Mo#

between the positions of the input (reference# and the output shafts&

Initially the windin5 $2 of the stator transmitter is positioned for ma0imum couplin5 with

rotor windin5& $uppose its volta5e is ?= the couplin5 between $1 and $2 of the stator and primary

(rotor# windin5 is a cosine function& Therefore the effective volta5es in these windin5s are

proportional to %8o or they are ?/2 each& $o lon5 as the rotors of the transmitters and receivers

remain in this position= no current will flow between the windin5s because of volta5e balance&

Dhen the rotor transmitter is moved to a new position= the volta5e balance is distributed&

Assume the rotor of the transmitter is moved throu5h 38o= the stator windin5 volta5es will be

chan5ed to Jero= 8&;%% ? and 8&;%% ? respectively& Thus there is a volta5e imbalance between

the windin5s cause a currents to flow throu5h the close circuit producin5 a tor:ue that tends to

rotate the rotor of the receiver to a new position where the volta5e balance is a5ain restored& This

balance is restored only if the receiver turns throu5h the same an5le as the transmitter and also

the direction of the rotation is the same as that of transmitter&

The transmitter and receiver pair thus serves to transmit information re5ardin5 thean5ular position at one point to a remote point&

The ma5nitude of the output induced volta5e eo developed across the rotor of the receiver is

5iven by the followin5 relation@

eo +r sin (Mr - Mo# (;#


86/106

where +r is a constant of proportionality&

In control systems the an5ular error= i&e& (Mr - Mo# is usually small and e0pressed in radian=

therefore=

sin (Mr - Mo# [ (Mr - Mo# radian

.ence= eo +r (Mr - Mo#

(Mr - Mo# is e0pressed as Me (an5ular error#

eo +r Me (radian#

where +r is e0pressed in ?/rad&

The above e:uation indicates that an5ular error is converted into a proportional volta5e&

'aplace transform of the above e:uation

Eo(s# +r Me(s#

The Transfer function is 5iven by (>#

Eo(s#/ Me(s# +r

Dhere +r is ,nown as the sensitivity or the 5ain of synchro-error detector&

'RECAUTIONS

• The pointers for both rotors are to be handled 5ently&

• The pointers should not pulled out

• The rotor and stator terminals should not be shorted&

'ROCEDURE

To o.!#i2 !5e I2-&! – O&!-&! "5#r#"!eri!i" o* S/2"5ro Tr#2$i!!er

1&The main supply to the system is connected with the help of cable provided (the

interconnections $1 = $2 and $3 to $1 = $2 and $3 should not be made#&‟ ‟ ‟

2&The mains supply to the unit is switched *N&The supply to the rotor transmitter is also

switched *N&


87/106

3&The ma5nitude of the AC volta5e supplied to the rotor is fi0ed as 48 ?&

4&The ma5nitude of the AC volta5e of between each of the stator terminals ?$1$2=

?$2$3 and ?$3$1 are measured and tabulated for different rotor positions at e:ual

intervals&

6& The 5raph= an5ular position ?s rotor volta5es for all the three phases are plotted as

shown in fi5ure 3&

To o.!#i2 !5e I2-&! – O&!-&! "5#r#"!eri!i" o* S/2"5ro Tr#2$i!!er Re"eier -#ir

1& The mains supply cable is connected&

2& The terminals of transmitter $1= $2 and $3 are connected to $1 = $2 and $3 of receiver usin5‟ ‟ ‟

patch cords respectively&

3& The mains supply is switched *N&

4& The rotor supply of both transmitter and receiver are also switched *N&

6& The rotor of receiver is ti5htly held at 8o&

%& The rotor position of synchro transmitter (pointer# is moved in steps of 18o and the new rotor

position of receiver is observed&

9& The output volta5e is also observed and it varies sinusoidally with an5ular error&

;& The plot input an5ular position in de5rees ?s output an5ular position in de5rees is plotted as

shown in fi5ure 4&

STE''ER MOTOR THEORY OF O'ERATION


88/106

STUDY OF DC STE''ER MOTOR

THEORY

The stepper motor is a special type of synchronous motor which is desi5ned to rotate

throu5h a specific an5le for each electrical pulse received from its control unit

In recent years= the 5rowth of computer industry induced a wide-spread demand for stepper

motor can be controlled directly by computers= microprocessors and pro5rammable controllers&


89/106

The steppin5 motor ideally suited for precision positionin5 of an obect or precision

control of speed without usin5 a closed loop feed bac,& The shaft of the stepper motor rotates in a

series of discrete an5ular intervals or steps= one step bein5 ta,en each time a command pulse is

received& Dhen a definite number of pulses are supplied= the shaft turns throu5h a definite ,nown

an5le this ma,es the motor well suited for open loop position control because no feedbac, is

re:uired from the shaft& The only movin5 part in a steppin5 motor its rotor which has no

windin5= commutator or brushes&

STE' ANGLE

The an5le throu5h which the motor shaft rotates for each command pulse is called step

an5le \& $maller the step an5le= 5reater the number of steps / revolution and hi5her the resolution

or accuracy of positionin5 obtained& The step an5le can be as small as 8&92] de5rees or as lar5e

as >8 & But most common step siJes are 1&; = 2&6 = 9&6 S 16 & The value of step an5le can bee0pressed either in terms of a rotor and stator poles (teeth# Nr and Ns respectively or in terms of

the number of stator phases (m# and number of rotor teeth (Nr#&

The stepper motor has the e0traordinary ability to operate at very hi5h steppin5 rate of

28=888 steps per second in some motors& *peration at very hi5h speed is called slewin5 & Dhen‟

in the slewin5 ran5e= the motor 5enerally emits an audible whine havin5 a fundamental

fre:uency e:ual to steppin5 rate &if f is the steppin5 fre:uency (or# pulse rate in pulse per second

and \ is step an5le then the motor shaft speed is 5iven by


90/106

$teppin5 motors are desi5ned to operate for lon5 periods with the rotor held in a fi0ed position

and with the rated current flowin5 in the stator windin5 for other motors this will result in

collapse of bac, emf and very hi5h current which can lead to :uic, burn out the stator windin5&

'er$#2e2!)M#2e! S!e--i2 Mo!or

Co2!r&"!io2@ It has a wound stator poles and the rotor is made of permanent ma5net material

li,e ma5netically ^hard ferrite& As shown in the i5&1= the rotor has proectin5 poles but the‟

rotor is cylindrical and has radially ma5netiJed permanent ma5nets& The operatin5 principle of

such a motor can be understood with the help of i5&1 (a# where the rotor has two poles and thestator has four poles& $ince two stator poles are ener5iJed by one windin5= the motor has two

windin5s or phases mar,ed A and B& The step an5le of this motor \ 3%8_/mNr 3%8_ / 2 0 2

>8_ or \ (4 - 2# 0 3%8_ /2 0 4 >8_&

;or>i2 Dhen a particular stator phase is ener5iJed= the rotor ma5netic poles move into

ali5nment with the e0cited stator poles& The stator windin5s A and B can be e0cited with either

polarity current& i5&1 (a# shows the condition when phase A is e0cited with positive current&

.ere= M 8_& If e0citation is now switched to 8_ in the cloc,wise direction& Ne0t= when phase A is e0cited with ne5ative current= the rotor

turns throu5h another >8_ in CD direction as shown in i5& 1 (c#& $imilarly= e0citation of phase Bwith ne5ative current further turns the rotor throu5h another >8_ in the same direction as shown

in i5& 1 (d#& After this= e0citation of phase A with positive current ma,es= the rotor turn throu5h

one complete revolution of 3%8_& It will be noted that in a permanent-ma5net stepper motor= the

direction of rotation depends on the polarity of the phase currents&

Si2%e S!e- ON $ode


91/106

Truth tables for three possible current se:uences for producin5 cloc,wise rotation are

5iven in i5&2& Table No&1 applies when only one phase is ener5iJed at a time in I-phase-*N

mode 5ivin5 step siJe of >8_& Table No&2 represents 2-phase-*N mode when two phases are

ener5iJed simultaneously& The resultin5 steps are of the same siJe but the effective rotor pole

positions are mid way between the two adacent full-step positions& Table No&3 represents half-

steppin5 when 1-phase-*N and2-phase-*N modes are used alternately& In this case= the step siJe

becomes half of the normal step or one-fourth of the pole-pitch (i&e& >8_ / 2 45° or 1;8_/4

45°). icro step can also be employed which will 5ive further reduced step siJe there byincreasin5 the resolution

The specification of the $tepper otor@


92/106

1&


93/106

(i# ?&e!io2

1& Dhat is step an5leL

2& )efine reluctance&

3& Dhat is stepper motorL

4& Dhat is application of stepper motorL

6& Dhat is full-step= half-step and micro-stepL

S!i$&%#!i2 ?&e!io2

1& Dhat do infer from the e0perimentL2& .ow do u adust the speed of stepper motorL3& *n what basis does the steppin5 an5le variedL4& "ive a practical field where stepper motor is used wildly&6& Dhat are the different types of stepper motorL

FORMATI(E ASSESSMENT

1&or a 1&;_= 2 - bipolar stepper motor= the steppin5 rate is 188 step / second& The rotationalspeed of the motor in rpm is

a) 16&

b) 38&

c) %8&

d) >8&

2&A stepper motor has a step-an5le of 2&6_& )etermine the resolutionL

a) 148&

b) 143&

c) 144&

d) 146&


94/106


95/106

Le#d "o$-e2#!or

Transfer function@

16

-------

s2 P s

Enter the desired phase mar5in@46

beta 8&2%99

ma -6&9241

wm 6&33;6

T 8&3%21

Transfer function@

6&431 s P 16


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---------------------------

8&8>%>1 s3 P 1&8>9 s2 P s

DESIGN AND SIMULATE LEAD COM'ENSATOR< LAG COM'ENSATOR AND LEAD

) LAG COM'ENSATOR

E' NO10 D#!e

AIM

To desi5n la5= lead= la5-lead compensator for a system to be stable&

GENERAL OB7ECTI(E

To understand the concepts of compensator and desi5n a compensator

S'ECIFIC OB7ECTI(E

1 To draw the bode plot

+ To analysis the un compensator

3 To desi5n a compensator

A''ARATUS REUIRED


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1


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ma-28lo518(1/s:rt(beta##

mms:rt(beta#V

Gma5=phase=w1Fbode(5=w#V

ma5reshape(ma5=188=1#V

phasereshape(phase=188=1#V

wminterp1(ma5=w=mm#

T1/(wms:rt(beta##

pcTbetaV

num1GT 1FV

den1Gpc 1FV

num2conv(num=num1#

crossover fre:uency to lower fre:uency point where the phase mar5in is acceptable& Thus

the la5 compensator will reduce the band width of the system and results in the slower transient

response&

LEAD COM'ENSAOR

A compensator havin5 the characteristic of lead networ, is called a lead compensator& If a

sinusoidal input is 5iven to the lead networ,= then in steady state the output will have the phase

lead&

'ead compensation increases the bandwidth= which improves the speed of response and also

reduces the amount of overshoot& 'ead compensation appreciably improves the transient

response= whereas there is a small chan5e in steady state accuracy& "enerally= lead compensation

is provided to ma,e an unstable system to a stable system&

'ead compensator is basically a hi5h pass filter and so it amplifies hi5h fre:uency noise si5nals&

If the pole introduced by the compensator is not cancelled by a Jero in the system = then the lead

compensation increases the order of the system by one&

Transfer function of the system is 1,91


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LAG LEAD COM'ENSATOR

Amon5 the simplest dynamic structures used in compensator desi5n is the lead-la5 compensator&

A lead-la5 compensator has a transfer function of the form

The phase plot of "c hints at the ori5in of the name lead-la5!& The phase la5s! at lower

fre:uencies and leads! at hi5her fre:uencies& The basic idea in lead-la5 desi5n is to choose the

lead portion of the compensator (p2 and J2# to add phase in the vicinity of the desired value of

8c& The la5 portion (p1 and J1# then attenuates the ma5nitude so that 8c is actually the

crossover fre:uency& The phase la5 is merely an artifact of the compensator structure and plays

no role in achievin5 the specifications&

m


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systf(num=den#

mar5in(sys#V

wlo5space(-1=2=188#V

Gma5 phFbode(sys=w#V

ph1reshape(ph=188=1#V

ma51reshape(ma5=188=1#V

pminput(Enter the desired phase mar5in @#V

RESULT

L# &2"o$-e2#!ed /!e$


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L# "o$-e2#!ed /!e$


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Le#d &2"o$-e2#!ed

L# Le#d Co$-e2#!ed


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A--%i"#!io2

To 5et desired output

(I(A UESTIONS

1& Dhat is compensationL

2& Dhat are the two types of compensation schemesL

3& Dhat are the factors to be considered for choosin5 series or shunt/feedbac, compensationL

4& Dhat is la5 compensationL

6& )raw the bode plot of la5 compensator&


1 Dhat is lead compensationL

2& Drite the transfer function of lead compensator and draw its pole-Jero plot&

3& Dhat is la5- lead compensatorL


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4& Drite the transfer function of la5-lead compensator and draw its pole-Jero plot&

6& Dhen la5/lead/la5-lead compensation is employedL

%& Dhy compensation is necessary in feedbac, control systemL

FORMATI(E ASSESSMENT

1& A lead compensator used for a closed loop controller has the followin5 transfer function

or such a lead compensator

a) a X b&

b) b X a&

c) a Y ,b&

d) a X ,b&

2&Time ta,en for the response to raise from Jero to 188 W for very first time is called

a) rise time&

b) settlin5 time&

c) delay time&

d) pea, time&


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Documents

RBT Lab Manuval 11E608 CE