ee 2257 control system lab manual

8/13/2019 Ee 2257 Control System Lab Manual

1/63

Control Systems Laboratory Manual

Page

DDEEPARPARTTEEMMEENNTT OFOF ELEELECCTTRRIICACALL ANANDD ELEELECCTTRROONNIICCSS

EENNGGIINNEEEERRIINNGG

EE2257 CONTROL SYSTEM LABORATORY

MMANUALANUAL

PRPREEPARPAREDED BYBY

VV.B.BAALLAAJIJI,, MM.Tech,.Tech, ((PPh.h.DD),), MM..II.S.T.E,.S.T.E, MM..II..AA.E.ENNG,G, MM..II.O..O.JJ.E.E

AASSSSIITTANANTT PRPROOFFESSOESSORREEEEEE DDEEPARPARTTMMEENNTT

DD!!ANAANALLAA"S!"S!MMII CCOLLEGEOLLEGE OFOF EENNGGIINNEEEERRIINNGG

CC!E!ENNANNAII


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Page


LLIISTST OFOF EE#P#PEERIMRIMEENNTSTS

1. Determination of transfer function of DC Servomotor

2. Determination of transfer function of AC Servomotor.

3. Analog simulation of Type - 0 and Type 1 systems

. Determination of transfer function of DC !enerator

". Determination of transfer function of DC #otor

$. Sta%ility analysis of linear systems

&. DC and AC position control systems

'. Stepper motor control system

(. Digital simulation of first systems

10. Digital simulation of second systems


3/63

Page


TTRANRANSSFFERER FFUNUNCCTTIIONON OFOF DDCC SESERVRVOO MMOTOROTOR

EE#P#PT.T.NNOO $$

DADATETE $$

AAIIMM$$

T% &e'e*+e 'he '+-e /+c'*%+ % 'he DC -e0%%'%


4/63

APPAAPPARRAATTUUSS RREE11UUIIRREEDD$$

S.N% Ne % 'he E/*3e+' R+4e T3e 1/+'*'

T!EOT!EORYRY$$

Speed can be controlled by varying (i) flux per pole (ii) resistance of armature circuit and(iii) applied voltage.

It is known tat ! "b. If applied voltage is kept# "b $ % & Ia'a will

'emain constant. en# !

*y decreasing te flux speed can be increased and vice versa. +ence tismetod is called field control metod. e flux of te ,C sunt motor can becanged by canging field current# Is wit te elp of sunt field reostat. Since

te Is relatively small# te sunt filed reostat as to carry only a small current#

wic means Is-

' loss is small. is metod is very efficient. In noninterpolarmacines# speed can be increased by tis metods up to te ratio -/ . In interpolarmacine# a ratio of maximum to minimum speed of 0/ wic is fairly common.

FFOORMURMULLAA$$

AA'/e'/e CC%%+'+'%%66 DD..CC.. SeSe00%% %%''%%$$

It is ,C sunt motor designed to satisfy te re1uirements of te servomotor.

e field excited by a constant ,C supply. If te field current is constant ten

speed is directly proportional to armature voltage and tor1ue is directly

proportional to armature current.


5/63

2 $ 3.345 6g-m

* $ 3.343 ! 7 rpm

ransfer 8unction $ 6m

S ( 9 mS) 6m $ 7 :vg 6b m $ 2'a 7 6b 6t 6t $ 7 Ia "b $ %Ia 'aConstant %alues


6/63

FF**ee66&& C%C%+'+'%%66 DD..CC.. SSee00%% %%''%%$$

It is ,C sunt motor designed to satisfy te re1uirements of te servomotor.

In tis motor te armature is supplied wit constant current or voltage. or1ue is

directly proportional to field flux controlling te field current controls te tor1ue ofS6.N% I. I, S7 S2 N V T E8 "8 9 E8

te motor.

ransfer 8unction $

6

2s-

( 9 s) 6 $ 6t 7 'f- $ Lf 7 'f $ % ;f-& 'f $ - ! 7 03 7 - f 7 'f $ r ( S& S- ) < 5.= !m and r $ .3>?m

OBSERVATION TABLE FOR TRANSFER FUNCTION ARMATURE

CONTROL DC SERVO MOTOR$

TT8866ee NN%%.. F*F*+&+&**++44 'he'he 0066//ee %% ""88


7/63

TT8866ee NN%%.. 22 TT%% **+&+& RR

:vg 6b

Sl.!o %olt %a Current Ia 'a $ %a 7 Ia

:vg 'a $

PRPREECAUCAUTTIIOONNS$S$

:t starting#

e field reostat sould be kept in minimum resistance position

PRPROOCCEEDURDUREE FFOROR TTRANRANSSFFERER FFUNUNCCTTIIONON OFOF ARMARMAATTURUREE CCOONNTTRROLOL

DDCC SESERVRVOOMMOTOOTORR$$


8/63

FF**+&+&**++44 ""88. 6eep all switces in @88 position.-. Initially keep voltage adAustment B@ in minimum potential position.

4. Initially keep armature and field voltage adAustment B@ in minimum

position.. Connect te module armature output : and :: to motor armature terminal

: and :: respectively# and field 8 and 88 to motor field terminal 8 and 88

respectively.

?. Switc @! te power switc# S# S-.

0. Set te field voltage ?3D of te rated value.

>. Set te field current ?3D of te rated value.

=. igt te belt an take down te necessary readings for te table & to find

te value of 6b.

5. Blot te grap or1ue as :rmature current to find 6t.

FF**+&+&**++44 RR. 6eep all switces in @88 position.-. Initially keep voltage adAustment B@ in minimum position.


potential position.. Connect module armature output : and :: to motor armature terminal : to

:: respectively.

?. Switc @! te power switc and S.

0. !ow armature voltage and armature current are taken by varying tearmature B@ wit in te rated armature current value.

>. e average resistance value in te table - gives te armature resistance.

PRPROOCCEEDURDUREE FFOORR TTRANRANSSFFERER FFUUNCNCTTIIONON OFOF FFIIEELLDD CCOONNTTRROLOL DD..CC..

SESERVRVOOMMOTOOTORR$$

FF**+&+&**++44 RR. 6eep all switces in @88 position.-. 6eep armature field voltage B@ in minimum potential position.


potential position.

. Connect module filed output 8 and 88 to motor filed terminal 8 and 88

respectively.


9/63

?. Switc @! te power# S and S-.0. !ow filed voltage and filed current are taken by varying te armature B@

wit in te rated armature current value.

>. abulate te value in te table no & 4 average resistance values give te fied

resistance.

FF**+&+&**++44 ::. 6eep all switces in @88 position.-. 6eep armature and field voltage B@ in minimum position.


position.

. Connect module varaic output B and ! to motor filed terminal 8 and 88

respectively.

?. Switc on te power note down reading for te various :C supply by

adAusting varaic for te table no & .

FF**+&+&**++44 ""''66

. 6eep all switces @88 position.-. Initially keep voltage adAustment B@ in minimum potential position.


position.

. Connect te module armature output : and :: to motor armature terminal

and :: respectively# and field 8 and 88 to motor field terminal 8 and 88

respectively.

?. Switc @! te power switc# S and S-.0. Set te filed voltage at rated value (=%).

>. :dAust te armature voltage using B@ on te armature side till it reaces

te 33 rpm.

=. igt te belt and take down te necessary reading for te table & ? 6tl

5. Blot te grap or1ue as 8ield current to find 6tl

OBSEOBSERVARVATTIIONON TTAABLEBLE FFOROR TTRARANNSSFFERER FUFUNNCCTTIIONON OFOF ARMAARMATTUURREE

CCOONNTTRROLOL DDCC SESERVRVOO MMOTOOTORR$$

TT8866ee NN%%$$;; T%T% **+&+& RR

Sl.!o If (amp) %f (%olt) ' f (om)


10/63


:vg 'f $

TT8866ee NN%%$$


11/63

Control Systems Laboratory Manual8ield Current :rmature Current


12/63


PREPARED BY V.BALAJI ,M.Tech, (Ph.D), Page

VIVA 1UESTIONS$

. Eat are te main parts of a ,C servo motorF

-. Eat are te two types of servo motorF

4. Eat are te advantages and disadvantages of a ,C servo motorF. Give te applications of ,C servomotorF

?. Eat do you mean by servo mecanismF

0. Eat do you mean by field controlled ,C servo motorF

MMOODDELEL CACALLCUCULLAATTIIOONN$$


13/63



Re-/6'$

TTRANRANSSFFERER FFUNUNCCTTIIONON OFOF AACC SESERVRVOO MMOTOROTOR

EE#P#PT.T.NNOO $$

DADATETE $$

AAIIMM$$


14/63



T% &e'e*+e 'he '+-e /+c'*%+ % 'he 4*0e+ AC -e0%%'%


S.N% Ne % 'he E/*3e+' R+4e T3e 1/+'*'

NAMNAMEE PPLLAATETE DDEETTAAIILS$LS$

@HBH /

%@L:G" /

CH''"! /

SB"", /

FUFUSESE RARATTIINNGS$GS$

*locked rotor test/ -?D of rated current.

T!EOT!EORYRY$$

:n servo motor is basically a two & pase induction type except for certainspecial design features. : two & pase servomotor differ in te following two ways

from a normal induction motor.

e rotor of te servomotor is built wit ig resistance. So tat its 7 '

(Inductive reactance 7 resistance) ratio is small wic result in liner speed & tor1ue

caracteristics. e excitation voltage applied to two & stator winding sould ave

a pase difference of 53o

==OORR""IINNGG PRPRIINNCCIIPPLELE OFOF AACC SESERRVVOOMMOTOROTOR

%oltages of e1ual rms magnitude and 53opase difference excite te stator

winding. ese results in exciting current i and i- tat are pase displaced by 53o

and ave e1ual rms value. ese current are rise to a rotating magnetic field of

constant magnitude. e direction of rotation depends on te pase relationsip of

te two current (or voltage).


15/63



e rotating magnetic field sweeps over te rotor conductor. e rotor

conductors experience a cange in flux and so voltage are induced in rotor

conductors. is voltage circulates current in te sort circuited rotor conductors

and te current creates rotor flux.

,ue to te interaction of stator and rotor flux# a mecanical force (or tor1ue)is developed on te rotor and te rotor starts moving in te same direction as tat

of rotating magnetic field.

FFOORMURMULLAA$$

ransfer 8unction $Laplace ransform of output

Laplace ransform of input

(s) 7 "s(s) $ 6 7 s2 9 6- 9 * $ 6m 7 9 s ()

6m $ 6 7 (6- 9 *) motor gain constant (-)

m $ 2 7 (6- 9 *) motor time constant (4)

or1ue () $ 5.= < r < s !m

S $ applied load in 6g

' $ radius of saft in m $ 3.30= m

CC%%++--''+'+' VV66//ee--$$

2 $ ?- gmcm-

$ 3.3?kg cm-# * $ 3.3=>?

TT8866ee NN%%$$

OBSEOBSERVARVATTIIONON TTAABLEBLE FFOROR DDETEETERMRMIINNIIGG MMOTOROTOR CCOONNSTSTANANTT

""$$

S.!oLoad

(kg)

Control

%oltage (%c)

or1ue

(!m)


16/63

TT8866ee NN%%$$ 22

OBSEOBSERVARVATTIIONON TTAABLEBLE FFOROR DDETEETERMRMIINNIINNGG MMOTOTOORR CCOONNSTSTANANTT

""22$$

S.!oSpeed (!)

rpm

Load

(kg)or1ue (!m)

PRPREECAUCAUTTIIOONNS$S$

i. Initially ,BS switc sould be in open condition.

ii. 6eep te autotransformer in minimum potential position.

iii. In blocked rotor test# block te rotor by tigtening te belt around te te

brake drum before starting te experiment.

BLOC" DIAGRAM OF SERVOMOTOR


17/63

PRPROOCCEEDURDURE$E$

FF%% &e'e&e'e**++**+4+4 %%''%% cc%%++--''+'+' ""77

. 6eep variac in minimum potential position.

-. Connect banana connectors JBout to BinK and J!out to !inK.

4. Connect 5pin , connector from te motor feed back to te input of module

%B" & 43-.

. Switc @! te -43% :C supply of te motor setup.

?. Switc @! te power switc.

0. Switc @! te S- (main winding) and S (control winding) switces.

>. Set te rated voltage (-43%) to control pase using %:'I:C.

=. :pply load to te motor step by step until it reacing 3 rpm.

5. ake necessary readings for te table .

3.o calculate 6plot te grap tor1ue vs control winding.

FF%% &e'e&e'e**++**+4+4 %%''%% cc%%++--''+'+' ""22

. 6eep variac in minimum potential position.

-. Connect banana connectors JBout to BinK and J!out to !inK.

4. Connect 5pin , connector from te motor feed back to te input of module

%B" & 43-.

. Switc @! te -43% :C supply of te motor setup.

?. Switc @! te power switc.

0. Switc @! te S- (main winding) and S (control winding) switces.


18/63

>. Set te rated voltage (-43%) to control pase using %:'I:C.

=. :pply load to te motor step by step until it reaces 3 rpm.

5. ake necessary readings for te table -.

3.o calculate 6- plot speed vs tor1ue curve.

MMOODDELEL GGRAPRAP!!

MMOTOROTOR CCOONNSTSTANANTT "2"2 MMOTOROTOR CCOONNSTSTANANTT ""

6-

$ 7 !

%

!6$ 7 %

S3ee& *+ 3 S3ee& *+ 3

MMOODDELEL CACALLCUCULLAATTIIOONN$$


19/63


VIVA 1UESTIONS$

. ,efine transfer functionF

-. Eat is :.C servo motorF Eat are te main partsF

4. Eat is servo mecanismF

. Is tis a closed loop or open loop system ."xplainF

?. Eat is back "M8F

Re-/6'$

ANALOG SIMULATION OF TYPE > ? +& TYPE > SYSTEM

AIM$o study te time response of first and second order type &3 and type systems.

APPARATUS RE1UIRED$. Linear system simulator kit

-. C'@

FORMULAE USED$

PREPARED BY V.BALAJI ,M.Tech, (Ph.D), AP/EEE, DCEPage 17


20/63

. ,amping ratio# $ (ln MB)-

7 (-

9 (ln MB)-)


Eere MB is peak percent oversoot obtained from te response grap

-. Hndamped natural fre1uency# n $ 7 tp ( -)

Eere tp is peak time obtained from te response grap

4. Closed loop transfer function of type3 second order system is

C(s) 7 '(s) $ G(s) 7 9G(s)

Eere G(s) $ 6 6- 64 7 (9s) ( 9 s-)6 is te gain

6- is te gain of te time constant & block $3

64 is te gain of te time constant & - block $3

is te time constant time constant & block $ ms- is te time constant time constant & - block $ ms

. Closed loop transfer function of type second order system is

C(s) 7 '(s) $ G(s) 7 9G(s)Eere G(s) $ 6 6 6- 7s ( 9 s)

6 is te gain

6 is te gain of Integrator $ 5.0

6- is te gain of te time constant & block $3 is te time constant of time constant & block $ ms

eoretical %alues of n and can be obtained by comparing te coefficients ofte denominator of te closed loop transfer function of te second order systemwit te standard format of te second order system were te standard format is

C(s) 7'(s) $ n-

7 s-

9 - ns 9 n-

T!EORY$

e type number of te system is obtained from te number of poles located at origin in a

given system. ype & 3 system means tere is no pole at origin. ype & system means tere isone pole located at te origin.

e order of te system is obtained from te igest power of s in te denominator of

closed loop transfer function of te system

e first order system is caracteriNed by one pole or a Nero. "xamples of first ordersystems are a pure integrator and a single time constant aving transfer function of te form 67sand 67 (s9). e second order system is caracteriNed by two poles and upto two Neros. e

standard form of a second order system is C(s) 7'(s) $ n-

7 (s-

9 - ns 9 n-) were is

damping ratio and n is undamped natural fre1uency.

BLOC" DIAGRAM$

. T% *+& -'e& -''e e% % '3e@ --'e



21/63



-. T% *+& -'e& -''e e% % '3e@ ? --'e

;. T% *+& 'he c6%-e& 6%%3 e-3%+-e % T3e@ -ec%+& %&e --'e


22/63



PROCEDURE$

. T% *+& 'he -'e& -''e e% % '3e > *-' %&e --'e

. e blocks are connected using te patc cords in te simulator kit.

-. e input triangular wave is set to % peak to peak in te C'@ and tis is appliedto te '"8 terminal of error detector block. e input is also connected to te

cannel of C'@.4. e output from te system is connected to te O cannel of C'@.. e experiment sould be conducted at te lowest fre1uency so keep te fre1uency

knob in minimum position to allow enoug time for te step response to reac near

steady state.

?. e C'@ is kept in O mode and te steady state error is obtained as te verticaldisplacement between te two curves.

0. e gain 6 is varied and different values of steady state errors are noted.

2. T% *+& 'he -'e& -''e e% % '3e > ? *-' %&e --'e

. e blocks are connected using te patc cords in te simulator kit.-. e input s1uare wave is set to % peak to peak in te C'@ and tis is applied

to te '"8 terminal of error detector block. e input is also connected to te

cannel of C'@.

4. e output from te system is connected to te O cannel of C'@.. e C'@ is kept in O mode and te steady state error is obtained as te vertical

displacement between te two curves.

?. e gain 6 is varied and different values of steady state errors are noted.

;. T% *+& 'he c6%-e& 6%%3 e-3%+-e % '3e > ? +& '3e@ -ec%+& %&e -5-'e

. e blocks are connected using te patc cords in te simulator kit.-. e input s1uare wave is set to % peak to peak in te C'@ and tis is applied

to te '"8 terminal of error detector block. e input is also connected to te cannel of C'@.

4. e output from te system is connected to te O cannel of C'@.

. e output waveform is obtained in te C'@ and it is traced on a grap

seet. 8rom te waveform te peak percent oversoot# settling time# rise time#

peak time are measured. Hsing tese values n and are calculated.


23/63



?. e above procedure is repeated for different values of gain 6 and te values arecompared wit te teoretical values.

TABULAR COLUMN$

. T% *+& 'he -'e& -''e e% % '3e > *-' %&e --'e

S.N%. G*+ ," S'e& -''e e% e-- (V)

2. T% *+& 'he -'e& -''e e% % '3e > ? *-' %&e --'e

S.N%. G*+ ," S'e& -''e e% e-- (V)

;. T% *+& 'he c6%-e& 6%%3 e-3%+-e % '3e > ? -ec%+& %&e --'e

S.N%. G*+,

"

Pe3ece+'

O0e-h%%',

MP

R*-e'*e,

'(-ec)

Pe'*e,

'3(-ec)

Se''6*+4'*e,'-(-ec)

G3h*c6 The%e'*c6

D

3*+4

'*%

U+&3e&

+'/6

e/e+c,

+ (&-ec)

D

3*+4

'*%

U+&3e&

+'/6

e/e+c,

+(&-ec)


24/63



-ec%+& %&e --'e

S.N%. G*+,

"

Pe

3ece+'

O0e-h%%',

MP

R*-e

'*e,

'

(-ec)

Pe

'*e,

'3

(-ec)

Se''6*+4

'*e,'-(-ec)

G3h*c6 The%e'*c6

D

3*+4

'*%

U+&3e&

+'/6

e/e+c,+

(&-ec)

D3*+4

'*%

U+&3e&

+'/6

e/e+c,+(,&-ec)

MODEL GRAP!$

MODEL CALCULATION$

RESULT


25/63


26/63



EE#P#PT.T.NNOO $$

DADATETE $$

AAIIMM$$

(*) T% %8'*+ 'he 8%&e 36%', N/*-' 36%' +& %%' 6%c/- % 'he 4*0e+

'+-e /+c'*%+.

(**) T% +6-*- 'he -'8*6*' % 4*0e+ 6*+e --'e /-*+4 MATLAB.

APPARATUS RE1UIRED$

System wit M:L:*

T!EOT!EORYRY$$

FFe/e+e/e+cc RRee--33%%++--e$e$

e fre1uency response is te steady state response of a system wen te

input to te system is a sinusoidal signal.

8re1uency response analysis of control system can be carried eiter

analytically or grapically. e various grapical tecni1ues available for

fre1uency response analysis are. *ode Blot

-. Bolar plot (!y1uist plot)

4. !icols plot

. M and ! circles

?. !icols cart

BB%%&e&e 336%6%''$$

e bode plot is a fre1uency response plot of te transfer function of a

system. : bode plot consists of two graps. @ne is plot of te magnitude of asinusoidal transfer function versus log . e oter is plot of te pase angle of a

sinusoidal transfer function versus log .

e main advantage of te bode plot is tat multiplication of magnitude can

be converted into addition. :lso a simple metod for sketcing an approximate log

magnitude curve is available.


27/63


PP%%66 3366%%'$'$

e polar plot of a sinusoidal transfer function G (A ) on polar coordinates

as is varied from Nero to infinity. us te polar plot is te locus of vectors

G (A ) G (A ) as is varied from Nero to infinity. e polar plot is also called!y1uist plot.

NN//**--'' SS''88*6*6**'' CC**'e'e**%%+$+$

If G(s)+(s) contour in te G(s)+(s) plane corresponding to !y1uist contour

in splane encircles te point & 9A3 in te anti & clockwise direction as many times

as te number of rigt alf splain of G(s)+(s). en te closed loop system is

stable.

RR%%%%'' LL%%cc//--$$

e root locus tecni1ue is a powerful tool for adAusting te location of

closed loop poles to acieve te desired system performance by varying one or

more system parameters.

e pat taken by te roots of te caracteristics e1uation wen open loop

gain 6 is varied from 3 to are called root loci (or te pat taken by a root of

caracteristic e1uation wen open loop gain 6 is varied from 3 to is called root

locus.)

FFe/e+e/e+cc DD%%**++ S3ecS3ec****cc''*%*%++--$$

e performance and caracteristics of a system in fre1uency domain are

measured in term of fre1uency domain specifications. e re1uirements of a

system to be designed are usually specified in terms of tese specifications.

e fre1uency domain specifications are

. 'esonant peak# Mr

-. 'esonant 8re1uency# r.

4. *andwidt.

. Cut & off rate

?. Gain margin

0. Base margin

PREPARED BY V.BALAJI ,M.Tech, (Ph.D), AP/EEE, DCEPage 2"


28/63


RRee-%-%+++'+' PPee,, MM

e maximum value of te magnitude of closed loop transfer function is

called te resonant peak# Mr. : large resonant peak corresponds to a large over

soot in transient response.

RRee-%-%+++'+' FFee//e+e+cc,,

e bandwidt is te range of fre1uency for wic te system gain is more

tan 4db. e fre1uency at wic te gain is 4db is called cut off fre1uency.

*andwidt is usually defined for closed loop system and it transmits te signals

wose fre1uencies are less tan cutoff fre1uency. e bandwidt is a measured of

te ability of a feedback system to produce te input signal# noise reAection

caracteristics and rise time. : large bandwidt corresponds to a small rise time orfast response.

CC/'@O/'@O RR'e$'e$

e slope of te logmagnitude curve near te cut off fre1uency is called

cutoff rate. e cutoff rate indicates te ability of te system to distinguis te

signal from noise.

GG**++ MM44**+,+, ""44

e gain margin# 6g is defined as te reciprocal of te magnitude of open

loop transfer function at pase cross over fre1uency. e fre1uency at witc te

pase of open loop transfer function is =3 is called te pase cross over

fre1uency# pc.

PPhh--ee MM4*4*+,+,

e pase margin # is tat amount of additional pase lag at te gain cross

over fre1uency re1uired to bring te system to te verge of instability# te gaincross over fre1uency gc is te fre1uency at wic te magnitude of open loop

transfer function is unity (or it is te fre1uency at wic te db magnitude is Nero).


PREPARED BY V.BALAJI ,M.Tech, (Ph.D), AP/EEE, DCEPage 2#


29/63


. "nter te command window of te M:L:*.

-. Create a new M & file by selecting 8ile & !ew & M & 8ile.

4. ype and save te program.

. "xecute te program by eiter pressing 8? or ,ebug & 'un.

?. %iew te results.0. :nalysis te stability of te system for various values of gain.

PP%%8866ee

@btain te bode diagram for te following system

x 3 x

y

x- -? Cx-

3 y-

y 3 x y- -? Cx-

MAMATLTLAABB PP%4%4

9 ? @25 @


30/63

PREPARED BY V.BALAJI ,M.Tech, (Ph.D),

AP/EsE(Es, DCE)Page27


31/63


32/63

Page 2


33/63


Re-/6'$

CCLOSEDLOSED LOOPLOOP SSPPEEDEED CCOONNTTRROLOL SSYYSTEMSTEM



34/63


35/63


. Make te connections as per te circuit diagram.

-. Set te speed of te motor using set position.

4. %ary te gain values of B#I# and , controller until to get te set speed to

current speed.

. 'epeat te above procedure for different values of set speed.

Re-/6'$

STSTUDUDYY OFOF AACC SSYYNCNC!!RROO TTRANRANSSMMIITTERTTER ANANDD RREECCEEIIVVERER



36/63


EE#P#PT.T.NNOO $$

DADATETE $$


AAIIMM$$

T% -'/& 'he %3e'*%+ % AC -+ch% '+-*''e +& ece*0e


S.N% Ne % 'he E/*3e+' 1/+'*'

S+ch% '+-*''e +& ece*0e /+*' N%-

2 M/6'*e'e (D*4*'6 A+6%4 ) N%-; P'ch c%&- A- e/*e&

T!EOT!EORYRY$$

: syncro is an electromagnetic transducer commonly used to

convert an angular position of a saft into an electric signal. It is commercially

known as a selsyn or an autosyn. e basic syncro unit is usually called a syncro

transmitter. Its construction is similar to tat of tree pase alternator. e stator is

of laminated silicon steel and is slotted to accommodate a balanced tree pase

winding wic is usually of concentric coil type and star connected. e rotor is

dumb bell construction and its wound wit a concentric coil.

:C voltage is applied to rotor winding troug slip rings. Let and

:C voltage

%r (t) $ %r sin ct be applied to te rotor of te syncro transmitter.

e voltage causes a flow of magnetiNing current in rotor coil wic produces a

sinusoidally time varying flux directed along its axis and distributed nearlysinusoidally in te air gap along te stator peripery. *ecause of transformer

action# voltage is induced in eac of te stator coil. :s te air gap flux sinusoidally

distributed te flux linking wit any stator coil is proportional to te cosine of te

angle between te axes of rotor and stator coil. is flux voltage in eac stator coil.

%oltages are in time.


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pase wit eac oter. us te syncro transmitter acts a like a singlepase

transformer in wic te rotor coil is te primary and te stator coil is te

secondary.

Let %sn# %s-n# %s4n# be te voltage induced in te stator coils# S# S-#

S4 respectively wit respect to te neutral. en for a rotor position of te syncrotransmitter# is te angle made by rotor axis wit te stator coil S-.

e various stator voltages are

%sn $ 6%r sin ct cos ( 9 -3o)

%s-n $ 6%r sin ct cos

%sn $ 6%r sin ct cos ( 9 -3o)

e terminal voltages of te stator are

Vss-

Vs-s4

Vsn

Vs-n

Vs-n

Vs4n

4KVr sin(

4KVr sin(

-3o

-3o

sin ct

) sin ct

Vs4s Vs4n Vs

n

4KVr sin sin ct

Een $ 3# %ss- and %s- s4 ave te maximum voltage and wile %s4s as

Nero voltage. is position of rotor is defined as t electrical Nero of te transmitter

and is used as reference for specifying te angular position of te rotor.

us it is seen tat te input to te syncro transmitter is te angular

position of its rotor saft and te output is a set of tree signal pase voltages. e

magnitudes of tis voltage are function of te sift position. e output of te

syncro transmitter is applied to stator winding of syncro control transformer.

e control transmitter is similar in construction to a syncro transmitter

except for te fact tat rotor of te control transformer in made cylindrical in sape

so tat te air gap is practically uniform. e system (transmitter and control

transformer pair) acts an error detector# circulating current to te same pase but of

different magnitudes flow troug two stator coils. e result is establisment of

an indentical flux pattern in te air gap of te control transformer as te voltage

drops in resistance and lockage reactancePs of two sets of stator coils are usually

small.

PREPARED BY V.BALAJI ,M.Tech, (Ph.D), AP/EEE, DCE

Page 33


38/63



OBSEOBSERVARVATTIIONON TTAABLE$BLE$

S.N%T,+-*''e

(De4ee)

Rece*0e

(De4ee)V- > V-2 V-2 > V-; V-; > V- E%

te syncro transmitter rotor# te voltage induced te control transformer rotor is

proportional to te cosine of te angle between te two rotors given by

" (t) $ 6%r cos sin r t


39/63


e syncro transmitter and control transformer tus act as an error detector giving

a voltage signal at te rotor terminals of te control transformer proportional to te

angular difference between te transmitter control transformer saft positions.

PRPROOCCEEDURDURE$E$. Make te connections as per te patcing diagram.

-. Switc @! te supply.

4. %ary te saft position of te transmitter and observe te corresponding

canges in te saft position of te receiver.

. 'epeat te above steps for different angles of te transmitter.

?. abulated te different voltage at te test points of S S-# S4S-# and S4S.

Re-/6'$

CYCL E > 2

7. () L4 C%3e+-'%.

PREPARED BY V.BALAJI ,M.Tech, (Ph.D), AP/EEE, DCEPage 3"


40/63



7. (8) Le& C%3e+-'%.

. D*4*'6 S*/6'*%+ % N%+@L*+e S-'e.

. D*4*'6 S*/6'*%+ % L*+e S-'e.

?. D*4*'6 S*/6'*%+ % T3e ? +& T3e S-'e.

DDIIGGIITTAALL SSIIMUMULLAATTIIONON OFOF NNOONN@L@LININEEAARR SSYYSTEMSTEM

EE#P#PT.T.NNOO $$


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DADATETE $$

AAIIMM$$

T% -*/6'e 'he '*e e-3%+-e chc'e*-'*c % 6*+e --'e K*'h -*36e+%+@6*+e*'*e- 6*e -'/'*%+ +& &e& %+e.


System wit M:L:* 0.?

T!EOT!EORYRY$$

NN%%+@L+@L**+e+e SS--'e'e--$$

e non linear system are system witc do not obey te principle of

superposition.

In practical engineering systems# tere will be always some non linearity due

to friction# inertia# stiffness# backslas# ysteresis# saturation and dead & None. e

effect of te non linear components can be avoided by restricting te operation of

te component over a narrow limited range.

CC66----****cc''**%%++ %% ++%%++ 6*6*++ee**''**ee--$$

e non linearities can be classified as incidental and intentional.

e incidental non linearities are tose wic are inerently present in

te system. Common examples of incidental non linearities are saturation# dead &

None# coulomb friction# stiction# backlas# etc.e intentional non linearities are tose wic are deliberately

inserted in te system to modify system caracteristics. e most common

example of tis type of non linearity is a relay.

SS'/'/''*%*%++$$



42/63


In tis type of non linearity te output proportional to input for limited

range of input signals. Een te input exceeds tis range# te output tends to

become nearly constant.

:ll devices wen driven by sufficient large signals# exibit te

penomenon of saturation due to limitations of teir pysical capabilities.

Saturation in te output of electronic# rotating and flow amplifiers# speed and

tor1ue saturation in electric and ydraulic motors# saturation in te output of

sensors for measuring position# velocity# temperature# etc. are te well known

examples.

DDee&& ::%%+e$+e$

e dead None is te region in witc te output is Nero for given input.

Many pysical devices do not respond to small signals# i.e.# if te input amplitude

is less tan some small value# tere will be no output. e region in wic te

output is Nero is called dead None. Een te input is increased beyond tis dead

None value# te output will be linear.


. ,ouble click on M:L:* 0.? icon on desktop command window opens.

-. 8rom 8ile ab# select !ew Model file.

4. : Simulink model screen opens a JuntitledK.

. 8rom Simulink library & select necessary blocks and place in new model

screen.*lock

Constant SimulinkContinuous

Simulator SimulinkMat operator

ransfer function SimulinkContinuous



43/63


Scope Simulink &sink

,ead ;one# Saturation Simulink!onlinear

?. Select properties for eac item and connect tem as sown in diagrams.

0. Select simulation ab and configuration parameters and select ode-4tb

model.

>. Save file under QworkP directory.

=. Simulated te system wit step and sine inputs wit and witout dead None#

saturation non & linearities.

5. !ame te signals as mentioned in diagram and observe signal names on

scope by rigt clicking on response curve and by opening axes.



44/63


PREPARED BY V.BALAJI ,M.Tech, (Ph.D), AP/EEE, DCEPage !0


45/63




46/63


Re-/6'$

EE#P#PT.T.NNOO $

DADATETE $

DDIIGGIITTAALL SSIIMUMULLAATTIIONON OFOF LLIINNEEAARR SSYYSTEMSTEM



47/63


AAIIMM$$

T% -*/6'e 'he '*e e-3%+-e chc'e*-'*c % h*4he@%&e M/6'*@

*+3/' /6'* %/'3/' (MIMO) 6*+e --'e /-*+4 -''e 0*86e %/6'*%+.


M:L:* 0.?

T!EOT!EORYRY$$

T*e D%*+ S3ec**c'*%+

e desired performance caracteristics of control systems are specified in

terms of time domain specification. System wit energy storage elements

cannot respond instantaneously and will exibit transient responses# wenever

tey are subAected to inputs or disturbances.

e desired performance caracteristics of a system of any order may be

specified in terms of te transient response to a units step input signal.

e transient response of a system to a unit step input depends on te initial

conditions. erefore to compare te time response of various systems it is

necessary to start wit standard initial conditions. e most practical standard is

to start wit te system at rest and output and all time derivatives tere of Nero.

e transient response of a practical control system often exibits damped

oscillation before reacing steady state.

e transient response caracteristics of a control system to a unit step input

are specified in terms of te following time domain specifications.. ,elay time# td

-. 'ise time# tr

4. Beak time# tp

. Maximum oversoot# Mp



48/63

-

-


?. Setting time# ts

FFOORMURMULLAA$$

Risetimed

where tan) )

D3e& e/e+c % %-c*66'*%+,d n


>. "nter te command window of te M:L:*.

=. Create a new workspace by selecting new file.

5. Complete your model.

3.'un te model by eiter pressing 8? or start simulation.

.%iew te results.

-.:nalysis te stability of te system for various values of gain.

PRPROBLEOBLEMM$$

@btain te step response of series 'LC circuit wit ' $ .46 # L $ -0m+ and

C$4.4 f using M:L:* M & 8ile.

MAMATLTLAABB PRPROGOGRRAAMM FFOROR UUNNIITT IIMMPUPULSELSE PRPRSSPPOONNSSEE$$

PRPROGOGRAMRAM$$

+/ 9 ? ?

&e+ 9 ?.2

PREPARED BY V.BALAJI ,M.Tech, (Ph.D), AP/EEE, DCEPage !!


49/63


*3/6-e (+/, &e+)

4*&

'*'6e ( /+*' *3/6-e e-3%+-e 36%')

MAMATLTLAABB PRPROGOGRRAAMM FFOROR UUNNIITT STEPSTEP PRPRSSPPOONNSE$SE$

PRPROGOGRAMRAM$$

F%' 6%+4 e

+/ 9 ? ? .e?

&e+ 9 5???? .e?

-'e3 (+/, &e+)

4*& %+

'*'6e (-'e3 e-3%+-e % -e*e- RLC c*c/*')

Re-/6'$

DIGITAL SIMULATION OF TYPE ? AND TYPE SYSTEM

E#PT.NO $

DATE $

PREPARED BY V.BALAJI ,M.Tech, (Ph.D), AP/EEE, DCEPage !"


50/63


AIM$

T% -*/6'e 'he '*e e-3%+-e chc'e*-'*c- % *-' %&e -ec%+&

%&e, '3e ? +& '3e --'e /-*+4 MATLAB.

APPARATUS RE1UIRED$

System employed wit M:L:* 0.?

T!EORY$

e desired performance caracteristics of control system are specified in

terms of time domain specification. Systems wit energy storage elements cannot

respond instantaneously and will exibit transient responses# wenever tey are

subAected to inputs or disturbances.

e desired performance caracteristics of a system pf any order may be

specified in terms of te transient response to a unit step input signal.

e transient response of a system to unit step input depends on te initial

conditions. erefore to compare te time response of various systems it is

necessary to start wit standard initial conditions. e most practical standard is to

start wit te system at rest and output and all time derivatives tere of Nero. e

transient response of a practical control system often exibits damped oscillations

before reacing steady state.

e transient response caracteristics of a control system to a unit step input

are specified in terms of te following time domain specifications.

. ,elay time# td

-. 'ise time# tr

4. Beak time# tp

. Maximum oversoot# Mp

?. Settling time# ts

PREPARED BY V.BALAJI ,M.Tech, (Ph.D), AP/EEE, DCEPage !#


51/63


e time domain specification is defined as follows.

. De6 T*e$

It is te taken for response to reac ?3D of te final value# for te very first

time.

2. R*-e T*e$

It is te time taken for response to raise from 3 to 33D for te very first

time. 8or under damped system# te rise time is calculated from 3 to 33D. *ut for

over damped system it is te time taken by te response to raise from 3D to 53D.

8or critically damped system# it is te time taken for response to raise from ?D to

5?D.

Risetimed

Where tan

s-

7s

D3e& e/e+c % %-c*66'*%+, d

;. Pe T*e$

n s-

It is te time taken for te response to reac te peak value for te very first

time. (or) It is te taken for te response to reac te peak oversoot# tp.

Beak time $ 7 d


52/63

ts

t

t

s

s

DMp e

s


4

x33

5. Se''6*+4 T*e$

It is defined as te time taken by te response to reac and stay witin a

specified error. It is usually expressed as D of final value. e usual tolerable error

is -D or ?D of te final value.

ts

forn

4for

n

- D erroe

? D erroe

FORMULA$

DMp e

s

4x)33

for

n

4for

n

-D erroe

?D erroe

PREPARED BY V.BALAJI ,M.Tech, (Ph.D), AP/EEE, DCEPage !


53/63


PROCEDURE$

C6%-e& 6%%3 e-3%+-e % *-' %&e --'e$


-. Create a new workspace by selecting new file.


. 'un te model by eiter pressing 8? or start simulation.

?. :nalysis te stability of te system for various values of gain

C6%-e& 6%%3 e-3%+-e % -ec%+& %&e --'e$


-. Create a new workspace by selecting new file.


. 'un te model by eiter pressing 8? or start simulation.

?. %iew te results.

0. :nalysis te stability of te system for various values of gain.

Ge+e6 MATLAB c%&*+4 % c6%-e& 6%%3 e-3%+-e % '3e ? +& '3e

--'e$

PROGRAM$

c6e 66



54/63


c6%-e 66

c6c

T 9 ' (2.25, ?.5 2.25 )

393%6e (T)

3e98- (e6 (3())) 3*98-

(*4 (3()))

K+9-'(3e3e3*3*)

&3*+4 '*%9(3eK+)

%-9(eH3(@3e3*3*))??

'393*3*

'-9


55/63



System employed wit M:L:* 0.?

T!EOT!EORYRY$$

e control systems are designed to perform specific taskes. Een

performance specification are given for single input. Single output linear time

invariant systems. en te system can be designed by using root locus or

fre1uency response plots.

e first step in design is te adAustment of gain to meet te desired

specifications. In practical system. :dAustment of gain alone will not be sufficient

to meet te given specifications. In many cases# increasing te gain may result poor

stability or instability. In suc case# it is necessary to introduce additional devices

or component in te system to alter te beavior and to meet te desired

specifications. Suc a redesign or addition of a suitable device is called

compensations. : device inserted into te system for te purpose or satisfying te

specifications is called compensator. e compensator beavior introduces pole R

Nero in open loop transfer function to modify te performance of te system.

e different types of electrical or electronic compensators used are lead

compensator and lag compensator.

In control systems compensation re1uired in te following situations.

. Een te system is absolutely unstable ten compensation is re1uired

to stabiliNe te system and to meet te desired performance.

-. Een te system is stable. Compensation is provided to obtain te

desired performance.

LAG COMPENSATOR$

: compensator aving te caracteristics of a lag network is called a lag

compensator. If a sinusoidal signal is applied to a lag network# ten in steady state

te output will ave a pase lag wit respect input.

PREPARED BY V.BALAJI ,M.Tech, (Ph.D), AP/EEE, DCEPage "1


56/63


Lag compensation result in a improvement in steady state performance but

result in slower response due to reduced bandwidt. e attenuation due to te lag

compensator will sift te gain crossover fre1uency to a lower fre1uency point

were te pase margin is acceptable. us te lag compensator will reduce te

bandwidt of te system and will result in slower transient response.

Lag compensator is essentially a low pass filter and ig fre1uency noise

signals are attenuated. If te pore introduce by compensator is cancelled by a Nero

in te system# ten lag compensator increase te order of te system by one.

FORMULA$

GainB

A

y3

x3

-3 log( B 7 A )

Phase sin (x3

7A)

sin (y

3

7B )

PROCEDURE$

=*'h %/' c%3e+-'%$

. Make te connection as per te circuit diagram.

2. :pply te -% pp sin wave input and observe te waveform.

;. %ery te fre1uency of te sin wave input and tabulate te values of xo and yo


57/63

Page "2


58/63


4. 8rom te transfer function calculated '# '- and C.

. Set te amplifier gain at unity.

?.

.

Insert te lag compensator wit te elp of passive

determine te pase margin of te plant.

@bserve te step response of te compensated system.

components and

MATLAB c%&*+4 K*'h C%3e+-'%$

PROGRAM$

+/ 9 ? ? ?? 5

&e+ 9


59/63


Re-/6'$

LEAD COMPENSATOR$

: compensator aving te caracteristics of a lead network is called a lead

compensator. If sinusoidal signal is applied to a lead network# ten in steady state

te output will ave a pase lead wit respect to input.

PREPARED BY V.BALAJI ,M.Tech, (Ph.D), AP/EEE, DCEPage "!


60/63


e lead compensator increase te bandwidt# wic improves te speed of

response and also reduces te amount of oversoot. Lead compensation

appreciably improves te transient response# wereas tere is a small cange in

steady state accuracy. Generally lead compensation is provided to make an

unstable system as a stable system. : lead compensator is basically a ig pass

filter and so it amplifies ig fre1uency noise signals. If te pole is introduced by

te compensator is not cancelled by a Nero in te system# ten lead compensator

increases order of te system by one.

FORMULA$

GainB

A

y3

x3

-3 log( B 7 A )

Phase sin (x3

7A)

sin(y3

7B )

PROCEDUR$

. "nter te command window of M:L:*.

-. Create a !ew M8ile by selecting file !ew M8ile.


. "xecute te program by pressing 8? or ,ebug 'un.

?. %iew te results.

0. :nalyNe te 'esults.

=*'h 6e& c%3e+-'%$


-. Create a new M & file by selecting 8ile & !ew &M8ile.

PREPARED BY V.BALAJI ,M.Tech, (Ph.D), AP/EEE, DCE


61/63

Page ""


62/63



. "xecute te program by eiter pressing 8? or ,ebug & 'un.

?. %iew te results.

0. :nalysis te result.

MATLAB c%&*+4 K*'h %/' C%3e+-'% % 6%%3 --'e

PROGRAM$

&e+9 ?.7; ?.2 ?

3*'ch9'(+/, &e+)

--c69ee&8c (3*'ch,)

&e9?.2

'9?$?.?$?*4/e

-'e3(&e--c6, ')

--c69ee&8c (3*'ch,?)

&e9?.2

'9?$?.?$?

8%&e(--c6, ')

4*& %+

'*'6e ( QBODE PLOT FOR CLOSED LOOP SYSTEM =IT!OUT

COMPENSATORQ)

MATLAB c%&*+4 K*'h C%3e+-'% % 6%%3 --'e

PROGRAM$

PREPARED BY V.BALAJI ,M.Tech, (Ph.D), AP/EEE, DCEPage "#


63/63


+/9 5 ?.77<

&e+9 ?.7; ?.2 ?

3*'ch9'(+/, &e+)

6e&92??

T6e&9?.??25

"9?.6e&9'("6e&T6e& , T6e& )

8%&e(6e&3*'ch)

--c69ee&8c(6e&3*'ch,?)

&e9?.2

'9?$?.?$?

*4/e

-'e3 (&e--c6, ')

'*'6e(QBODE PLOT FOR CLOSED LOOP SYSTEM =IT!

COMPENSATORQ)

Re-/6'$

ee 2257 control system lab manual

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