ee2257 lab manual

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EE2257 Control Systems Laboratory Manual / II EEE A, V SEM

RAJALAKSHMI ENGINEERING COLLEGE

THANDALAM, CHENNAI 602 105

DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

LABORATORY MANUAL

CLASS : II YEAR EEE - A

SEMESTER : IV (DEC 2010 MAY 2011

S!"JECT CODE : EE225#

S!"JECT : CONTROL SYSTEMS

LA"ORATORY

STAFF IN-CHARGE : P$S$MAY!RAPPRIYAN A%%&')*+ P&+%%&

EEE D+.)*/+*

Department of EEE, Rajalakshmi Engineering College, Chennai 1


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RAJALAKSHMI ENGINEERING COLLEGE

THANDALAM, CHENNAI 602 105

DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

EE225# CONTROL SYSTEMS LA"ORATORY MAN!AL

NAME :

CLASS :

SEMESTER :

ROLL N!M"ER :

REGISTER N!M"ER :



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INDE

S$N&$

D)*+ T*+ & E3.+/+*P)4+N&$

M)% S4)*+



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SYLLA"!S

EE225# CONTROL SYSTEM LA"ORATORY 0 0 7 2

1. Determination of transfer function of DC Servomotor2. 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 order systems10.Digital simulation of second order systems

) * " Total * "DETAILED SYLLA"!S

1$ D+*+/)*& & T)%+ F'*& P))/+*+% & ) DC S+8&M&*&

A/To derive t+e transfer function of t+e given D.C Servomotor and e,perimentallydetermine t+e transfer function parameters

E3+'%+1. Derive t+e transfer function from %asic principles for a separately e,cited DC

motor.2. Determine t+e armature and field parameters %y conducting suita%le e,periments.3. Determine t+e mec+anical parameter %y conducting suita%le e,periments.. )lot t+e freuency response.

E9./+*1. DC servo motor field separately e,cited loading facility varia%le voltage

source - 1 /o2. Tac+ometer 1 /o3. #ultimeter 2 /os. Stop atc+ 1 /o

2$ D+*+/)*& & T)%+ F'*& P))/+*+% & AC S+8& M&*&

A/To derive t+e transfer function of t+e given A.C Servo #otor and e,perimentallydetermine t+e transfer function parameters

Department of EEE, Rajalakshmi Engineering College, Chennai


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E3+'%+1. Derive t+e transfer function of t+e AC Servo #otor from %asic )rinciples.2. %tain t+e D.C gain %y operating at rated speed.3. Determine t+e time constant mec+anical

. )lot t+e freuency response E9./+* 1. AC Servo #otor #inimum of 100 necessary sources for main inding and control inding 1 /o 2. Tac+ometer 1 /o 3. Stopatc+ 1 /o . 4oltmeter 1 /o

7$ A)&4 S/)*& & T.+-0 A; T.+-1 S%*+/

A/To simulate t+e time response c+aracteristics of 5 order and 55 order6 type 0 and type-1systems.

E3+'%+1. %tain t+e time response c+aracteristics of type 0 and type-16 5 order and 55

order systems mat+ematically.2. Simulate practically t+e time response c+aracteristics using analog rigged up

modules.3. 5dentify t+e real time system it+ similar c+aracteristics.

E9./+*1. 7igged up models of type-0 and type-1 system using analog components.2. 4aria%le freuency suare ave generator and a normal C7 - 1 /o or DC source and storage scilloscope - 1 /o


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5$ D+*+/)*& & T)%+ '*& & DC M&*&

A/To determine t+e transfer function of DC motor

E3+'%+

1. %tain t+e transfer function of DC motor %y calculating and gain

E9./+*1. DC #otor2. Tac+ometer3. 4arious meters. Stop atc+

6$ S*)=* A)%% & L+) S%*+/%

A/To analyse t+e sta%ility of linear systems using 8ode 9 7oot locus 9 /yuist plot

E3+'%+1. :rite a program to o%tain t+e 8ode plot 9 7oot locus 9 /yuist plot for t+e given

system2. Access t+e sta%ility of t+e given system using t+e plots o%tained3. Compare t+e usage of various plots in assessing sta%ility

E9./+*

1. System it+ #AT;A8 9 #AT


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>$ S*+..+ M&*& C&*& S%*+/

A/To study t+e or=ing of stepper motor

E3+'%+1. To verify t+e or=ing of t+e stepper motor rotation using microprocessor.

E9./+* 1. Stepping motor

2. #icroprocessor =it3. 5nterfacing card. )oer supply

?$ D4*) S/)*& & F%* O;+ S%*+/

A/To digitally simulate t+e time response c+aracteristics of first -order system

E3+'%+1. :rite a program or %uild t+e %loc= diagram model using t+e given softare.2. %tain t+e impulse6 step and sinusoidal response c+aracteristics.3. 5dentify real time systems it+ similar c+aracteristics.

E9./+*1. System it+ #AT;A8 9 #AT


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LIST OF EPERIMENTS

FIRST CYCLE:

1. Determination of transfer function of armature controlled DCservomotor.

2. Determination of transfer function of field controlled DC servomotor.

3. Determination of transfer function of AC servomotor.

. Determination of transfer function of separately e,cited DC generator.". Determination of transfer function of DC motor.

$. DC position control system.

SECOND CYCLE:

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

'. Digital simulation of first order systems.

(. Digital simulation of second order systems

10. Sta%ility analysis of linear systems.

11. Stepper motor control system.

12. AC position control system.

Department of EEE, Rajalakshmi Engineering College, Chennai '


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E3.*$ N&: D)*+:

DETERMINATION OF TRANSFER F!NCTION OFARMAT!RE CONTROLLED DC SERVO MOTOR

AIM: To determine t+e transfer function of armature controlled DC servo motor.APPARAT!S @ INSTR!MENTS RE!IRED:

S$ N& D+%'.*& R)4+ T.+ )**1. DC servo motor trainer =it - 12. DC servo motor 13. 7+eostat "00>91A 1

. Ammeter 0-1A #C 10-100 mA #5 1

". 4oltmeter 0300 4 #C 1

0&" 4 #5 1$. Stopatc+ - 1&. )atc+ cords - As reuired

THEORY:

5n servo applications a DC motor is reuired to produce rapid accelerations from standstill.T+erefore t+e p+ysical reuirements of suc+ a motor are lo inertia and +ig+ starting torue.;o inertia is attained it+ reduced armature diameter it+ a conseuent increase in t+earmature lengt+ suc+ t+at t+e desired poer output is ac+ieved. T+us6 e,cept for minordifferences in constructional features a DC servomotor is essentially an ordinary DC motor.

A DC servomotor is a torue transducer +ic+ converts electrical energy into mec+anicalenergy. 5t is %asically a separately e,cited type DC motor. T+e torue developed on t+emotor s+aft is directly proportional to t+e field flu, and armature current6 T m* ?m @ 5a. T+e%ac= emf developed %y t+e motor is % * ?% @ Bm.. 5n an armature controlled DC Servomotor6 t+e field inding is supplied it+ constant current +ence t+e flu, remains constant.T+erefore t+ese motors are also called as constant magnetic flu, motors. Armature controlsc+eme is suita%le for large sie motors.

ARMAT!RE CONTROLLED DC SERVOMOTOR:

Department of EEE, Rajalakshmi Engineering College, Chennai (


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FORM!LAE !SED:

Transfer function of t+e armature controlled DC servomotor is given as

s 9 4as * ?m 9 Es 1FsGa1FsGm F ?%?t97a8H+ere

#otor gain constant6 ?m * ?t97a8

#otor torue constant6 ?t * T 9 5a Torue6 T in /m * (."" %5a

8ac= emf6 %in volts * 4a 5a7a 4a* ,citation voltage in volts

8ac= emf constant6 ?% * 4a9 B

Angular velocity in rad9 sec * 2I/ 9 $0

Armature time constant6 Ga * ;a 9 7aArmature 5nductance6 ;a in


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DETERMINATION OF TRANSFER F!NCTION OF ARMAT!RE CONTROLLED DC SERVO MOTORPATCHING DIAGRAM TO DETERMINE THE MOTOR TOR!E CONSTANT K* AND "ACK EMF CONSTANT K=



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PROCED!RE:

2$ T& ;+*+/+ )/)*+ +%%*)'+ R):

C+ec= +et+er t+e #C8 is in NN position in t+e DC servomotor trainer =it

)atc+ t+e circuit as per t+e patc+ing diagram )ut t+e selection %utton of t+e trainer =it in t+e armature control mode. T+e field terminal is left opened. C+ec= t+e position of t+e potentiometerP let it initially %e in minimum position. Sitc+ / t+e #C8. 4ary t+e pot and apply rated voltage of 220 4 to t+e armature of t+e servomotor. /ote t+e values of t+e armature current 5a6 armature voltage 4a. Nind t+e value of armature resistance 7ausing t+e a%ove values

N&*+:

5f t+e voltmeter and ammeter in t+e trainer =it is found not or=ing e,ternal metersof suita%le range can %e used.

O"SERVATIONS:

S$ N&$A/)*+ V&*)4+, V)1

(VA/)*+ C+*, I)1

(A

A/)*+ +%%*)'+,

R) (

CALC!LATIONS:



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DETERMINATION OF TRANSFER F!NCTION OF ARMAT!RE CONTROLLED DC SERVO MOTORPATCHING DIAGRAM TO DETERMINE ARMAT!RE RESISTANCE R)



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PROCED!RE:

7$ T& ; )/)*+ ;'*)'+, L)


)atc+ t+e circuit as per t+e patc+ing diagram )ut t+e selection %utton of t+e trainer =it in t+e armature control mode. T+e field terminal is left opened. Sitc+ / t+e #C8. /ote t+e values of t+e armature current 5a6 armature voltage 4a. Nind t+e value of armature inductance ;a.using t+e a%ove values

N&*+:5f t+e voltmeter and ammeter in t+e trainer =it is found not or=ing e,ternal metersof suita%le range can %e used.

O"SERVATIONS:

S$ N&$A/)*+ V&*)4+, V)2

(VA/)*+ C+*, I)2

(/A

A/)*+ /.+;)'+

) (

CALC!LATIONS:

Department of EEE, Rajalakshmi Engineering College, Chennai 1"


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DETERMINATION OF TRANSFER F!NCTION OF ARMAT!RE CONTROLLED DC SERVO MOTORPATCHING DIAGRAM TO DETERMINE ARMAT!RE IND!CTANCE, L)

Department of EEE, Rajalakshmi Engineering College, Chennai 1$


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PROCED!RE:


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Department of EEE, Rajalakshmi Engineering College, Chennai 1'


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DETERMINATION OF TRANSFER F!NCTION OF ARMAT!RE CONTROLLED DC SERVO MOTORPATCHING DIAGRAM TO DETERMINE MOMENT OF INERTIA J , FRICTIONAL CO-EFFICIENT ": ( *1 N& &);

Department of EEE, Rajalakshmi Engineering College, Chennai 1(


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DETERMINATION OF TRANSFER F!NCTION OF ARMAT!RE CONTROLLED DC SERVO MOTORPATCHING DIAGRAM TO DETERMINE MOMENT OF INERTIA J , FRICTIONAL CO-EFFICIENT ": ( *2 &);



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E3.*$ N&: D)*+:

DETERMINATION OF TRANSFER F!NCTION PARAMETERS OFFIELD CONTROLLED DC SERVO MOTOR

AIM: To determine t+e transfer function of field controlled DC servo motor.APPARAT!S @ INSTR!MENTS RE!IRED:

S$ N& D+%'.*& R)4+ T.+ )**1. DC servo motor trainer =it - 12. DC servo motor 13. 7+eostat "00>91A 1

. Ammeter 0-1A #C 10-100 mA #5 1

". 4oltmeter 0300 4 #C 1

0&" 4 #5 1$. Stopatc+ - 1&. )atc+ cords - As reuired

THEORY:

5n a field controlled DC Servo motor6 t+e electrical signal is e,ternally applied to t+e fieldinding. T+e armature current is =ept constant. 5n a control system6 a controller generates t+eerror signal %y comparing t+e actual o9p it+ t+e reference i9p. Suc+ an error signal is noenoug+ to drive t+e DC motor.


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Transfer function of field controlled DC servo motor is given as6

s 9 4fs * ?m9 s 1FsTf 1FsTm+ere

#otor gain constant ?m* ?tf9 7f8 #otor torue constant ?tf in /-m 9 A * T 9 5f Torue T in /-m * (."" %5a9 /

8ac= #N %in volts * 4a 5a7a 4a* ,citation voltage in voltsArmature resistance67ain * 4a19 5a1Nield resistance67f in * 4f19 5f1

Nield time constant Tf* ;f9 7f

Nield 5nductance6;f in


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PROCED!RE:

1$ T& ;+*+/+ *B+ /&*& *&9+ '&%*)* K* :


)ress t+e reset %utton to reset t+e over speed. )atc+ t+e circuit as per t+e patc+ing diagram. )ut t+e selection %utton of t+e trainer =it in t+e field control mode. C+ec= t+e position of t+e potentiometerP let it initially %e in minimum position. Sitc+ / t+e #C8. 4ary t+e pot and apply rated voltage of 2204 to t+e armature of t+e servomotor. /ote t+e values of t+e armature current 5a6 armature voltage 4a6 and speed /. Nind t+e motor torue constant ?t f using t+e a%ove values.

N&*+:


O"SERVATIONS:

S$ N&$A/)*+ V&*)4+,V)

(VA/)*+ C+*,I)

(AS.++;,N

(./

CALC!LATIONS:



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EE2257 Control Systems Laboratory Manual / II EEE A, V S

DETERMINATION OF TRANSFER F!NCTION OF FIELD CONTROLLED DC SERVO MOTORPATCHING DIAGRAM TO DETERMINE THE MOTOR TOR!E CONSTANT K*



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PROCED!RE:

2$ T& ;+*+/+ )/)*+ +%%*)'+ R):


)atc+ t+e circuit as per t+e patc+ing diagram )ut t+e selection %utton of t+e trainer =it in t+e armature control mode. T+e field terminal is left opened. C+ec= t+e position of t+e potentiometerP let it initially %e in minimum position. Sitc+ / t+e #C8. 4ary t+e pot and apply rated voltage of 2204 to t+e armature of t+e servomotor. /ote t+e values of t+e armature current 5a6 armature voltage 4a. Nind t+e value of armature resistance 7ausing t+e a%ove values

N&*+:


O"SERVATIONS:

S$ N&$A/)*+ V&*)4+, V)1

(VA/)*+ C+*, I)1

(A

A/)*+ R+%%*)'+,

R) (

CALC!LATIONS:



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DETERMINATION OF TRANSFER F!NCTION OF FIELD CONTROLLED DC SERVO MOTORPATCHING DIAGRAM TO DETERMINE ARMAT!RE RESISTANCE R)

Department of EEE, Rajalakshmi Engineering College, Chennai 2&


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PROCED!RE:

7$ T& ;+*+/+ +; +%%*)'+ R:


)atc+ t+e circuit as per t+e patc+ing diagram )ut t+e selection %utton of t+e trainer =it in t+e field control mode. T+e armature terminal is left opened. C+ec= t+e position of t+e potentiometerP let it initially %e in minimum position. Sitc+ / t+e #C8. 4ary t+e pot and apply rated voltage of 2204 to t+e field of t+e servomotor. /ote t+e values of t+e field current 5f6 field voltage 4f. Nind t+e value of field resistance 7fusing t+e a%ove values

N&*+:


O"SERVATIONS:

S$ N&$F+; V&*)4+, V)1

(VF+; C+*, I)1

(A

F+; R+%%*)'+,

R (

CALC!LATIONS:



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DETERMINATION OF TRANSFER F!NCTION OF FIELD CONTROLLED DC SERVO MOTORPATCHING DIAGRAM TO DETERMINE FIELD RESISTANCE RF



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PROCED!RE:


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DETERMINATION OF TRANSFER F!NCTION OF FIELD CONTROLLED DC SERVO MOTORPATCHING DIAGRAM TO DETERMINE MOMENT OF INERTIA J , FRICTIONAL CO-EFFICIENT ": ( *1 N& &);



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DETERMINATION OF TRANSFER F!NCTION OF ARMAT!RE CONTROLLED DC SERVO MOTORPATCHING DIAGRAM TO DETERMINE MOMENT OF INERTIA J , FRICTIONAL CO-EFFICIENT ": ( *2 &);



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CALC!LATIONS:

RES!LT:

T+e transfer function of field controlled DC servomotor is determined as

VIVA-VOCE !ESTIONS:

1. :+at are t+e main parts of a DC servo motorR2. /ame t+e to types of servo motor.

3. State t+e advantages and disadvantages of a DC servo motor.. !ive t+e applications of DC servomotor.". :+at is servo mec+anismR$. :+at do you mean %y field controlled DC servo motorR



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E3.*$ N&: D)*+:

DETERMINATION OF TRANSFER F!NCTION OFAC SERVO MOTOR

AIM:

To derive t+e transfer function of t+e given AC Servomotor.APPARAT!S @ INSTR!MENTS RE!IRED:

S$ N& D+%'.*& R)4+ T.+ )**1. AC servo motor trainer =it - 12. AC servo motor 1

3. Ammeter 0-1 A #C 10-100 mA #5 1

. 4oltmeter 0300 4 #C 10&" 4 #5 1

". )atc+ cords - As reuired

THEORY:

An AC servo motor is %asically a to p+ase induction motor it+ some special designfeatures. T+e stator consists of to pole pairs A-8 and C-D mounted on t+e inner perip+eryof t+e stator6 suc+ t+at t+eir a,es are at an angle of (0oin space. ac+ pole pair carries ainding6 one inding is called reference inding and ot+er is called a control inding. T+ee,citing current in t+e inding s+ould +ave a p+ase displacement of (0 o. T+e supply used todrive t+e motor is single p+ase and so a p+ase advancing capacitor is connected to one of t+ep+ase to produce a p+ase difference of (0o.T+e rotor construction is usually suirrel cage or

drag-cup type. T+e rotor %ars are placed on t+e slots and s+ort-circuited at %ot+ ends %y endrings. T+e diameter of t+e rotor is =ept small in order to reduce inertia and to o%tain goodaccelerating c+aracteristics. T+e drag cup construction is employed for very lo inertiaapplications. 5n t+is type of construction t+e rotor ill %e in t+e form of +ollo cylindermade of aluminium. T+e aluminium cylinder itself acts as s+ort-circuited rotor conductors.lectrically %ot+ t+e types of rotor are identical.

ORKING PRINCIPLE :

T+e stator indings are e,cited %y voltages of eual magnitude and (0o p+ase difference.T+ese results in e,citing currents i1and i2t+at are p+ase displaced %y (0o and +ave

eual values. T+ese currents give rise to a rotating magnetic field of constantmagnitude. T+e direction of rotation depends on t+e p+ase relations+ip of t+e tocurrents or voltages. T+is rotating magnetic field seeps over t+e rotorconductors. T+e rotor conductor e,perience a c+ange in flu, and so voltages areinduced rotor conductors. T+is voltage circulates currents in t+e s+ort-circuitedrotor conductors and currents create rotor flu,. Due to t+e interaction of stator rotor flu,6 a mec+anicalforce or torue is developed on t+e rotor and so t+e rotorstarts moving in t+e same direction as t+at of rotating magnetic field.

Department of EEE, Rajalakshmi Engineering College, Chennai 3&


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GENERAL SCHEMATIC OF AC SERVOMOTOR:

FORM!LAE !SED:

Transfer function6 !m s * ?m9 1F sm

:+ere

#otor gain constant6 ?m * ? 9 NF N

? is T 9 CN is T 9 /Torue6 T is (.'1 J 7 S1 S2

7 is radius of t+e rotor in m Nrictional co-efficient6 N * : 9 2/ 9 $02

Nrictional loss6 : is 30 O of constant loss in :attsConstant loss in atts * /o load input Copper loss/o load i9p * 4 57F5C4 is supply voltage6 457is current t+roug+ reference inding6 A5C is current t+roug+ control inding6 ACopper loss in atts * 5C27C7C * 1&/ is rated speed in rpm

#otor time constant6 m* L 9 NF N#oment of inertia L is d ;7 9 32d is diameter of t+e rotor in m !iven d *3(." mm;7is lengt+ of t+e rotor in m !iven ; 7 *&$ mm is density * &.' J 102gm 9 m



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PROCED!RE:

1$ DETERMINATION OF FRICTIONAL CO-EFFICIENT, F

1. C+ec= +et+er t+e #C8 is in NN position.2. )atc+ t+e circuit using t+e patc+ing diagram.3. Sitc+ / t+e #C8. 4ary t+e control pot to apply rated supply voltage". /ote t+e control inding current6 reference inding current6 supply voltage and

speed.$. Nind t+e frictional co-efficient using t+e a%ove values

O"SERVATIONS:

S$ N&$ S.. V&*)4+V(V

C&*& ;4C+* I'(A

R+++'+ ;4C+* I(A

S.++;N(./

CALC!LATIONS:



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DETERMINATION OF TRANSFER F!NCTION OF AC SERVO MOTORPATCHING DIAGRAM TO DETERMINE FRICTIONAL CO-EFFICIENT F:



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PROCED!RE:

2$ T& ;+*+/+ *B+ /&*& 4) '&%*)* K/

DETERMINATION OF FO FROM TOR!E - SPEED CHARACTERISTICS:

1. C+ec= +et+er t+e #C8 is in NN position.2. )atc+ t+e circuit using t+e patc+ing diagram.3. Set t+e control pot in minimum position.. C+ec= +et+er t+e motor is in no load condition". Sitc+ / t+e #C8$. 4ary t+e control pot and apply rated voltage to t+e reference p+ase inding and

control p+ase inding. /ote don t+e no load speed.&. Apply load in steps. Nor eac+ load applied note don t+e speed and spring %alance

readings. Ta=e 3 or sets of readings'. 7educe t+e load fully and allo t+e motor to run at rated speed.(. 7epeat steps & and ' for &" O control inding voltage.

10. Dra t+e grap+ %eteen speed and torue6 t+e slope of t+e grap+ gives N.

O"SERVATIONS:

S$ N&

C&*& 8&*)4+ V'1 C&*& 8&*)4+ V'2

S.++;N

(./

S.4 "))'+8)+% T&9+

T(N/

S.++;N

(./

S.4 "))'+8)+%

T&9+T

(N/S1

(4S2

(4S1

(4S2

(4

MODEL GRAPH: TOR!E - SPEED CHARACTERISTICS



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DETERMINATION OF K FROM TOR!E - CONTROL VOLTAGECHARACTERISTICS:

1. C+ec= +et+er t+e #C8 is in NN position.2. )atc+ t+e circuit using t+e patc+ing diagram.

3. Set t+e control pot in minimum position.. C+ec= +et+er t+e motor is in no load condition". Sitc+ / t+e #C8

$. 4ary t+e control pot and apply rated voltage to t+e reference p+ase inding andcontrol p+ase inding. /ote don t+e no load speed.

&. ;oad t+e motor graduallyP t+e speed of t+e motor ill decrease. 4ary t+e control potand increase t+e control inding voltage till t+e speed o%tained at no load is

reac+ed. /ote don control voltage and spring %alance readings. '. 7epeat step & for various speeds and ta%ulate. for 1000 rpm

(. )lot t+e grap+ %eteen torue and control inding voltage. T+e slope of t+e grap+gives t+e value of ?.

O"SERVATIONS:

S$ N&

S.++; N1 S.++; N2

C&*&V&*)4+

V'(V

S.4 "))'+8)+%

T&9+T

N/

S.++;

./

S.4 "))'+8)+%

C&*&V&*)4+

V'V

S1(4

S24

S1K4

S2K4

MODEL GRAPH: TOR!E - CONTROL VOLTAGE CHARACTERISTICS



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CALC!LATIONS:

RES!LT:

T+e transfer function of AC servomotor is determined as

VIVA-VOCE !ESTIONS:

1. :+at are t+e main parts of an AC servomotorR2. State t+e advantages and disadvantages of an AC servo motor.3. !ive t+e applications of AC servomotor.. :+at do you mean %y servo mec+anismR". :+at are t+e c+aracteristics of an AC servomotorR

Department of EEE, Rajalakshmi Engineering College, Chennai "


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E3.*$ N&: D)*+:

DETERMINATION OF TRANSFER F!NCTION OFSEPARATELY ECITED DC GENERATOR

AIM:

To o%tain t+e transfer function of separately e,cited DC generator on no load andloaded condition.

APPARATUS / INSTRUMENTS REQUIRED:

S$ N& D+%'.*& R)4+ T.+ )**

THEORY:

Derivation of transfer function of separately e,cited DC generator is as follos6Applying ?4; to t+e field side6

ef * 7f if F ;fdif9 dt U 1

Applying ?4; to t+e armature side6

eg* 7a iaF ;adia9 dt F 7; ia U 2

4; * 7; ia U 3

Also since eg V if 6 let eg * ?g if U

Ta=ing ;aplace transform of euation 1 e getf s * 7f 5fs F s;f 5fs

f s *5fs E7fF s;fH

5fs * f s 9 E7fF s;fH U "

Department of EEE, Rajalakshmi Engineering College, Chennai $


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Ta=ing ;aplace transform of euation 2 e getgs * 7a 5as F s;a 5as F 7; 5asgs * 5as E7aF s;aF 7;H U $

Ta=ing ;aplace transform of euations 3 and e get

4;s* 7; 5a sT+erefore6 5a s * 4;s 9 7; U &gs * ?g 5fs U '

Su%stituting. euations & and ' in euation $ e get?g 5fs * E7aF s;aF 7;H E4;s 9 7;H U (

Su%stituting t+e value of 5fs in t+e a%ove euation e get?g f s 9 E7fF s;fH * E7aF s;aF 7;H E 4;s 9 7;H


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1$ T& ;+*+/+ *B+ 4) '&%*)* K4 :

N& &); & &.+ ''* 'B))'*+%*'%:

1. Connections are made as s+on in t+e circuit diagram

2. T+e motor field r+eostat s+ould %e in /// +%%*)'+position and t+e generatorfield r+eostat s+ould %e in /)3// +%%*)'+ .&%*& & /// .&*+*).&%*&+ile sitc+ing / and sitc+ing NN t+e supply side D)ST sitc+.

3. nsure t+at t+e D)ST sitc+ on t+e load side is open.. Sitc+ / t+e supply D)ST sitc+.". Zsing t+e 3- point starter t+e DC motor is started and it is %roug+t to rated speed %y

adQusting t+e motor field r+eostat.$. ?eeping t+e D)ST sitc+ on t+e load side open6 t+e generated voltage gand field

currentIf of generator is noted don %y varying t+e generator field r+eostat.&. T+e a%ove step is repeated till 12" O of rated voltage is reac+ed.'. A grap+ is plotted %eteen gand 5fta=ing 5falong ,- a,is. A tangent to t+e linear

portion of t+e curve is dran from t+e origin and slope of t+is line gives ?g.O"SERVATIONS:

MODEL GRAPH:


S$ N&$F+; '+*, I

(AI;'+; V&*)4+, E4

(V

'


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CIRC!IT DIAGRAM:

T& ;+*+/+ 4) '&%*)*, K4:

CALC!LATIONS:



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L&); 'B))'*+%*'%:

1. Connections are made as s+on in t+e circuit diagram2. T+e motor field r+eostat s+ould %e in /// +%%*)'+position and t+e generator

field r+eostat s+ould %e in /)3// +%%*)'+ .&%*& & /// .&*+*).&%*&+ile sitc+ing / and sitc+ing NN t+e supply side D)ST sitc+.3. nsure t+at t+e D)ST sitc+ on t+e load side is open.. Sitc+ / t+e supply D)ST sitc+". T+e generator is %roug+t to its rated voltage %y varying t+e generator field r+eostat.$. T+e D)ST sitc+ on t+e load side is closed6 and t+e load is varied for convenient

steps of load current up to 120 O of its rated capacity and t+e voltmeter 4 ; andammeter 5areadings are o%served. n eac+ loading t+e speed s+ould %e maintained atrated speed.

&. A grap+ is plotted %eteen 4;and 5;ta=ing 5;on ,- a,is. T+e slope of t+e grap+gives ?g.

O"SERVATIONS:


S$ N&$T+/) V&*)4+, VL

(VL&); C+*, IL

(A

"0


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MODEL GRAPH:

PROCEDURE:

2$ T& ;+*+/+ +; I;'*)'+ L

1. Connections are made as per t+e circuit diagram.

2. Auto transformer is varied in steps for different voltages and corresponding voltmeterand ammeter readings are noted don.

3. Nield impedance Kf is calculated as 495 and t+e average value of Kf is o%tained.. Nield resistance 7f is measured using multimeter.". Nield inductance ;f can %e calculated using formula

;f * Y Kf2 7f2 9 2If

CIRC!IT DIAGRAM:

Department of EEE, Rajalakshmi Engineering College, Chennai "1


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O"SERVATIONS:

S$ N& F+; V&*)4+, V(V F+; C+*, I

(A F+; I/.+;+'+,

(OB/%

CALCULATIONS:

PROCED!RE:

7$ D+*+/)*& & )/)*+ ;'*)'+ L)


2. Auto transformer is varied in steps for different voltages and corresponding voltmeterand ammeter readings are noted don.3. Armature impedance Ka is calculated as 495 and t+e average value of Kais o%tained.. Armature resistance 7ais measured using multimeter.". Armature inductance ;acan %e calculated using formula6

;a * Y Ka2 7a2 9 2If

CIRC!IT DIAGRAM



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O"SERVATIONS:

S$ N&A/)*+

V&*)4+, V (V

A/)*+

C+*, I(A

A/)*+ I/.+;+'+, )(OB/%

CALCULATIONS:

CALC!LATIONS:



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RES!LT:

T+e transfer function of separately e,cited DC generator is determined as

E3.*$ N&: D)*+:

DETERMINATION OF TRANSFER F!NCTION OF DC MOTOR

AIM:

To o%tain t+e transfer function of field controlled DC motor.

APPARATUS / INSTRUMENTS REQUIRED:

S$ N& D+%'.*& R)4+ T.+ )**

Department of EEE, Rajalakshmi Engineering College, Chennai "


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Transfer function of field controlled DC motor6

s 9 4fs * ?m 9 Es 1FsGf 1 F sGmH+ere

#otor gain constant6 ?m * ?tf 9 87f

?tf is motor torue constant Torue6 T is (.'1 J 7 S1 S2 7 is radius of t+e %ra=e drum in m

7 * circumference of t+e %ra=e drum9 2 [8 is viscous co-efficient of friction7f is field resistance in +ms

Nield time constant Gf * ;f9 7f7f is field resistance in +ms;fis field inductance in


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S$ N&$A/)*+ '+*

I)(A

F+; '+*I

(A

S.4 =))'+ +);4% T&9+T

(N/S1

(4S2

(4

MODEL GRAPH:

CIRC!IT DIAGRAM:

Department of EEE, Rajalakshmi Engineering College, Chennai "&


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CALC!LATIONS:

PROCED!RE

2$ T& ;+*+/+ +; I;'*)'+ L


Department of EEE, Rajalakshmi Engineering College, Chennai "'


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2. Auto transformer is varied in steps for different voltages and corresponding voltmeterand ammeter readings are noted don.

3. Nield impedance Kf is calculated as 495 and t+e average value of Kf is o%tained.. Nield resistance 7f is measured using multimeter.". Nield inductance ;f can %e calculated using formula

;f * Y Kf2

7f2

9 2IfCIRC!IT DIAGRAM:

O"SERVATIONS:

S$ N&$F+; V&*)4+, V

(VF+; C+*, I

(AF+; I/.+;+'+,

(

CALCULATIONS:

PROCED!RE:

7$ T& ;+*+/+ /&/+* & +*) J ); V%'&% '*& C&-+'+* ":

Department of EEE, Rajalakshmi Engineering College, Chennai "(


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1. Connections are made as s+on in t+e circuit diagram2. T+e field current of t+e motor is set to some value %y adQusting t+e field resistance.3. D)DT sitc+ is t+ron to position 1611 and t+e motor is made to run at a speed / 1

1&00 rpm %y adQusting t+e armature r+eostat.. D)DT sitc+ is opened from position 1611 and t+e stop atc+ is started

simultaneously. T+e time ta=en t1for t+e speed to drop from /11&00 rpm to /2 1300 rpm is noted.". Again t+e D)DT sitc+ is t+ron to position 1611 and t+e motor is made to run at a

speed greater t+an /1 1&00 rpm %y adQusting t+e armature r+eostat.$. D)DT sitc+ is t+ron to position 2621and t+e stop atc+ is started +en t+e motor

speed reac+es /1 1&00 rpm. T+e time ta=en t2 for t+e speed to drop from / 1 1&00rpm to /2 1300 rpm is noted. Simultaneously t+e readings of t+e ammeter andvoltmeter corresponding to /1and /2are noted.

O"SERVATIONS:

S$ N&$ N1(./ *1

(S+' V1

(V I1

(A N2

(./ T2

(S+' V2

(V I2

(A

CALC!LATIONS:

CIRC!IT DIAGRAM:

Department of EEE, Rajalakshmi Engineering College, Chennai $0


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CALC!LATIONS:

CALC!LATIONS:



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AIM:

To study t+e c+aracteristics of a DC position control system.

APPARAT!S @ INSTR!MENTS RE!IRED:

i DC position control =it and #otor unit

ii #ultimeter

THEORY:

A DC position control system is a closed loop control system in +ic+ t+e position of t+emec+anical load is controlled it+ t+e position of t+e reference s+aft. A pair ofpotentiometers acts as error-measuring device. T+ey convert t+e input and output positionsinto proportional electric signals. T+e desired position is set on t+e input potentiometer and

t+e actual position is fed to feed%ac= potentiometer. T+e difference %eteen t+e to angularpositions generates an error signal6 +ic+ is amplified and fed to armature circuit of t+e DCmotor. T+e tac+ogenerator attac+ed to t+e motor s+aft produces a voltage proportional to t+espeed +ic+ is used for feed%ac=. 5f an error e,ists6 t+e motor develops a torue to rotate t+eoutput in suc+ a ay as to reduce t+e error to ero. T+e rotation of t+e motor stops +en t+eerror signal is ero6 i.e.6 +en t+e desired position is reac+ed.

PROCED!RE:

1. T+e input or reference potentiometer is adQusted nearer to ero initially7.2. T+e command sitc+ is =ept in continuous mode and some value of forard gain ?A

is selected.3. Nor various positions of input potentiometer 7 t+e positions of t+e responsepotentiometer 0 is noted. Simultaneously t+e reference voltage 47 measured%eteen t+e terminals 47 and t+e output voltage 4 measured %eteen t+eterminals 4 are noted.

. A grap+ is plotted it+ 0along y-a,is and 7 along ,-a,is.

O"SERVATIONS:



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S$ N&

R+++'+)4) .&%*&,

R(;+4++%

O*.* )4).&%*&, O(;+4++%

R+++'+V&*)4+, V

(V

O*.*V&*)4+VO

(V

KA KA KA KA KA KA KA KA

MODEL GRAPH:

Department of EEE, Rajalakshmi Engineering College, Chennai $


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E3.*$ N&$ D)*+:

ANALOG SIM!LATION OF TYPE 0 ); TYPE 1 SYSTEMS

AIM:

To study t+e time response of first and second order type 0 and type- 1 systems.APPARAT!S @ INSTR!MENTS RE!IRED:

1. ;inear system simulator =it 2. C7 3. )atc+ cords

FORM!LAE !SED:

Damping ratio6 * ln #)29 2Fln #)2:+ere #)is pea= percent overs+oot o%tained from t+e time response grap+

Zndamped natural freuency6 n * 9 Etp1 - 2H+ere tpis t+e pea= time o%tained from t+e time response grap+

Closed loop transfer function of t+e type 0 second order system is

Cs97s * !s 9 E1 F !s


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c+aracteried %y one pole or a ero. ,amples of first order systems are a pure integrator and asingle time constant +aving transfer function of t+e form ?9s and ?9sTF1. T+e second ordersystem is c+aracteried %y to poles and up to to eros. T+e standard form of a second ordersystem is !s * n29 s2F 2ns F n2 +ere is damping ratio and nis undamped naturalfreuency.

PROCED!RE:

1$ T& ; *B+ %*+); %*)*+ +& & *.+ 0 %* &;+ %%*+/

1. Connections are made in t+e simulator =it as s+on in t+e %loc= diagram.2. T+e input suare ave is set to 2 4pp in t+e C7 and t+is is applied to t+e 7N

terminal of error detector %loc=. T+e input is also connected to t+e J- c+annel of C7.3. T+e output from t+e simulator =it is connected to t+e \- c+annel of C7.. T+e C7 is =ept in J-\ mode and t+e steady state error is o%tained as t+e vertical

displacement %eteen t+e to curves.

". T+e gain ? is varied and different values of steady state errors are noted."&' ;)4)/ & T.+-0 %* &;+ %%*+/

O"SERVATIONS:

S$ N&$ G), K S*+); %*)*+ +&, +%%123

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TRACES FROM CRO:

F& G), K

F& G), K

F& G), K

Department of EEE, Rajalakshmi Engineering College, Chennai $(


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LINEAR SYSTEM SIM!LATORPATCHING DIAGRAM TO O"TAIN THE STEADY STATE ERROR OF TYPE 0 FIRST ORDER SYSTEM

Department of EEE, Rajalakshmi Engineering College, Chennai &0


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2$ T& ; *B+ %*+); %*)*+ +& & *.+ 1 %* &;+ %%*+/

1. T+e %loc=s are Connected using t+e patc+ c+ords in t+e simulator =it.2. T+e input triangular ave is set to 2 4pp in t+e C7 and t+is applied o t+e 7N

terminal of error detector %loc=. T+e input is also connected to t+e J- c+annel of C7.3. T+e output from t+e system is connected to t+e \- c+annel of C7.. T+e e,periment s+ould %e conducted at t+e loest freuency to allo enoug+

time for t+e step response to reac+ near steady state.". T+e C7 is =ept in J-\ mode and t+e steady state error is o%tained as t+e vertical

displacement %eteen t+e to curves. $. T+e gain ? is varied and different values of steady state errors are noted. &. T+e steady state error is also calculated t+eoretically and t+e to values are compared.

"&' ;)4)/ & T.+- 1 F%* &;+ %%*+/

O"SERVATIONS:

S$ N&$ G), K S*+); %*)*+ +&, +%%123



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LINEAR SYSTEM SIM!LATORPATCHING DIAGRAM TO O"TAIN THE STEADY STATE ERROR OF TYPE 1 FIRST ORDER SYSTEM



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7$ T& ; *B+ '&%+; &&. +%.&%+ & *.+ 0 ); *.+- 1 %+'&; &;+ %%*+/

1. T+e %loc=s are connected using t+e patc+ c+ords in t+e simulator =it.2. T+e input suare ave is set to 2 4pp in t+e C7 and t+is applied to t+e 7N terminal

of error detector %loc=. T+e input is also connected to t+e J- c+annel of C7.

3. T+e output from t+e system is connected to t+e \- c+annel of C7.. T+e output aveform is o%tained in t+e C7 and it is traced on a grap+ s+eet. Nromt+e aveform t+e pea= percent overs+oot6 settling time6rise time6 pea= time aremeasured. Zsing t+ese values nand are calculated.

". T+e a%ove procedure is repeated for different values of gain ? and t+e values arecompared it+ t+e t+eoretical values.

"&' ;)4)/ *& &=*) '&%+; &&. +%.&%+ & T.+-0 %+'&; &;+ %%*+/

O"SERVATIONS:

S$ N&$G)

K

P+).+'+*

O8+%B&&*

MP

R%+*/+

*(%+'

P+)T/+

*.

(%+'

S+**4*/+

*%(%+'

D)/.4)*&

!;)/.+;N)*)

+9+'();@%+'

1

2

TRACES FROM CRO:

F& G), K F& G), K

Department of EEE, Rajalakshmi Engineering College, Chennai &


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"&' ;)4)/ *& &=*) '&%+; &&. +%.&%+ & T.+-1 %+'&; &;+ %%*+/

O"SERVATIONS:

S$ N&$G)

K

P+).+'+*

O8+%B&&*

MP

R%+*/+

*(%+'

P+)T/+

*.

(%+'

S+**4*/+

*%(%+'

D)/.4)*&

!;)/.+;N)*)

+9+'();@%+'

1

2

TRACES FROM CRO:

F& G), K F& G), K

Department of EEE, Rajalakshmi Engineering College, Chennai &"


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LINEAR SYSTEM SIM!LATORPATCHING DIAGRAM TO O"TAIN THE CLOSED LOOP RESPONSE OF TYPE 0 SECOND ORDER SYSTEM

Department of EEE, Rajalakshmi Engineering College, Chennai &$


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LINEAR SYSTEM SIM!LATORPATCHING DIAGRAM TO O"TAIN THE CLOSED LOOP RESPONSE OF TYPE 1 SECOND ORDER SYSTEM

Department of EEE, Rajalakshmi Engineering College, Chennai &&


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CALC!LATIONS:

RES!LT:

T+e time response of first and second order type-0 and type-1 systems are studied.

VIVA-VOCE !ESTIONS:

1. Define order and type num%er.2. :+at are dominant polesR3. :+at is a closed loop systemR. :+at is t+e effect of negative feed%ac=R". :+at are poles and eros of a systemR$. Define transfer function.

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E3.*$ N&$ D)*+:

DIGITAL SIM!LATION OF FIRST ORDER SYSTEMSAIM:

To digitally simulate t+e time response c+aracteristics of a linear system it+out

non- linearities and to verify it manually.

APPARAT!S RE!IRED:

A )C it+ #AT;A8 pac=age

THEORY:

T+e time response c+aracteristics of control systems are specified in terms of timedomain specifications. Systems it+ energy storage elements cannot respondinstantaneously and ill e,+i%it transient responses6 +enever t+ey are su%Qected to inputs or

distur%ances.T+e desired performance c+aracteristics of a system of any order may %e specified in

terms of transient response to a unit step input signal. T+e transient response c+aracteristicsof a control system to a unit step input is specified in terms of t+e folloing time domainspecifications

Delay time td 7ise time tr )ea= time tp #a,imum pea= overs+oot #p Settling time ts

ST!DY OF "ASIC MATLA" COMMANDS:

T+e name MATLA" stands for MATRI LA"ORATORY. #AT;A8 as originallyritten to provide easy access to matri, softare developed %y t+e ;5/)AC? and 5S)AC?proQects. Today6 #AT;A8 engines incorporate t+e ;A)AC? and 8;AS li%raries6em%edding t+e state of t+e art in softare for matri, computation. 5t +as evolved over aperiod of years it+ input from many users. 5n university environments6 it is t+e standardinstructional tool for introductory and advanced courses MATHEMATICS,ENGINEERING, AND SCIENCE. 5n industry6 #AT;A8 is t+e tool of c+oice for +ig+-productivity researc+6 development6 and analysis.

#AT;A8 is a +ig+-performance language for tec+nical computing. 5t integratescomputation6 visualiation6 and programming in an easy-to-use environment +ere pro%lemsand solutions are e,pressed in familiar mat+ematical notation. Typical uses include6

#at+ and computation Algorit+m development Data acuisition #odeling6 simulation6 and prototyping Data analysis6 e,ploration6 and visualiation

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Scientific and engineering grap+ics Application development6 including grap+ical user interface %uilding

5t is an interactive system +ose %asic data element is an array t+at does not reuiredimensioning. T+is allos you to solve many tec+nical computing pro%lems6 especially t+ose

it+ matri, and vector formulations6 in a fraction of t+e time it ould ta=e to rite a programin a scalar non-interactive language suc+ as C or Nortran. 5t also features a family of add-onapplication-specific solutions called tool%o,es. 4ery important to most users of #AT;A86tool%o,es allo you to learn and apply specialied tec+nology. Tool%o,es are compre+ensivecollections of #AT;A8 functions #-files t+at e,tend t+e #AT;A8 environment to solveparticular classes of pro%lems. Areas in +ic+ tool%o,es are availa%le include SIGNALPROCESSING, CONTROL SYSTEMS, NE!RAL NETORKS, F!Y LOGIC,AVELETS, SIM!LATION, AND MANY OTHERS.

Some practical e,amples of first order systems are 7; and 7C circuits.

PROCED!RE:

1. Derive t+e transfer function of a 7; series circuit.2. Assume 7* 1 +ms ; * 0. 1


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Sine response of a first order system:

2$ MATLA" (/-+ .&4)/ *& &=*) *B+ %*+. +%.&%+ ); /.%+ +%.&%+

O #AT;A8 program to find t+e step response

num*E HP

den*E HPsys * tf num6denPstep sysPgrid

O!TP!T: (P)%*+ *B+ 4).B &=*)+; &/ PC

Department of EEE, Rajalakshmi Engineering College, Chennai '1


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O #AT;A8 program to find t+e impulse response

num*E HPden*E HP

sys * tf num6denPimpulse sysPgrid

O!TP!T: (P)%*+ *B+ 4).B &=*)+; &/ PC

CALC!LATIONS:

!* %*+. +%.&%+ & *B+ 48+ RL %++% ''*:



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!* I/.%+ +%.&%+ & *B+ 48+ RLC %++% ''*:

RES!LT:

T+e time response c+aracteristics of a first order system is simulated digitally and verifiedmanually.

VIVA-VOCE !ESTIONS:

1. :+at is #AT;A8R



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2. :+at is t+e use of #AT;A8 )ac=ageR3. :+at are t+e tool%o,es availa%le in #AT;A8R. :+at is t+e use of a simulationR". Differentiate real time systems and simulated systems.$. !ive to e,amples for first order system.

&. /ame t+e standard test signals used in control system.'. :+at is time responseR

E3.*$ N&: D)*+:

DIGITAL SIM!LATION OF SECOND ORDER SYSTEMSAIM:

To digitally simulate t+e time response c+aracteristics of a second order system and verifymanually.

APPARAT!S RE!IRED

A )C it+MATLA"Softare

THEORY

T+e time c+aracteristics of control systems are specified in terms of time domainspecifications. Systems it+ energy storage elements cannot respond instantaneously andill e,+i%it transient responses6 +enever t+ey are su%Qected to inputs or distur%ances. T+edesired performance c+aracteristics of a system of any order may %e specified in terms of

transient response to a unit step input signal. T+e transient response c+aracteristics of acontrol system to a unit step input is specified in terms of t+e folloing time domainspecifications

Delay time td 7ise time tr )ea= time tp #a,imum overs+oot #p Settling time ts

PROCED!RE:

1. Derive t+e transfer function of a 7;C series circuit.2. Assume 7* 1 +ms6 ; * 0. 1 < and C * 1 micro Narad. Nind t+e step response

t+eoretically and plot it on a grap+ s+eet.3. To %uild a S5#Z;5/? model to o%tain step response 9 sine response of a second

order system6 t+e folloing procedure is folloed1. 5n #AT;A8 softare open a ne model in S5#Z;5/? li%rary %roser.2. Nrom t+e continuous %loc= in t+e li%rary drag t+e transfer function %loc=.3. Nrom t+e source %loc= in t+e li%rary drag t+e step input9 sine input.

Department of EEE, Rajalakshmi Engineering College, Chennai '


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. Nrom t+e sin= %loc= in t+e li%rary drag t+e scope.". Nrom t+e mat+ operations %loc= in t+e li%rary drag t+e summing point.$. Connect all to form a system and give unity feed%ac= to t+e system.&. Nor c+anging t+e parameters of t+e %loc=s connected dou%le clic= t+e

respective %loc=.

'. Start simulation and o%serve t+e results in scope. Zse a mu, from t+e signalrouting %loc= to vie more t+an one grap+ in t+e scope(. Nrom t+e step response o%tained note don t+e rise time6 pea= time6 pea=

overs+oot and settling time.10. Compare t+e simulated and t+eoretical results.

"LOCK DIAGRAM:

Step response of a second order system:

Sine response of a second order system:

2$ MATLA" .&4)/ *& &=*) *B+ %*+. +%.&%+ ); /.%+ +%.&%+ & %+'&; &;+%%*+/.

O #AT;A8 program to find t+e step responsenum*E HPden*E HPsys * tf num6denPstep sysP

Department of EEE, Rajalakshmi Engineering College, Chennai '"


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O!TP!T: (P)%*+ *B+ 4).B &=*)+; &/ PC

O #AT;A8 program to find t+e impulse response

num*E HPden*E HP

sys * tf num6denPimpulse sysP

O!TP!T: (P)%*+ *B+ 4).B &=*)+; &/ PC

CALC!LATIONS:

!* %*+. +%.&%+ & *B+ 48+ RLC %++% ''*:

Department of EEE, Rajalakshmi Engineering College, Chennai '$


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!* /.%+ +%.&%+ & *B+ 48+ RLC %++% ''*:

Department of EEE, Rajalakshmi Engineering College, Chennai '&


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RES!LT:

T+e time response c+aracteristics of t+e given second order system is simulated digitally andverified manually.

VIVA-VOCE !ESTIONS:

1. :+at is #AT;A8R2. :+at is t+e use of #AT;A8 )ac=ageR3. :+at are t+e tool%o,es availa%le in #AT;A8R. :+at is t+e use of a simulationR". Differentiate real time systems and simulated systems.$. !ive to e,amples for second order system.&. /ame t+e standard test signals used in control system.

Department of EEE, Rajalakshmi Engineering College, Chennai ''


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'. :+at is time responseR

Department of EEE, Rajalakshmi Engineering College, Chennai '(


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E3.*$ N&: D)*+:

STA"ILITY ANALYSIS OF LINEAR SYSTEMS

a. USING BOD !LOT

AIM:

To o%tain t+e %ode plot and c+ec= for sta%ility of t+e system it+ open loop transfer function6!S *

APPARAT!S RE!IRED:

A )C it+ #AT;A8 Softare

THEORY:

A ;inear Time-5nvariant Systems is sta%le if t+e folloing to notions of system sta%ility aresatisfied

:+en t+e system is e,cited %y 8ounded input6 t+e output is also a 8oundedoutput.

5n t+e a%sence of t+e input6 t+e output tends toards ero6 irrespective of t+einitial conditions.

T+e folloing o%servations are general considerations regarding system sta%ility6

5f all t+e roots of t+e c+aracteristic euation +ave negative real parts6 t+en t+e

impulse response is %ounded and eventually decreases to ero6 t+en system is%*)=+. 5f any root of t+e c+aracteristic euation +as a positive real part6 t+en system is

%*)=+. 5f t+e c+aracteristic euation +as repeated roots on t+e QB-a,is6 t+en system is

%*)=+. 5f one are more non-repeated roots of t+e c+aracteristic euation on t+e QB-

a,is6 t+en system is %*)=+.

"ODE PLOT :

Consider a Single-5nput Single-utput system it+ transfer function

Cs %0smF %1sm-1F UUF %m *

7s a0 snF a1sn-1F UUFan:+ere m ] n.

R+ 1 A system is sta%le if t+e p+ase lag is less t+an 1'0^ at t+e freuencyfor +ic+ t+e gain is unity one.

Department of EEE, Rajalakshmi Engineering College, Chennai (0


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R+ 2 A system is sta%le if t+e gain is less t+an one unity at t+e freuencyfor +ic+ t+e p+ase lag is 1'0^.

T+e application of t+ese rules to an actual process reuires evaluation of t+e gain and p+ases+ift of t+e system for all freuencies to see if rules 1 and 2 are satisfied. T+is is o%tained %y

plotting t+e gain and p+ase versus freuency. T+is plot is called "ODE PLOT$ T+e gaino%tained +ere is&.+ &&. 4)$ T+e e,act terminology is in terms of a G) M)4andPB)%+ M)4from t+e limiting values uoted.

5f t+e p+ase lag is less t+an 10^ at t+e unity gain freuency6 t+e system issta%le. T+is t+en6 is a 0^ PB)%+ M)4 from t+e limiting values of 1'0^.

5f t+e gain is "d8 %elo unity or a gain of a%out 0."$ +en t+e p+ase lag is1'0^6 t+e system is sta%le. T+is is "d8 G) M)4.

PROCED!RE:

Step 1 :rite a program to o%tain t+e 8ode plot for t+e given system.Step 2 Assess t+e sta%ility of given system using t+e plot o%tained.

PROGRAM

O8D );T N T


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MAN!AL CALC!LATIONS:

Department of EEE, Rajalakshmi Engineering College, Chennai (2


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O!TP!T (&/ /)) ')')*&:

O!TP!T (&/ .&4)/:

RES!LT:

T+e 8ode plot is dran for t+e given transfer function using #AT;A8 and verifiedmanually. Nrom t+e plot o%tained6 t+e system is found to %e ``````````````.

VIVA-VOCE !ESTIONS:

1. Define sta%ility of ;inear Time 5nvariant System.2. !ive t+e sta%ility conditions of system using )ole-Kero plot.3. Define 8ode )lot.. :+at is t+e use of 8ode )lotR". :+at t+e conditions of sta%ility are in 8ode plotR$. Define Sta%ility criteria.&. Define ;imits of sta%ility.'. Define safe regions in sta%ility criteria.(. Define )+ase margin and !ain margin.



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". Usin# Root Loc$s

AIM:

To o%tain t+e 7oot locus plot and to verify t+e sta%ility of t+e system it+ transfer function6

!s *APPARAT!S RE!IRED:

A )C it+ #AT;A8 Softare

THEORY:

ROOT LOC!S PLOT:

T+e c+aracteristic of t+e transient response of a closed-loop system is related to t+e location

of t+e closed loop poles. 5f t+e system +as a varia%le loop gain6 t+en t+e location of t+eclosed-loop poles depend on t+e value of t+e loop gain c+osen. A simple tec+niue =non as7oot ;ocus Tec+niueb used for studying linear control systems in t+e investigation of t+etraQectories of t+e roots of t+e c+aracteristic euation.

T+is tec+niue provides a grap+ical met+od of plotting t+e locus of t+e roots in t+e s-plane asa given system parameter is varied over t+e complete range of values may %e from ero toinfinity. T+e roots corresponding to a particular value of t+e system parameter can t+en %elocated on t+e locus or t+e value of t+e parameter for a desired root location can %edetermined form t+e locus. T+e root locus is a poerful tec+niue as it %rings into focus t+ecomplete dynamic response of t+e system. T+e root locus also provides a measure of

sensitivity of roots to t+e variation in t+e parameter %eing considered. T+is tec+niue isapplica%le to %ot+ single as ell as multiple-loop systems.

PROCED!RE:

1. :rite a program to o%tain t+e root locus plot for t+e given system.2. Assess t+e sta%ility of given system using t+e plot o%tained.

PROGRAM:

O7T ;CZS N T


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,la%el_7eal A,is_

yla%el_5maginary A,is_

title_7oot ;ocus of t+e system_

title_7oot ;ocus )lot of t+e system _


Department of EEE, Rajalakshmi Engineering College, Chennai ($


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Department of EEE, Rajalakshmi Engineering College, Chennai (&


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O!TP!T (&/ /)) ')')*&

O!TP!T (&/ .&4)/:

RES!LT:

T+e 7oot locus plot is dran for t+e given transfer function6 !s* ```````````````````using #AT;A8 and t+e range of gain ? for sta%ility is``````````````.

VIVA-VOCE !ESTIONS:

1. Define root locus tec+niue.2. :+at are t+e conditions of sta%ility in root locus criteriaR3. :+at is t+e advantage of root locus tec+niueR. :+ic+ met+od of sta%ility analysis is more advantageousR".


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c. USING NY%UIST !LOT

AIM:

To o%tain t+e /yuist plot and c+ec= t+e sta%ility of t+e system using /yuist Sta%ility

Criterion for t+e given unity feed%ac= system it+ transfer function!s


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PROGRAM

O/\Z5ST );TOnter t+e numerator and denominator of t+e transfer functionnum*E H

den*E Hsys*tfnum6den

OSpecify t+e freuency range and enter t+e commandnyuistsysv*E Ha,isv,la%el_7eal A,is_Pyla%el_5maginary A,is_Ptitle_/yuist )lot of t+e system




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O!TP!T ( &/ M)) ')')*&

O!TP!T (&/ .&4)/



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RES!LT:

T+e /yuist plot is dran for t+e given transfer function6 !s * ``````````````````````

using #AT;A8 and t+e system is found to %e ``````````````````````.

VIVA-VOCE !ESTIONS:

1. :+at is polar plotR2. :+at is /yuist plotR3. Define t+e conditions of sta%ility in polar plot.. :+at is t+e use and advantage of polar plotR". State /yuist sta%ility criterion.



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E3.*$ N&: D)*+:

STEPPER MOTOR CONTROL SYSTEM



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ee2257 lab manual

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