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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"ORATORYSTAFF IN-CHARGE : P$S$MAY!RAPPRIYAN

A%%&' )*+ P & +%%& EEE D+.) */+ *

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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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INDES$

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

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SYLLA"!S

EE225# CONTROL SYSTEM LA"ORATORY 0 0 7 2

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 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,perimdetermine t+e transfer function parameters

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

motor.2. Determine t+e armature and field parameters %y conducting suita%le e,p3. Determine t+e mec+anical parameter %y conducting suita%le e,periment

. )lot t+e fre uency response.

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

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,perimdetermine t+e transfer function parameters

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E3+ ' %+1. Derive t+e transfer function of t+e AC Servo #otor from %asic )rinciples2. %tain t+e D.C gain %y operating at rated speed.3. Determine t+e time constant mec+anical

. )lot t+e fre uency response

E9 ./+ * 1. AC Servo #otor #inimum of 100 necessary sources for main ind control inding 1 /o 2. Tac+ometer 1 /o 3. Stop atc+ 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 0systems.

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

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

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 components2. 4aria%le fre uency s uare ave generator and a normal C7 - 1 /o or DC source and storage scilloscope - 1 /o

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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

. )o er supply

?$ D 4 *) 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 soft2. %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 E PERIMENTS

FIRST CYCLE:

1. Determination of transfer function of armature controlledservomotor.

2. Determination of transfer function of field controlled DC servomo

3. Determination of transfer function of AC servomotor.

. Determination of transfer function of separately e,cited DC gener". 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.

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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 0-1 A #C 10-100 mA #5 1". 4oltmeter 0300 4 #C 1

0&" 4 #5 1$. Stop atc+ - 1&. )atc+ cords - As re uired

THEORY:

5n servo applications a DC motor is re uired to produce rapid accelerations fromT+erefore t+e p+ysical re uirements of suc+ a motor are lo inertia and +ig+ star;o inertia is attained it+ reduced armature diameter it+ a conse uent increaarmature lengt+ suc+ t+at t+e desired po er output is ac+ieved. T+us6 e,cept differences in constructional features a DC servomotor is essentially an ordinary D

DC servomotor is a tor ue transducer +ic+ converts electrical energy into menergy. 5t is %asically a separately e,cited type DC motor. T+e tor ue developed os+aft is directly proportional to t+e field flu, and armature current6 Tm * ? m@ 5a. T+e %ac=emf developed %y t+e motor is % * ? % @ Bm.. 5n an armature controlled DC Servo motor6field inding is supplied it+ constant current +ence t+e flu, remains constant. Tt+ese motors are also called as constant magnetic flu, motors. Armature control suita%le for large si e motors.

ARMAT!RE CONTROLLED DC SERVOMOTOR:

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FORM!LAE !SED:

Transfer function of t+e armature controlled DC servomotor is given ass 9 4a s * ? m9 Es 1FsGa 1FsGm F ? % ? t 97 a8 H

+ere

#otor gain constant6 ? m* ? t97 a8

#otor tor ue constant6 ? t * T 9 5a Tor ue6 T in /m * (."" % 5a

8ac= emf6 % in volts * 4a 5a 7 a 4 a * ,citation voltage in volts

8ac= emf constant6 ? % * 4a 9 B

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

Armature time constant6Ga* ; a9 7 aArmature 5nductance6 ;a in

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PROCED!RE:

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

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

)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 armature control mode. C+ec= t+e position of t+e potentiometerP let it initially %e in minimum posi S itc+ / t+e #C8. 4ary t+e pot and apply rated voltage of 220 4 to t+e armature of t+e servomo /ote t+e values of t+e armature current 5a6 armature voltage 4a6 and speed /. Nind t+e motor tor ue constant ? tand 8ac= emf constant ? % using t+e a%ove values.

N&*+:

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

O"SERVATIONS:

S$ N&$ A /)* + V& *)4+,V)(VA /)* + C + *,I)

(AS.++;,N

( ./

CALC!LATIONS:

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DETERMINATION OF TRANSFER F!NCTION OF ARMAT!RE CONTROLLED DC SERVO MOTOR PATCHING DIAGRAM TO DETERMINE THE MOTOR TOR !E CONSTANT K *AND "ACK EMF 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 posi S itc+ / t+e #C8. 4ary t+e pot and apply rated voltage of 220 4 to t+e armature of t+e servomo /ote t+e values of t+e armature current 5a6 armature voltage 4a. Nind t+e value of armature resistance 7 a using t+e a%ove values

N&*+:


O"SERVATIONS:

S$ N&$ A /)* + V& *)4+, V)1(VA /)* + C + *, I)1

(AA /)* + +% %*) '+,

R ) (

CALC!LATIONS:

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DETERMINATION OF TRANSFER F!NCTION OF ARMAT!RE CONTROLLED DC SERVO MOTOR PATCHING 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. S itc+ / 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,ternalof suita%le range can %e used.

O"SERVATIONS:

S$ N&$ A /)* + V& *)4+, V)2(VA /)* + C + *, I)2

(/AA /)* + /.+;) '+

) (

CALC!LATIONS:

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

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PROCED!RE:

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

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CALC!LATIONS:

RES!LT:

T+e transfer function of armature controlled DC servomotor is determined a

VIVA-VOCE !ESTIONS:

1. Define transfer function.2. :+at is DC servo motorR State t+e main parts.3. :+at is servo mec+anismR

. 5s t+is a closed loop or open loop system . ,plain.". :+at is %ac= #NR

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

DETERMINATION OF TRANSFER F!NCTION PARAMETERS OF FIELD 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 0-1 A #C 10-100 mA #5 1". 4oltmeter 0300 4 #C 1

0&" 4 #5 1$. Stop atc+ - 1&. )atc+ cords - As re uired

THEORY:

5n a field controlled DC Servo motor6 t+e electrical signal is e,ternally applied tinding. T+e armature current is =ept constant. 5n a control system6 a controller g

error signal %y comparing t+e actual o9p it+ t+e reference i9p. Suc+ an error enoug+ to drive t+e DC motor.

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Transfer function of field controlled DC servo motor is given as6

s 9 4f s * ? m 9 s 1FsTf 1FsTm+ere

#otor gain constant ? m * ? tf 9 7 f 8 #otor tor ue constant ? tf in /-m 9 A * T 9 5f Tor ue T in /-m * (."" % 5a 9 /

8ac= #N % in volts * 4a 5a 7 a 4 a * ,citation voltage in voltsArmature resistance67 a in * 4a1 9 5a1Nield resistance67 f in * 4f1 9 5f1

Nield time constant Tf * ; f 9 7 f

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 posi S itc+ / t+e #C8. 4ary t+e pot and apply rated voltage of 2204 to t+e armature of t+e servomot /ote t+e values of t+e armature current 5a6 armature voltage 4a6 and speed /. Nind t+e motor tor ue 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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DETERMINATION OF TRANSFER F!NCTION OF FIELD CONTROLLED DC SERVO MOTOR PATCHING 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 S itc+ / 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 7 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 mof suita%le range can %e used.

O"SERVATIONS:

S$ N&$ A /)* + V& *)4+, V)1(VA /)* + C + *, I)1

(AA /)* + R+% %*) '+,

R ) (

CALC!LATIONS:

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

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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 S itc+ / 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 5f 6 field voltage 4f . Nind t+e value of field resistance 7 f 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 mof suita%le range can %e used.

O"SERVATIONS:

S$ N&$ F + ; V& *)4+, V)1(VF + ; C + *, I)1

(AF + ; R+% %*) '+,

R (

CALC!LATIONS:

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DETERMINATION OF TRANSFER F!NCTION OF FIELD CONTROLLED DC SERVO MOTOR PATCHING DIAGRAM TO DETERMINE FIELD RESISTANCE R F

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PROCED!RE:

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DETERMINATION OF TRANSFER F!NCTION OF FIELD CONTROLLED DC SERVO MOTOR PATCHING DIAGRAM TO DETERMINE FIELD IND!CTANCE, L F

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PROCED!RE:

5$ T& ;+*+ / + /&/+ * & + * ) J ) ; '* & ) '&-+ ' + * ":


)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 and s itc+ in po er circuit position.

C+ec= t+e position of t+e potentiometerP let it initially %e in minimum posi S itc+ / t+e #C8. 4ary t+e pot and adQust t+e motor to run at rated speed. /ote t+e values of armature current 5a6 armature voltage 4a6 field current 5f 6 Speed /. C+ange t+e D)DT s itc+ position from po er circuit side to load

simultaneously noting t+e time ta=en t1 of t+e motor to come to rest from rausing a stop atc+.

Set t+e potentiometer to minimum position and c+ange t+e D)DT s itc+ tcircuit side Connect a load of "00 +ms in t+e load position 4ary t+e pot and adQust t+e motor to run at rated speed C+ange t+e D)DT s itc+ position from po er circuit side to load

simultaneously noting t+e time ta=en t2 of t+e motor to come to rest from rausing a stop atc+.

Nind t+e values of moment of inertia L and frictional co-efficient 8 using values

O"SERVATIONS:

S$ N&A /)* +

V& *)4+, V)(V

A /)* +C + *,

I )(A

F + ;C + *, I

(A

S.++;, N

( ./

*1

(%+'%

*2

(%+'%

CALC!LATIONS:

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DETERMINATION OF TRANSFER F!NCTION OF FIELD CONTROLLED DC SERVO MOTOR PATCHING 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 MOTOR PATCHING 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 t o 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 13. Ammeter 0-1 A #C 10-100 mA #5 1

. 4oltmeter 0300 4 #C 10&" 4 #5 1". )atc+ cords - As re uired

THEORY:

An AC servo motor is %asically a t o p+ase induction motor it+ some specfeatures. T+e stator consists of t o pole pairs A-8 and C-D mounted on t+e innof t+e stator6 suc+ t+at t+eir a,es are at an angle of (0o in space. ac+ pole pair carries a

inding6 one inding is called reference inding and ot+er is called a control ine,citing current in t+e inding s+ould +ave a p+ase displacement of (0o. T+e supply used todrive t+e motor is single p+ase and so a p+ase advancing capacitor is connected to p+ase to produce a p+ase difference of (0o.T+e rotor construction is usually s uirrel cagedrag-cup type. T+e rotor %ars are placed on t+e slots and s+ort-circuited at %ot+rings. T+e diameter of t+e rotor is =ept small in order to reduce inertia and to o%accelerating c+aracteristics. T+e drag cup construction is employed for very loapplications. 5n t+is type of construction t+e rotor ill %e in t+e form of +ollomade of aluminium. T+e aluminium cylinder itself acts as s+ort-circuited rotor c

lectrically %ot+ t+e types of rotor are identical.

ORKING PRINCIPLE :

T+e stator indings are e,cited %y voltages of e ual magnitude and (0o p+ase difference.T+ese results in e,citing currents i1 and i2 t+at are p+ase displaced %y (0oand +ave

e ual values. T+ese currents give rise to a rotating magnetic field of cmagnitude. T+e direction of rotation depends on t+e p+ase relations+ip ocurrents or voltages . T+is rotating magnetic field s eeps over tconductors. T+e rotor conductor e,perience a c+ange in flu, and so voltainduced rotor conductors. T+is voltage circulates currents in t+e s+ort-rotor conductors and currents create rotor flu,. Due to t+e interaction of rotor flu,6 a mec+anical force or tor ue is developed on t+e rotor and so t+starts moving in t+e same direction as t+at of rotating magnetic field.

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GENERAL SCHEMATIC OF AC SERVOMOTOR:

FORM!LAE !SED:Transfer function6 !m s * ? m 9 1F sm

:+ere

#otor gain constant6 ? m* ? 9 N F N

? is T 9CN isT 9 /Tor ue6 T is (.'1 J 7 S1 S27 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 57 F5C4 is supply voltage6 457 is current t+roug+ reference inding6 A5Cis current t+roug+ control inding6 ACopper loss in atts * 5C2 7 C 7 C* 1& / is rated speed in rpm

#otor time constant6m * L 9 N F N#oment of inertia L isd ; 7 9 32d is diameter of t+e rotor in m !iven d *3(." mm; 7 is lengt+ of t+e rotor in m !iven ;7 *&$ mm

is density * &.' J 102 gm 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. S itc+ / t+e #C8

. 4ary t+e control pot to apply rated supply voltage". /ote t+e control inding current6 reference inding current6 supply volt

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 F O 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". S itc+ / t+e #C8$. 4ary t+e control pot and apply rated voltage to t+e reference p+ase ind

control p+ase inding. /ote do n t+e no load speed.&. Apply load in steps. Nor eac+ load applied note do n t+e speed and spri

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+ %et een speed and tor ue6 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". S itc+ / t+e #C8

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

&. ;oad t+e motor graduallyP t+e speed of t+e motor ill decrease. 4ary t+e co and increase t+e control inding voltage till t+e speed o%tained at n

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

(. )lot t+e grap+ %et een tor ue and control inding voltage. T+e slope of gives t+e value of ?.

O"SERVATIONS:

S$ N&

S.++; N 1 S.++; N 2 C& * &V& *)4+

V'(V

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

T& 9 +T

N/

S.++;

./

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

C& * &V& *)4+

V'V

S1( 4

S24

S1K 4

S2K 4

MODEL GRAPH: TOR !E - CONTROL VOLTAGE CHARACTERISTICS

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DETERMINATION OF TRANSFER F!NCTION OF AC SERVO MOTOR PATCHING DIAGRAM TO DETERMINE MOTOR GAIN CONSTANT K M:

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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

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

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DETERMINATION OF TRANSFER F!NCTION OFSEPARATELY E CITED DC GENERATOR

AIM:

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

APPARATUS / INSTRUMENTS REQUIRED:

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

THEORY:

Derivation of transfer function of separately e,cited DC generator is as follo s6

Applying ?4; to t+e field side6

ef * 7 f if F ;f dif 9 dt U 1

Applying ?4; to t+e armature side6eg * 7 aia F ;a dia 9 dt F 7 ; ia U 2

4 ; * 7 ; ia U 3

Also since egV if 6 let eg* ? gif U

Ta=ing ;aplace transform of e uation 1 e get

f s * 7 f5f s F s;f5f s

f s * 5f s E7 f F s;f H

5f s * f s 9 E7 f F s;f H U "

Ta=ing ;aplace transform of e uation 2 e getg s * 7 a5a s F s;a5a s F 7 ; 5a sg s * 5a s E7 a F s;a F 7 ; H U $

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Ta=ing ;aplace transform of e uations 3 and e get4 ; s * 7 ; 5a sT+erefore6 5a s * 4; s 9 7 ; U &

g s * ? g5f s U '

Su%stituting. e uations & and ' in e uation $ e get? g5f s * E7 a F s;a F 7 ; H E4; s 9 7 ; H U (Su%stituting t+e value of 5f s in t+e a%ove e uation e get? g f s 9 E7 f F s;f H * E7 a F s;a F 7 ; H E 4; s 9 7 ; H

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1. Connections are made as s+o n 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 s itc+ing / and s itc+ing NN t+e supply side D)ST s itc+.

3. nsure t+at t+e D)ST s itc+ on t+e load side is open.. S itc+ / t+e supply D)ST s itc+.

". Zsing t+e 3- point starter t+e DC motor is started and it is %roug+t to ratedadQusting t+e motor field r+eostat.$. ?eeping t+e D)ST s itc+ on t+e load side open6 t+e generated voltage g and fieldcurrent I f of generator is noted do n %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 %et een g and 5f ta=ing 5f along ,- a,is. A tangent to t+e linear

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

MODEL GRAPH:

CIRC!IT DIAGRAM:

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

S$ N&$ F + ; ' + *, I(AI ; '+; V& *)4+, E 4

(V

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CALC!LATIONS:

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

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

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

3. nsure t+at t+e D)ST s itc+ on t+e load side is open.. S itc+ / t+e supply D)ST s itc+

". T+e generator is %roug+t to its rated voltage %y varying t+e generator field$. T+e D)ST s itc+ on t+e load side is closed6 and t+e load is varied for c

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

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

O"SERVATIONS:

MODEL GRAPH:

PROCEDURE:

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

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

S$ N&$ T+ / ) V& *)4+, VL(VL&); C + *, IL

(A

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

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

". Nield inductance ;f can %e calculated using formula; f* Y Kf 2 7 f 2 9 2If

CIRC!IT DIAGRAM:

O"SERVATIONS:

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

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

(OB/%

CALCULATIONS:

PROCED!RE:

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

1. Connections are made as per t+e circuit diagram.2. Auto transformer is varied in steps for different voltages and corresponding

and ammeter readings are noted do n.

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3. Armature impedance Ka is calculated as 495 and t+e average value of Ka is o%tained.. Armature resistance 7 a is measured using multimeter.

". Armature inductance ;a can %e calculated using formula6; a* Y Ka2 7 a2 9 2If

CIRC!IT DIAGRAM

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 .+ ) * *

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THEORY:

FIELD CONTROLLED MOTOR:

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FORM!LAE !SED:

Transfer function of field controlled DC motor6 s 9 4f s * ? m9 Es 1FsGf 1 F sGm H

+ere

#otor gain constant6 ? m *? tf 9 87 f ? tf is motor tor ue constant Tor ue6 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 friction7 f is field resistance in +ms

Nield time constantGf* ; f 9 7 f 7 f is field resistance in +ms; f is field inductance in

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O"SERVATIONS:

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

I )(A

F + ; ' + *I

(A

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

(N/S1

( 4S2

( 4

MODEL GRAPH:

CIRC!IT DIAGRAM:

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CALC!LATIONS:

PROCED!RE

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

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

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

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

". Nield inductance ;f can %e calculated using formula; f* Y Kf 2 7 f 2 9 2If

CIRC!IT DIAGRAM:

O"SERVATIONS:

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

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

(

CALCULATIONS:

PROCED!RE:

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

1. Connections are made as s+o n in t+e circuit diagram2. T+e field current of t+e motor is set to some value %y adQusting t+e field re

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3. D)DT s itc+ is t+ro n to position 1611 and t+e motor is made to run at a speed 11&00 rpm %y adQusting t+e armature r+eostat.

. D)DT s itc+ is opened from position 1611 and t+e stop atc+ is startedsimultaneously. T+e time ta=en t1 for t+e speed to drop from /1 1&00 rpm to /2

1300 rpm is noted.". Again t+e D)DT s itc+ is t+ro n to position 1611 and t+e motor is made to run at

speed greater t+an /1 1&00 rpm %y adQusting t+e armature r+eostat.$. D)DT s itc+ is t+ro n to position 2621 and t+e stop atc+ is started +en t+e motspeed reac+es /1 1&00 rpm . T+e time ta=en t2 for t+e speed to drop from /1 1&00

rpm to /2 1300 rpm is noted. Simultaneously t+e readings of t+e ammvoltmeter corresponding to /1 and /2 are noted.

O"SERVATIONS:

S$ N&$ N1( ./

*1(S+'

V1(V

I1(A

N2( ./

T2(S+'

V2(V

I2(A

CALC!LATIONS:

CIRC!IT DIAGRAM:

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CALC!LATIONS:

CALC!LATIONS:

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RES!LT:

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

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

DC POSITION CONTROL SYSTEM

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 unitii #ultimeter

THEORY:

A DC position control system is a closed loop control system in +ic+ t+e positmec+anical load is controlled it+ t+e position of t+e reference s+aft. A potentiometers acts as error-measuring device. T+ey convert t+e input and outpuinto proportional electric signals. T+e desired position is set on t+e input potentiot+e actual position is fed to feed%ac= potentiometer. T+e difference %et een t+e positions generates an error signal6 +ic+ is amplified and fed to armature circuimotor. T+e tac+ogenerator attac+ed to t+e motor s+aft produces a voltage proportspeed +ic+ is used for feed%ac=. 5f an error e,ists6 t+e motor develops a tor ueoutput in suc+ a ay as to reduce t+e error to ero. T+e rotation of t+e motor stoperror 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 s itc+ is =ept in continuous mode and some value of for arAis selected.

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

. A grap+ is plotted it+0 along y-a,is and7 along ,-a,is.

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O"SERVATIONS:

S$ N&

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

R

(;+4 ++%

O *. * ) 4 ).&% * & , O

(;+4 ++%

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

(V

O *. *V& *)4+VO

(V

K A K A K A K A K A K A K A K A

MODEL GRAPH:

RES!LT:

T+e DC position control system c+aracteristics are studied and corresponding gdra n.

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DC POSITION CONTROL SYSTEM

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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 sysAPPARAT!S @ INSTR!MENTS RE !IRED:

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

FORM!LAE !SED:

Damping ratio6* ln #) 2 9 2 F ln #) 2:+ere # ) is pea= percent overs+oot o%tained from t+e time response grap+

Zndamped natural fre uency6n * 9 Et p 1 -2 H+ere t p is 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

C s 97 s * ! s 9 E1 F ! s < s H+ere

< s * 1! s * ? ? 2 ? 3 9 1FsT1 1 F sT2

+ere ? is t+e gain

? 2 is t+e gain of t+e time constant 1 %loc= *10? 3 is t+e gain of t+e time constant 2 %loc= *10T1 is t+e time constant of time constant 1 %loc= * 1 msT2 is t+e time constant of time constant 2 %loc= * 1 ms

Closed loop transfer function of t+e type 1-second order system isC s 97 s * ! s 9 E1 F ! s < s H

+ere < s * 1

! s * ? ? 1 ? 2 9 s 1 F sT1+ere ? is t+e gain

? 1 is t+e gain of 5ntegrator * (.$ ? 2 is t+e gain of t+e time constant 1 %loc= *10 T1 is t+e time constant of time constant 1 %loc= * 1 ms

THEORY:

T+e type num%er of t+e system is o%tained from t+e num%er of poles located atsystem. Type 0 system means t+ere is no pole at origin. Type 1 system mean pole located at t+e origin. T+e order of t+e system is o%tained from t+e +ig+est pdenominator of closed loop transfer function of t+e system. T+e first orde

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c+aracteri ed %y one pole or a ero. ,amples of first order systems are a pure isingle time constant +aving transfer function of t+e form ?9s and ?9 sTF1 . T+system is c+aracteri ed %y t o poles and up to t o eros. T+e standard form ofsystem is ! s *n2 9 s2 F 2ns Fn2 +ere is damping ratio andn is undamped naturafre uency.

PROCED!RE:

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

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

terminal of error detector %loc=. T+e input is also connected to t+e J- c+an3. 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 tdisplacement %et een t+e t o 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

TRACES FROM CRO:

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F& G) , K

F& G) , K

F& G) , K

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

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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

terminal of error detector %loc=. T+e input is also connected to t+e J- c+an3. 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 lo est fre uency to al

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

displacement %et een t+e t o 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 t o values ar

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

O"SERVATIONS:

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

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TRACES FROM CRO:

F& G) , K

F& G) , K

F& G) , K

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LINEAR SYSTEM SIM!LATOR PATCHING 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 s uare ave is set to 2 4pp in t+e C7 and t+is applied to t+e 7

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

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+t+e aveform t+e pea= percent overs+oot6 settling time6rise time6 pmeasured. Zsing t+ese valuesn and are calculated.

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

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

O"SERVATIONS:

S$ N&$ G)K

P+) .+ '+ *

O8+ %B&&*

M P

R %+* /+

*(%+'

P+) T /+

*.

(%+'

S+** 4* /+

*% (%+'

D)/. 4)* &

! ;)/.+;N)* )

+9 + '

( );@%+'

1

2

TRACES FROM CRO:

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

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

O"SERVATIONS:

S$ N&$ G)K

P+) .+ '+ *

O8+ %B&&*

M P

R %+* /+

*(%+'

P+) T /+

*.

(%+'

S+** 4* /+

*% (%+'

D)/. 4)* &

! ;)/.+;N)* )

+9 + '

( );@%+'

1

2

TRACES FROM CRO:

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

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

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

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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 SYSTEMS AIM: To digitally simulate t+e time response c+aracteristics of a linear systemnon- 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 termdomain specifications. Systems it+ energy storage elements cannot instantaneously and ill e,+i%it transient responses6 +enever t+ey are su%Qectedistur%ances.T+e desired performance c+aracteristics of a system of any order may %e sterms of transient response to a unit step input signal. T+e transient response c+aof a control system to a unit step input is specified in terms of t+e follo ing timspecifications

Delay time td7ise time tr )ea= time t p#a,imum pea= overs+oot # pSettling time ts

ST!DY OF "ASIC MATLA" COMMANDS:

T+e nameMATLA" stands forMATRI LA"ORATORY . #AT;A8 as originallyritten to provide easy access to matri, soft are developed %y t+e ;5/)AC? and 5

proQects. Today6 #AT;A8 engines incorporate t+e ;A)AC? and 8;AS li%raries6 emt+e state of t+e art in soft are for matri, computation. 5t +as evolved over a perio

it+ input from many users. 5n university environments6 it is t+e standard instrufor introductory and advanced courses MATHEMATICS, ENGINEERING, ANDSCIENCE . 5n industry6 #AT;A8 is t+e tool of c+oice for +ig+-productivity resdevelopment6 and analysis.

#AT;A8 is a +ig+-performance language for tec+nical computing. 5t intcomputation6 visuali ation6 and programming in an easy-to-use environment +eand solutions are e,pressed in familiar mat+ematical notation. Typical uses include

#at+ and computationAlgorit+m developmentData ac uisition #odeling6 simulation6 and prototypingData analysis6 e,ploration6 and visuali ation

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

5t is an interactive system +ose %asic data element is an array t+at does ndimensioning. T+is allo s you to solve many tec+nical computing pro%lems6 esp

it+ matri, and vector formulations6 in a fraction of t+e time it ould ta=e to rite in a scalar non-interactive language suc+ as C or Nortran. 5t also features a familapplication-specific solutions called tool%o,es. 4ery important to most users of #tool%o,es allo you to learn and apply speciali ed tec+nology. Tool%o,es are comcollections of #AT;A8 functions #-files t+at e,tend t+e #AT;A8 environment to particular classes of pro%lems. Areas in +ic+ tool%o,es are availa%le includSIGNALPROCESSING, CONTROL SYSTEMS, NE!RAL NET ORKS, 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 num6den Pstep sys Pgrid

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

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

num*E HPden*E HP

sys * tf num6den Pimpulse sys Pgrid

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

CALC!LATIONS:

! * %*+. +%.& %+ & *B+ 4 8+ RL %+ +% ' ' *:

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! * I/. %+ +%.& %+ & *B+ 4 8+ RLC %+ +% ' ' *:

RES!LT:

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

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 t o 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 manually.

APPARAT!S RE !IRED

A )C it+ MATLA" Soft are

THEORY

T+e time c+aracteristics of control systems are specified in terms of timespecifications. Systems it+ energy storage elements cannot respond instantane

ill e,+i%it transient responses6 +enever t+ey are su%Qected to inputs or distudesired performance c+aracteristics of a system of any order may %e specified transient response to a unit step input signal. T+e transient response c+aractercontrol system to a unit step input is specified in terms of t+e follo ing timespecifications

Delay time td7ise time tr )ea= time t p#a,imum overs+oot # pSettling 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 respo

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

order system6 t+e follo ing procedure is follo ed1. 5n #AT;A8 soft are open a ne model in S5#Z;5/? li%rary %ro ser.2. Nrom t+e continuous %loc= in t+e li%rary drag t+e transfer function %3. Nrom t+e source %loc= in t+e li%rary drag t+e step input9 sine input.

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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 poi$. 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

respective %loc=.

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

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 num6den Pstep sys P

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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 num6den Pimpulse sys P

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

CALC!LATIONS:

! * %*+. +%.& %+ & *B+ 4 8+ RLC %+ +% ' ' *:

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! * /. %+ +%.& %+ & *B+ 4 8+ RLC %+ +% ' ' *:

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RES!LT:

T+e time response c+aracteristics of t+e given second order system is simulated diverified 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 t o e,amples for second order system.&. /ame t+e standard test signals used in control system.

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'. :+at is time responseR

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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 tran! S *

APPARAT!S RE !IRED:

A )C it+ #AT;A8 Soft are

THEORY:

A ;inear Time-5nvariant Systems is sta%le if t+e follo ing t o notions of system ssatisfied

:+en t+e system is e,cited %y 8ounded input6 t+e output is also a 8ounoutput.5n t+e a%sence of t+e input6 t+e output tends to ards ero6 irrespectinitial conditions.

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

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

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

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

%*)= +.5f one are more non-repeated roots of t+e c+aracteristic e uation ona,is6 t+en system is%*)= +.

"ODE PLOT :

Consider a Single-5nput Single- utput system it+ transfer functionC s %0 sm F %1 sm-1 F UUF %m

*7 s a0sn F a1sn-1 F 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 frefor +ic+ t+e gain is unity one .

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

T+e application of t+ese rules to an actual process re uires evaluation of t+e gains+ift of t+e system for all fre uencies to see if rules 1 and 2 are satisfied. T+is is o

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

5f t+e p+ase lag is less t+an 1 0^ at t+e unity gain fre uency6 t+e sta%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 p1'0^6 t+e system is sta%le. T+is is "d8G) 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

O8 D ); T N T< S\ST #O nter t+e numerator and denominator of t+e transfer functionnum*E HPden*E HPsys*tf num6denOSpecify t+e fre uency range and enter t+e command

*logspace -26 61000 P %ode sys6,la%el _Nre uency_yla%el _ )+ase angle in degrees #agnitude of ! s in deci%els_title _8ode )lot of t+e system _

OTo determine t+e !ain #argin6 )+ase #argin6 !ain crossover fre uency andO)+ase cross over fre uencymargin sysE !m6 )m6 :pc6 :gc H* margin sys

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MAN!AL CALC!LATIONS:

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

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

RES!LT:

T+e 8ode plot is dra n for t+e given transfer function using #AT;A8 and vemanually. 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+ transfe

! s *APPARAT!S RE !IRED:


THEORY:

ROOT LOC!S PLOT:

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

of t+e closed loop poles. 5f t+e system +as a varia%le loop gain6 t+en t+e locclosed-loop poles depend on t+e value of t+e loop gain c+osen. A simple tec+ni u7oot ;ocus Tec+ni ueb used for studying linear control systems in t+e investiga

traQectories of t+e roots of t+e c+aracteristic e uation.

T+is tec+ni ue provides a grap+ical met+od of plotting t+e locus of t+e roots in t+a given system parameter is varied over t+e complete range of values may %e finfinity . T+e roots corresponding to a particular value of t+e system parameter located on t+e locus or t+e value of t+e parameter for a desired root locatiodetermined form t+e locus. T+e root locus is a po erful tec+ni ue as it %rings incomplete dynamic response of t+e system. T+e root locus also provides a m

sensitivity of roots to t+e variation in t+e parameter %eing considered. T+is teapplica%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:

O7 T ; CZS N T< S\ST #O

num*E Hden*E Hsys*tf num6denrlocus sysv*E-106106-'6'HPa,is v

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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 _


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

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

RES!LT:

T+e 7oot locus plot is dra n 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+ni ue.2. :+at are t+e conditions of sta%ility in root locus criteriaR3. :+at is t+e advantage of root locus tec+ni ueR

. :+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 /y uist plot and c+ec= t+e sta%ility of t+e system using /y uis

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

APPARAT!S RE !IRED


THEORY:

NY !IST STA"ILITY CRITERION

POLAR PLOTS @ NY !IST PLOTS:T+e sinusoidal transfer function ! QB is a comple, function is given %y

! QB * 7eE ! QB H F Q 5mE! QB H or ! QB * ! QB ! QB * # @ ----------- 1

Nrom e uation 1 6 it is seen t+at ! QB may %e represented as a p+asor of m p+ase angle @. As t+e input fre uency varies from 0 to 6 t+e magnitude # and @ c+anges and +ence t+e tip of t+e p+asor ! QB traces a locus in t+e complelocus t+us o%tained is =no n asPOLAR PLOT . T+e maQor advantage of t+e polar plot in sta%ility study of systems. /y uist related t+e sta%ility of a system to t+e fo plots. )olar plots are referred as /\ Z5ST PLOTS .

PROCED!RE:

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

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PROGRAM

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

den*E Hsys*tf num6den

OSpecify t+e fre uency range and enter t+e commandny uist sysv*E Ha,is v,la%el _7eal A,is_ Pyla%el _5maginary A,is_ Ptitle _/y uist )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 /y uist plot is dra n 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 /y uist plotR3. Define t+e conditions of sta%ility in polar plot.

. :+at is t+e use and advantage of polar plotR". State /y uist sta%ility criterion.

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

STEPPER MOTOR CONTROL SYSTEM

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EE2257-LM.doc

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