51355420 Lab Manual for e e Cs

EC2259 Electrical Engineering And Control System Lab Manual

LAB MANUAL

VEL TECH MULTI TECH ( ISO 9001: 2000 Certified Institution & NBA Accredited )

(Owned by VEL Sree R.Rangarajan Dr. Sagunthala Rangarajan Educational Academy)

Approved by AICTE, New Delhi & Affiliated to Anna University No 42, Alamathi Road, Near Avadi Chennai – 600 062

DEPARTMENT OE ELECTRONICS

AND COMMUNICATION

ENGINEERING

EC 2259 - ELECTRICAL ENGINEERING AND

CONTROL SYSTEM LAB

II YEAR IV SEM ECE

Prepared By HOD/ECE


EC 2259 ELECTRICAL ENGINEERING AND CONTROL SYSTEM LAB 0 0 3 2

AIM

To expose the students to the basic operations of electrical machines and help them to develop experimental skills.

1. To study the concepts, performance characteristics, time and frequency response of linear systems.

2. To study the effects of controllers.

1. Open circuit and load characteristics of separately excited and self excited D.C. generator.

2. Load test on D.C. shunt motor.

3. Swinburne’s test and speed control of D.C. shunt motor.

4. Load test on single phase transformer and open circuit and short circuit test on single phase transformer

5. Regulation of three phase alternator by EMF and MMF methods.

6. Load test on three phase induction motor.

7. No load and blocked rotor tests on three phase induction motor (Determination of equivalent circuit parameters)

8. Study of D.C. motor and induction motor starters.

9. Digital simulation of linear systems.

10. Stability Analysis of Linear system using Mat lab.

11. Study the effect of P, PI, PID controllers using Mat lab.

12. Design of Lead and Lag compensator.

13. Transfer Function of separately excited D.C.Generator.

14. Transfer Function of armature and Field Controller D.C.Motor.

P = 45 Total = 45

1. Open circuit and load characteristics of separately excited and self excited D.C.

generator.

Sl. No. Apparatus Range Quantity 1 Motor Generator set - 1

2 Rheostat 200Ω, 5A

175Ω, 1.5A

1 2

3 Voltmeter DC 300V 30V

1 1

4 Ammeter DC 30A 2A

1 2

5 DPST switch 2

6 Three point starter 1

7 Tachometer 1


2. Load test on D.C. shunt motor.

Sl. No. Apparatus Range Quantity

1 DC Motor - 1

2 Rheostat 175Ω, 1.5A 1

3 Voltmeter DC 300V 1

4 Ammeter DC 30A 1

5 DPST switch 1


7 Tachometer 1

3. Swinburne’s test and speed control of D.C. shunt motor

Sl. No. Apparatus Range Quantity 1 DC Motor - 1

2 Rheostat 100Ω, 5A & 175Ω, 1.5A 1 1


4 Ammeter DC 5A 2A

1 1

5 DPST switch 1

6 Tachometer 1

4. Load test on single-phase transformer and open circuit and short circuit test on

single-phase transformer.

Sl. No. Apparatus Range Quantity 1 Single phase Transformer - 1

2 Wattmeter 300V, 5A,UPF & 300V, 5A,LPF

1 1

3 Voltmeter AC 300V 2

4 Ammeter AC 5A 30A

1 1

5 Single phase auto-transformer 1

6 Resistive load 1

5. Regulation of three-phase alternator by EMF and MMF method.

Sl. No. Apparatus Range Quantity

1 Motor Alternator set - 1

2 Rheostat 200Ω, 5A &175Ω, 1.5A 1 1

3 Voltmeter DC Voltmeter AC

300V 600V

1 1

4 Ammeter DC Ammeter AC

2A 30A

1 1

5 DPST switch TPST switch

1 1

6 Tachometer 1


6. Load test on three phase Induction motor.

Sl. No. Apparatus Range Quantity 1 Three Phase Induction Motor - 1

2 Wattmeter 600V, 10A,UPF 2

3 Voltmeter AC 600V 1

4 Ammeter AC 10A 1

5 Brake drum arrangement

6 Star delta starter 1

7 Tachometer 1

7. No load and blocked rotor test on three-phase induction motor (Determination of

equivalent circuit parameters)

Sl. No. Apparatus Range Quantity 1 Three Phase Induction Motor - 1

2 Wattmeter 600V, 10A,UPF 600V, 5A,LPF

2 2

3 Voltmeter AC 600V 150V

1 1

4 Ammeter AC 10A 5A

1 1

5 Brake drum arrangement

6 Three phase auto-transformer 1

8. Study of D.C. motor and Induction motor starters.

Sl. No. Apparatus Quantity 1 Three point starter 1

2 Four point starter 1

3 Star-delta starter 1

4 DOL starter 1

5 Three phase auto-transformer 1

9. Digital simulation of linear systems.

Simulink software for minimum 3 users license

10. Stability analysis of linear system using Mat lab.

Matlab software for minimum 3 users license

11. Study of effect of P, PI, PID controllers using Mat lab.

Matlab software for minimum 3 users license


12. Design of lead and lag compensator.

Sl. No. Apparatus

1 Resistor

2 Capacitor

3 Function generator

4 Bread Board

13. Transfer function of separately excited D.C. generator.

Sl. No. Apparatus Range Quantity 1 Motor Generator set - 1

2 Rheostat 200Ω, 5A

175Ω, 1.5A

1 2

3 Voltmeter DC 300V 30V

1 1

4 Ammeter DC 30A 2A

1 2

5 DPST switch 2


7 Tachometer 1

14. Transfer function of armature and field controller D.C. motor.

Sl. No. Apparatus Range Quantity 1 DC Motor - 1

2 Rheostat 175Ω, 1.5A 1


4 Ammeter DC 30A 1

5 DPST switch 1


7 Tachometer 1


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LOAD TEST ON DC SHUNT MOTOR

AIM

To conduct the load test on a given dc shunt motor and draw its performance curves.

NAME PLATE DETAILS

FUSE RATING

125% of rated current (full load current)

APPRATUS REQUIRED

S. NO NAME OF THE

APPARATUS TYPE RANGE QUANTITY

1

2

3

4

Ammeter

Voltmeter

Rheostat

Tachometer

MC

MC

Wire wound

Digital

(0-20A)

(0-300V)

250, 2A

1

1

1

1

FORMULAE

1. Torque T = (S1~S2) × (R+t/2) × 9.81 in N-m.

Where R- Radius of the Break drum in m.

t- Thickness of the Belt in m.

S1,S2- Spring balance reading in Kg.

2. Input power = VL × IL in Watts.

Where VL – Load Voltage in Volts.

IL- Load current in Amps.

3. Output power = 2NT/60 in Watts.

Where N- Speed of the armature in rpm.

T- Torque in N-m.

4. Percentage of Efficiency = (Output power/Input power) × 100


CIRCUIT DIAGRAM FOR LOAD TEST ON DC SHUNT MOTOR

Model Graph

(A) Electrical characteristics (B) Mechanical characteristics

(C) Torque, Speed Vs Load Current

Fuse

Fuse

BRAKE DRUM

S1 S2

220V DC SUPPLY

L F A

3 POINT STARTER

D

P

S

T

S

250, 2A F

FF

M

A

AA

V (0-300V)

MC

A

(0-20A) MC

Output power in watts

N

N in rpm

IL in Amps

T in N-m

%

T IL %

Sp

eed

in

rp

m

Torque in N-m

Torque Vs Speed

Sp

eed

in

rp

m

Load Current in Amps

Speed

To

rqu

e in

N-m

Torque


PRECAUTION

• The motor field rheostat should be kept at minimum resistance position.

• At the time of starting, the motor should be in no load condition.

• The motor should be run in anticlockwise direction.

PROCEDURE

• Connections are given as per the circuit diagram.

• Using the three-point starter the motor is started to run at the rated speed by adjusting the field rheostat if necessary.

• The meter readings are noted at no load condition.

• By using the Break drum with spring balance arrangement the motor is loaded and the corresponding readings are noted up to the rated current.

• After the observation of all the readings the load is released gradually.

• The motor is switched off by using the DPIC switch.

GRAPH

The graphs are drawn as

• Output power Vs Efficiency

• Output power Vs Armature current

• Output power Vs Torque

• Output power Vs Speed

• Torque Vs Speed

• Torque Vs Armature current

• Speed Vs Armature current


Tabulation for load test on DC shunt motor

Radius of the brake dram = Thickness of the belt =

Spring balance reading

Load

Current (IL)

Load

Voltage (VL)

Speed of the motor

(N)

S1

S2

S1~S2

Torque (T)

(S1~S2)(R+t/2)(9.81)

Output power

2NT/60

Input power (VLIL)

Efficiency (ηηηη) O/p / I/p

x100

S.No

Amps Volts Rpm Kg Kg Kg N-m Watts Watts %


MODEL CALCULATION

RESULT

Thus the load test on DC shunt motor and its performance curves are drawn.


SPEED CONTROL OF DC SHUNT MOTOR

AIM

To conduct an experiment to control the speed of the given dc shunt motor by field and armature control method also to draw its characteristic curves.

NAME PLATE DETAILS

FUSE RATING


APPRATUS REQUIRED

S.NO NAME OF THE


1

2

3

4

5

6

Ammeter

Ammeter

Voltmeter

Rheostat

Rheostat

Tachometer

MC

MC

MC

Wire wound

Wire wound

Digital

(0-2A)

(0-10A)

(0-300V)

250, 2A

50, 5A

1

1

1

1

1

1

PRECAUTION


• The motor armature rheostat should be kept at maximum resistance position.

• The motor should be in no load condition throughout the experiment.



Prepared by G.Panneerselvam, Vel Tech Multi Tech

CIRCUIT DIAGRAM FOR SPEED CONTROL OF DC SHUNT MOTOR

Tabulation for Speed control of DC Shunt motor

Armature Control Method Field Control Method

Field Current: Armature Current:

Armature

Voltage (Va)

Speed (N)

Field Current

(If)

Speed (N)

S.No.

Volts RPM Amps RPM

Fuse

Fuse

220V DC SUPPLY

L F A

3 POINT STARTER

D

P

S

T

S

250, 2A F

FF

M

A

AA

A

(0-2A) MC

50, 5A

V (0-300V) MC

A

(0-10A) MC



Model Graph

(A) Armature Control Method: (B) Field Control Method:

PROCEDURE

Field Control Method (Flux Control Method) • Connections are given as per the circuit diagram.

• Using the three point starter the motor is started to run.

• The armature rheostat is adjusted to run the motor at rated speed by means of applying the rated voltage.

• The field rheostat is varied gradually and the corresponding field current and speed are noted up to 120% of the rated speed by keeping the Armature current as constant.

• The motor is switched off using the DPIC switch after bringing all the rheostats to their initial position.

Armature Control Method (Voltage Control Method)


• Using the three point starter the motor is started to run.

• The armature rheostat is adjusted to run the motor at rated speed by means of applying the rated voltage.

• The armature rheostat is varied gradually and the corresponding armature voltage armature current and speed are noted up to the rated voltage.

• The motor is switched off using the DPIC switch after bringing all the rheostats to their initial position

GRAPH The graph are drawn as

• Field current Vs Speed

• Armature current Vs Speed

RESULT Thus the speed control of the given DC shunt motor using field control and armature

control method and its characteristic curves are drawn.

Sp

eed

in

rp

m

Armature Voltage in Volts

Armature Voltage Vs Speed

Sp

eed

in

rp

m

Field Current Vs Speed

Field Current in Amps


SWINBURNE’S TEST

AIM

To predetermine the efficiency of a given dc shunt machine when working as a motor as well as generator by Swinburne’s test and also draw the characteristic curves.

NAME PLATE DETAILS

FUSE RATING


APPRATUS REQUIRED

S.NO NAME OF THE


1

2

3

4

5

Ammeter

Ammeter

Voltmeter

Rheostat

Tachometer

MC

MC

MC

Wire wound

Digital

(0-2A)

(0-10A)

0-300V

250,2A

1

1

1

1

1


CIRCUIT DIAGRAM FOR SWINEBURN’S TEST

Tabulation to find out the Constant loss (Wco)

Terminal Voltage (V)

No load Current (I0)

Field Current

(If)

No load Armature

Current (Ia0)

Constant Loss

WCO = VI0-Ia02 Ra

S.No. Volts Amps Amps Amps Watts

Resultant tabulation to find out the Efficiency (Running as motor)

Armature Resistance (Ra)= Rated Current (Ir)=

Constant loss (WC)= Field Current (If) =

Load Current IL=

X×Ir

Armature Current

Ia= IL- If

Armature Cu Loss

WCu=Ia2Ra

Total Loss WTotal

Input Power

Wi=VLIL

Output Power

Wo =Wi- WTotal

Efficiency

= Wo/ Wi

S.No.

Fraction

of Load (X) Amps Amps Watts Watts Watts Watts %

1 1/4

2 1/2

3 3/4

4 1

Fuse

Fuse

220V DC SUPPLY

L F A

3 POINT STARTER

D

P

S

T

S

250, 2A F

FF

M

A

AA

V (0-300V)

MC

A

(0-2A) MC

A

(0-10A) MC


FORMULAE

1. Armature resistance (Ra) = 1.6 × RDC in Ohms.

Where,

RDC – Resistance of the Armature coil, when it is energized by DC supply.

2. Constant loss (WCO ) = (V Io-Iao2Ra) in Watts..

Where V = Terminal Voltage in Volts

Io = No Load Current in Amps

Iao = No Load Armature Current. in Amps

3. Armature Current (Ia) = (IL ± If ) in Amps.

Where, + is used for Generator,

- is used for Motor.

4. Copper loss (WCU ) = Ia2Ra in Watts.

5. Total loss = Constant loss + Copper loss in Watts

6. Input power for motor / Output power for generator = V IL in Watts

Where, IL is Load current in Amps

7. Output power for motor = Input power + losses

Input power for Generator = Output power - losses

8. Percentage of Efficiency = (Output power/Input power) × 100

PRECAUTION


• The motor should be at no load condition through out the experiment.


PROCEDURE


• By using the three point starter the motor is started to run at the rated speed.

• The meter readings are noted at no load condition.

• The motor is switched off using the DPIC switch.

• After that the Armature resistive test is conducted as per the circuit diagram and the voltage and current are noted for various resistive loads.

• After the observation of readings the load is released gradually.


Running as generator

Armature Resistance (Ra)= Rated Current (Ir)=

Constant loss (WC)= Field Current (If)=

Load Current

IL= X×Ir

Armature Current

Ia= IL+ If

Armature Cu Loss

WCu=Ia2Ra

Total Loss WTotal

Output Power

Wo=VLIL

Input Power

Wi

=Wo+WTotal

Efficiency

= Wo/ Wi

S.No.

Fraction

of Load (X)

Amps Amps Watts Watts Watts Watts %

1 1/4

2 1/2

3 3/4

4 1


Model Graph

GRAPH

The graph drawn between Load current Vs Efficiency

RESULT

Thus the efficiency of the given DC shunt machine by Swinburne’s test when working as a motor as well as generator and also draw the characteristic curves are drawn.

Eff

icie

ncy

Output Power (Wo) in Watts

Generator

Motor


OPEN CIRCUIT TEST AND LOAD TEST ON SELF EXCITED DC SHUNT GENERATOR

AIM

To conduct the open circuit test and the load test on a given self excited dc shunt generator and draw the characteristic curves.

NAME PLATE DETAILS

FUSE RATING


APPRATUS REQUIRED

S.NO NAME OF THE


1

2

3

4

5

6

7

Ammeter

Ammeter

Voltmeter

Rheostat

Rheostat

Tachometer

Resistive Load

MC

MC

MC

Wire wound

Wire wound

Digital

Variable

(0-2A)

(0-20A)

(0-300V)

250, 2A

350, 1.5A

-

-

1

2

1

1

1

1

1

PRECAUTION


• The generator field rheostat should be kept at maximum resistance position.

• At the time of starting, the generator should be in no load condition.



CIRCUIT DIAGRAM FOR OPEN CIRCUIT AND LOAD TEST ON SELF EXCITED DC SHUNT GENERATOR

Fuse

Fuse

Fuse

Fuse

M

A

AA

220V DC SUPPLY

L F A

3 POINT STARTER

D

P

S

T

S

250, 2A F

FF

G

A

AA

F

FF

10

50

, 1

.5A

V (0-300V) MC

D

P

S

T

S

A

(0-20A) MC

LOAD

A

(0-2A) MC

A

(0-20A) MC

17



PROCEDURE

Open circuit test


• The Prime Mover is started with the help of the three point starter and it is made to run at rated speed when the Generator is disconnected from the load by DPST switch.

• By varying the Generator field rheostat gradually, the Open Circuit Voltage (Eo) and corresponding Field Current (If) are tabulated upto 150 % of Rated Voltage of Generator.

• The motor is switched off by using the DPIC switch after bringing all the rheostats to their initial position.

Load test



• By varying the Generator field rheostat gradually, the Rated Voltage (Eg) is obtained.

• The Ammeter and Voltmeter readings are observed at no load condition.

• The Ammeter and Voltmeter readings are observed for different loads up to the rated current by closing the DPST switch.

• After tabulating all the readings the load is brought to its initial position gradually.

• The Prime Mover is switched off using the DPIC switch after bringing all the rheostats to their initial position.

GRAPH

The graph are drawn as

• Open Circuit Voltage Vs Field Current

• Load Voltage Vs Load Current



Tabulation for OC and Load test on self excited DC Shunt Generator

Generator Armature Resistance (Ra):

OC Test Load Test

Open circuit Voltage

(E0)

Field Current

(If)

Load Voltage

(VL)

Load Current

(IL)

Armature Current

(Ia)

Armature Drop

Ia Ra

Generated emf

Eg=VL+ Ia Ra

S.No.

Volts Amps Volts Amps Amps Volts Volts

Model Graph

(A) Open Circuit Characteristics (B) Internal (EgVs Ia) and External (VLVs IL) Characteristics

RESULT

Thus the open circuit test and load test on a given self excited DC generator and the characteristic curves are drawn.

Op

en C

ircu

it V

olt

age

(E0)

in V

olt

s

Field Current (If) in

Amps

(E0) Vs (If)

Lo

ad V

olt

age

(VL)

in V

olt

s

Load Current (IL) in Amps

(VLVs IL)

Gen

erat

ed E

MF

(E

g)

in V

olt

s

Armature Current (Ia)

in Amps

(EgVs Ia)



OPEN CIRCUIT TEST AND LOAD TEST ON SEPARATELY EXCITED DC GENERATOR

AIM

To conduct the open circuit test and the load test on a given separately excited dc generator and draw the characteristic curves.

NAME PLATE DETAILS

FUSE RATING


APPRATUS REQUIRED

S.NO NAME OF THE


1

2

3

4

5

6

7

Ammeter

Ammeter

Voltmeter

Rheostat

Rheostat

Tachometer

Resistive Load

MC

MC

MC

Wire wound

Wire wound

Digital

Variable

(0-2A)

(0-20A)

(0-300V)

250, 2A

350, 1.5A

-

-

1

2

1

1

1

1

1

PRECAUTION


• The generator field rheostat should be kept at maximum resistance position.

• At the time of starting, the generator should be in no load condition.



CIRCUIT DIAGRAM FOR OPEN CIRCUIT AND LOAD TEST ON SEPERATELY EXCITED DC GENERATOR

Fuse

Fuse

220V DC SUPPLY

D

P

S

T

S

350, 1.5A

Fuse

Fuse

Fuse

Fuse

M

A

AA

220V DC SUPPLY

L F A

3 POINT STARTER

D

P

S

T

S

250, 2A F

FF

G

A

AA

V

(0-300V) MC

D

P

S

T

S

A

(0-20A) MC

LOAD

FF

F

A

(0-2A) MC

A

(0-20A) MC

23



PROCEDURE

Open circuit test



• By varying the Generator field rheostat gradually, the Open Circuit Voltage (Eo) and corresponding Field Current (If) are tabulated upto 150 % of Rated Voltage of Generator.

• The motor is switched off by using the DPIC switch after bringing all the rheostats to initial position.

Load test


• The Prime Mover is started with the help of the three point starter and it is made to run at rated speed when the Generator is disconnected from the load by DPST switch..

• By varying the Generator field rheostat gradually, the Rated Voltage (Eg) is obtained.

• The Ammeter and Voltmeter readings are observed at no load condition.

• The Ammeter and Voltmeter readings are observed for different loads up to the rated current by closing the DPST switch..

• After tabulating all the readings the load is brought to initial position.

• The motor is switched off using the DPIC switch after bringing all the rheostats to initial position.

GRAPH

The graph drawn as

• Open Circuit Voltage Vs Field Current

• Load Voltage Vs Load Current



Tabulation for OC and Load test on separately excited DC Generator

Generator Armature Resistance (Ra):

OC Test Load Test

Open circuit Voltage

(E0)

Field Current

(If)

Load Voltage

(VL)

Load Current

(IL)

Armature Current

(Ia)

Armature Drop

Ia Ra

Generated emf

Eg=VL+ Ia Ra

S.No.

Volts Amps Volts Amps Amps Volts Volts

Model Graph

(A) Open Circuit Characteristics (B) Internal (EgVs Ia) and External (VLVs IL) Characteristics

RESULT

Thus the open circuit test and load test on a given separately excited DC generator and the characteristic curves are drawn.

Op

en C

ircu

it V

olt

age

(E0)

in V

olt

s

Field Current (If) in

Amps

(E0) Vs (If)

Lo

ad V

olt

age

(VL)

in V

olt

s

Load Current (IL) in Amps

(VLVs IL)

Gen

erat

ed E

MF

(E

g)

in V

olt

s

Armature Current (Ia)

in Amps

(EgVs Ia)



LOAD TEST ON SINGLE PHASE TRANSFORMER

AIM

To conduct the load test on a given single phase transformer and draw its performance curves.

NAME PLATE DETAILS

FUSE RATING

Primary Current = KVA Rating of the Transformer / Primary Voltage.

Secondary Current = KVA Rating of the Transformer / Secondary Voltage.

125% of Primary current (fuse rating for primary side)

125% of Secondary current (fuse rating for secondary side)

APPRATUS REQUIRED

S.NO NAME OF THE


1

2

3

4

5 6

Ammeter

Ammeter

Voltmeter

Voltmeter

Watt meter

Auto Transformer

MI

MI

MI

MI

UPF

1φ

(0-5A)

(0-20A)

(0-150V)

(0-300V)

300V, 5A

230/(0-270V

1

1

1

1

1

1


CIRCUIT DIAGRAM FOR LOAD TEST ON SINGLE PHASE TRANSFORMER

300V, 5A UPF

L M

C P1

P2

150V

A

V (0-300V) MI

A

C

230/(0-270V) 1Ø AUTO

TRANSFORMER

NL

1Ø, 230V, 50Hz AC SUPPLY

N

P

Fuse

B

SPSTS

V

(0-150V) MI

1Ø 230/110V, 1KVA STEP DOWN

TRANSFORMER

Fuse

Fuse

D

P

S

T

S

(0-10A) MI

LOAD

(0-5A) MI

S1

S2

33

A



FORMULAE

1. Input Power =Wattmeter reading × Multiplication factor in Watts

Where,

Multiplication factor =

2.Output power = VSY × ISY × cosφ in Watts.

Where VSY - Secondary Voltage in Volts.

ISY- Secondary current in Amps.

3.Percentage of Efficiency = × 100 %

4.Percentage of Regulation = × 100 %

Where, VO – No Load Voltage in Volts

VL – Load Voltage in Volts

PRECAUTION

• No Load Condition should be observed at the time of starting

• Meters are checked for proper Type and rating.

PROCEDURE


• The SPST Switch on the Primary side is closed and the DPST Switch on the Secondary side is opened.

• The Autotransformer is adjusted to Energize the transformer with rated Primary Voltage

• The Volt meters and Ammeters Readings are noted and tabulated at No load condition

• The DPST switch on the secondary side is closed.

• The transformer is loaded upto 130% of the Rated Load, corresponding Ammeters, Voltmeters and Wattmeters readings are noted and tabulated.

• After the observation of all the readings the load is released gradually to its initial position.

• The Autotransformer is brought to its initial position

• The Supply is switched off.

GRAPH

The graph drawn as


• Output power Vs Regulation

(Rating of pressure coil × Rating of current coil × pf ) Full Scale Reading

VO – VL

VO

Output Power

Input Power



Tabulation for Load test on single phase transformer

Multiplication Factor =

Wattmeter readings

(W)

Primary Voltage

(VPy)

Primary Current

(IPy)

Secondary Voltage

(VSy)

Secondary Current

(ISy) Obs.

Act.

Input power (W)

Output power

VSy ISy cosφφφφ

Efficiency

(ηηηη) O/p / I/p

×100

S.No

Volts Amps Volts Amps Watts Watts Watts %

% Of

Regulation VNL-VLOAD

VLOAD



Model Graph

RESULT

Thus the load test on a given single phase transformer is done and the characteristic curves are drawn.

% O

f E

ffec

ien

cy

Effeciency

Output power in watts

% O

f R

egu

lati

on

Regulation



OPEN CIRCUIT TEST AND SHORT CIRCUIT TEST

ON SINGLE PHASE TRANSFORMER

AIM

To Predetermine the Efficiency and Regulation on a given single phase transformer by conducting the Open Circuit test and Short Circuit test and also draw its Equivalent circuit.

NAME PLATE DETAILS

FUSE RATING

Primary Current = KVA Rating of the Transformer / Primary Voltage.

Secondary Current = KVA Rating of the Transformer / Secondary Voltage.

10% of Primary current (fuse rating for Open Circuit test)

125% of Secondary current (fuse rating for Short circuit test)

APPARATUS REQUIRED

S.No Name of the apparatus Type Range Quantity

1

2

3

4

5 6 7

Ammeter

Ammeter

Voltmeter

Voltmeter

Watt meter

Watt meter

Auto Transformer

MI

MI

MI

MI

UPF

UPF

1φ

(0-1A)

(0-10A)

(0-150V)

(0-300V)

300V, 1A

75V, 5A

230/(0-270V)

1

1

1

1

1

1

1



CIRCUIT DIAGRAM FOR OPEN CIRCUIT TEST ON SINGLE PHASE TRANSFORMER


A

C

230/(0-270V) 1Ø AUTO

TRANSFORMER

NL

N

P

Fuse

B

SPSTS 150V

150V, 5A LPF

L M

C

A

V (0-150V) MI

(0-300V) MI

V

1Ø 110/230V, 1KVA STEP UP

TRANSFORMER

P1

P2

S1

S2

(0-5A) MI

39



CIRCUIT DIAGRAM FOR SHORT CIRCUIT TEST ON SINGLE PHASE TRANSFORMER

(0-75V) MI

75V

300V, 10A UPF

L M

C

A

V

A

C

230/(0-270V) 1Ø AUTO

TRANSFORMER

NL


N

P

Fuse

B

SPSTS

A

(0-10A) MI P1

P2

S1

S2

(0-5A) MI

SC

1Ø 230/110V, 1KVA STEP DOWN

TRANSFORMER

41



Tabulation for OC and SC test on Single phase transformer

Open Circuit test Multiplication Factor =

Short

Circuit test Multiplication Factor =

Short Circuit power (WSC) Short Circuit Primary

Current (ISC)

Short circuit Primary

Voltage (VSC) Obs. Act.

Short Circuit secondary

Current (I2S)

S.No.

Amps Volts Watts Watts Volts

Resultant Tabulation to find out the Efficiency

Core (Or) Iron Loss = A Rating of Transformer = Rated Short Circuit Current (ISC) = Short Circuit Power (WSC) =

Output power

Short circuit

Current

(ISC×X) 0.2 0.4 0.6 0.8 1

Copper

Loss (X2 WSC)

Total Loss

WT =

Wi+WSC

Efficiency

O/p O/p+TL

Fraction of Load (X)

Amps Watts Watts Watts %

1/4

1/2

3/4

1

Open Circuit power (WOC) Open Circuit Primary

Current (IOC)

Open circuit Primary

Voltage (VOC) Obs. Act.

Open Circuit secondary

Voltage (V2O)

S.No.

Amps Volts Watts Watts Volts

η=



FORMULAE

EQUIVALENT CIRCUIT

Open Circuit Test

1. No Load Power Factor (Cosφφφφo) =

Where, Woc – Open Circuit Power in Watts

Voc – Open Circuit Voltage in Volts

Ioc – Open Circuit Current in Amps

2.No Load Working Component Resistance (Ro) = in Ohms

Where Voc – Open Circuit Voltage in Volts.

Ioc – Open Circuit current in Amps.

3. No Load Magnetizing Component Reactance( Xo) = in Ohms

Where Voc – Open Circuit Voltage in Volts.

Ioc – Open Circuit current in Amps.

Short Circuit Test

4. Equivalent impedance referred to HV side ( Z02 ) = in Ohms

Where, Vsc – Short circuit Voltage in Volts

Isc – Short circuit current in Amps

5. Equivalent resistance referred to HV side (R02 ) = in Ohms

Where, Wsc – Short circuit Power in Watts

6. Equivalent reactance referred to HV side (X02) = Z022 - R02

2 in Ohms

7. Transformation ratio (K) =

Where, V1 – Primary voltage in Volts

V2 – Secondary Voltage in Volts

8. Equivalent resistance referred to LV side (R01) = in Ohms

9. Equivalent reactance referred to LV side (X01) = in Ohms

Efficiency and Regulation

10. Output Power = X ×KVA × cosφ in Watts. Where, X-Fraction of load

KVA - power rating of Transformer and Cosφ - Power factor

Vsc

Isc

Woc Voc × Ioc

Voc

Ioc × Cosφo

Voc

Ioc × Sinφo

Wsc

Isc2

V2

V1

R02

K2

X02

K2



11. Copper loss = X2 × Wsc in Watts Where, Wsc- Copper Loss in Short Circuit condition 12. Total Loss = (Cu Loss + Iron Loss) in Watts 13. Efficiency = x 100 in % 14. Regulation = × 100 in % Where, V2o – Open Circuit Voltage on HV side.

PRECAUTION

• No Load Condition should be observed at the time of starting

• Meters are checked for proper Type and rating.

PROCEDURE

OPEN CIRCUIT TEST


• The SPST Switch on the Primary side is closed.

• The Autotransformer is adjusted to Energize the transformer with rated Primary Voltage on the LV side

• The Volt meter, Watt meter and Ammeter Readings are noted at No load condition



SHORT CIRCUIT TEST


• The SPST Switch on the Primary side is closed

• The Autotransformer is adjusted to energize the transformer with rated Primary Current on the HV side.

• The Voltmeter, Wattmeter and Ammeter Readings are noted down at short circuit condition.



GRAPH



• Output power Vs Regulation

Output power

(Output power +Total Losses)

X × Isc [R02 x cosφ ± X02 x sinφ] V2o



Resultant Tabulation to find out the Regulation

ISC = RO2 = XO2 = V2(OC) =

% Of Regulation

Value of Cosø

Value of Sinø 0.8 0.6 0.4 0.2

Fraction of Load

(X) 1 0.8 0.6 0.4 0.2 1 0.8 0.6 0.4 0.2

1 Lag. Lead. Lag. Lead. Lag. Lead. Lag. Lead.



Equivalent circuit for Single phase Transformer

Model Graph

RESULT

Thus the efficiency and regulation of a given single phase transformer by conducing the open

circuit test and short circuit test is determined and the equivalent circuit is drawn.

P

N

V1 ZL

I1 X01R01

X0 R0

I0

Iw I

Eff

ecie

ncy

0.2 pf

Short Circuit Current (ISC) in Amps

0.4 pf

0.6 pf

0.8 pf

1.0 pf

Reg

ula

tio

n

Lagging pf Leading pf

X=1

X =3/4

X =1/2

X =1/4

Unity pf



LOAD TEST ON THREE PHASE SQUIRREL CAGE INDUCTION MOTOR

AIM

To conduct a load test on a three phase squirrel cage induction motor and to draw the performance characteristic curves.

NAME PLATE DETAILS

! " "#$%"&'"

FUSE RATING

125% of rated current (Full load current)

APPARATUS REQUIRED

FORMULAE USED

1.Torque = (S1-S2) (R+t/2) x 9.81 N-m

Where, S1, S2 – spring balance readings in Kg.

R - Radius of brake drum in m.

t - Thickness of belt in m.

2. Output Power = 2 πNT/60 watts.

N- Rotor speed in rpm.

T- Torque in N-m.

S.NO NAME OF THE


1. 2. 3.

4.

Ammeter Voltmeter Wattmeter

Tachometer

MI MI

UPF

-

(0-10 A) (0-600 V)

(500V, 10A)

-

1 1 1

1

3. Input Power = (W1+W2) Watts.

W1, W2 – Wattmeter readings in Watts.



CIRCUIT DIAGRAM FOR LOAD TEST ON THREE PHASE SQUIRRAL CAGE INDUCTION MOTOR

BRAKE DRUM

S1 S2

(0-10) A MI

415V, 50Hz, 3Ø

AC SUPPLY

R

Y

B

N

STAR-DELTA STARTER

A

T

P

S

T

S

Fuse

Fuse

Fuse

V (0-600) V MI

600V, 10A UPF

L

600V

M

C

R

STATOR

A1

A2

B1 B2

C1

C2

M

600V, 10A UPF

C

L

600V

A1 A2 B1 B2 C1 C2

L2

L3

L1

NL N

51



4. Percentage of Efficiency = (Output Power/ Input Power) x 100%.

5. Percentage of Slip = (NS-Nr)/Ns x 100%

Ns-Synchronous speed in rpm.

Nr-Rotor speed in rpm.

6.Power factor = (W1+W2)/√3 VLIL.

PRECAUTION

The motor should be started without any load

PROCEDURE:


• The TPSTS is closed and the motor is started using On Line starter to run at rated speed.

• At no load the speed, current, voltage and power are noted down.

• By applying the load for various values of current the above-mentioned readings are noted.

• The load is later released and the motor is switched off and the graph is drawn. .

GRAPH


• Output Power Vs Speed

• Output Power Vs Line current

• Output Power Vs Torque

• Output Power Vs Power factor

• Output Power Vs % Efficiency

• Output Power Vs % Slip.



Tabulation for load test on three phase squirrel cage induction motor

Multiplication Factor:

Wattmeter readings

W1

W2

Input power

Spring balance

reading

Load

Current

(IL)

Load

Voltage (VL)

Obs. Act. Obs. Act.

W1+W2

Speed of the motor (N)

S1 S2 S1~S2

Torque (T) (S1~S2) (R+t/2)

(9.81)

Output power

2NT/60

Efficiency

(ηηηη) O/p / I/p

X100

S.No

Amps Volts Watts Watts rpm Kg Kg Kg N-m Watts %

Power Factor

(cosφφφφ) I/p /

√3 VLIL



Load test on Three phase squirrel cage induction motor

Model Graphs: (A) Mechanical characteristics (B) Electrical characteristics:

RESULT

Thus the load test on a given three phase squirrel cage induction motor is done and the

characteristic curves are drawn.

Speed in RPM

Torque in N-m

Torque Vs Speed

O/P power in watts

N

N in rpm

IL in Amps

T in N-m

% T

IL %

Cos φ

Cos φφφφ



EQUIVALENT CIRCUIT OF THREE PHASE SQUIRREL CAGE INDUCTION MOTOR

AIM

To conduct a No Load test and Blocked Rotor test on three phase squirrel cage induction motor and to draw the equivalent circuit.

NAME PLATE DETAILS

! " "#$%"&'"

FUSE RATING

No Load: 10 % of rated current (Full load current)

Load: 125 % of rated current (Full load current)

APPARATUS REQUIRED

FORMULAE USED

OC Test

1. No load power factor (Cos φ0) = P0/V0I0

V0 - No load voltage per phase in volts.

I0 - No load current per phase in amps.

P0 - No load power per phase in watts.

2. Working component current (Iw) = I0 (ph) X Cos φ0

3. Magnetizing current (Im) = I0 (ph) X Sin φ0

4. No load resistance (R0) =V0/I0 (ph) Cos φ0 in Ω.

S.NO. NAME OF THE

APPARATUS

TYPE RANGE QUANTITY

1. 2. 3. 4. 5. 6. 7.

Ammeter Ammeter Voltmeter Voltmeter Voltmeter Wattmeter Wattmeter

Tachometer

MC MI MI MI MC LPF UPF

-

(0-10 A) (0-10 A)

(0-150 V) (0-600 V) (0-50 V)

(600V, 10A) (150V, 10A)

-

1 2 1 1 1 2 2 1



CIRCUIT DIAGRAM FOR NO LOAD TEST ON THREE PHASE SQUIRREL CAGE INDUCTION MOTOR

(Equivalent circuit)

57

415V, 50Hz, 3Ø

AC SUPPLY

R

Y B2

B

T

P

S

T

S

N

A1

A3

B3

V (0-600) V MI

A2

B1

Fuse

415 / (0-470) V 3Ø AUTO TRANSFORMER

A

(0-10) A MI

600V, 10A LPF

600V

C2

C3

C1

R

STATOR

A1

A2

B1 B2

C1

C2

L M

C

M

600V, 10A LPF

C

L

600V

Fuse

Fuse

NL



CIRCUIT DIAGRAM FOR BLOCKED ROTOR TEST ON THREE PHASE SQUIRREL CAGE INDUCTION MOTOR

(Equivalent circuit)

5

9

A1

A3

B3

Fuse

A2

415 / (0-470) V 3Ø AUTO TRANSFORMER

C2

C3

C1

Fuse

Fuse

NL

B1

B2 BRAKE DRUM

S1 S2

R 415V, 50Hz, 3Ø

AC SUPPLY

R

Y

B

T

P

S

T

S

N

V (0-150) V MI

STATOR

A

(0-10) A MI

150V, 10A UPF

L

150V

M

C

M

150V, 10A UPF

C

L

150V

A1

A2

B1 B2

C1

C2



Tabulation for No Load test on three phase Squirrel cage Induction motor

Speed of the Induction motor: Type of the Stator connection: Multiplication Factor:

Tabulation for Blocked rotor test on three phase Squirrel cage Induction motor

Type of the Stator connection: Multiplication Factor:

Short Circuit Power

W1 W2

Short Circuit Current

(ISC)

Short Circuit Voltage (VSC)

Observed Actual Observed Actual

Total Short Circuit Power PSC=(W1+W

2)

Short Circuit Power/Phase

PSC

(Ph)=(P0/3)

Short Circuit Current/Phase

ISC (Ph)

Short Circuit Voltage/Phase

VSC (Ph)

S.No

Amps Volts Watts Watts Watts Watts Watts Watts Amps Volts

No Load Power

W1

W2

No Load Current

(I0)

No Load Voltage

(V0)

Observed Actual Observed Actual

Total No Load Power

P0=(W1+W2) No Load Power/Phase

P0 (Ph)=(P0/3) No Load Current/Phase

I0 (Ph)

No Load Voltage/Phase

V0 (Ph)

S.No

Amps Volts Watts Watts Watts Watts Watts Watts Amps Volts



5. No load reactance (X0) = V0/I0 (ph) Sin φ0 in Ω.

SC Test

6. Motor equivalent Impedance referred to stator (Zsc(ph)) = Vsc(ph) / Isc(ph) in Ω.

7. Motor equivalent Resistance referred to stator (Rsc(ph)) = Psc(ph) / I2sc(ph) in Ω.

8. Motor equivalent Reactance referred to stator (Xsc(ph)) = √(Z sc(ph)2- R sc(ph)

2) in Ω.

9. Rotor Resistance referred to stator (R2’(ph)) = Rsc(ph) – R1 in Ω.

10. Rotor Reactance referred to stator (X2’(ph)) = Xsc(ph) / 2 = X1 in Ω.

Where R1 - stator resistance per phase

X1 – stator reactance per chapter

R1 = R(ac) =1.6 x R(dc)

11. Equivalent load resistance (RL’) = R2’ (1/s – 1) in Ω.

Where Slip (S) = (Ns-Nr) / Ns

Ns – Synchronous speed in rpm.

Nr – Rotor speed in rpm.

PRECAUTION

• The autotransformer should be kept at minimum voltage position

PROCEDURE


• For No-Load or open circuit test by adjusting autotransformer, apply rated voltage and

• Note down the ammeter and wattmeter readings. In this test rotor is free to rotate.

• For short circuit or blocked rotor test by adjusting autotransformer, apply rated current

and note down the voltmeter and wattmeter readings. In this test rotor is blocked.

• After that make the connection to measure the stator resistance as per the circuit diagram.

• By adding the load through the loading rheostat note down the ammeter, voltmeter

reading for various values of load.



Equivalent circuit for three phase squirrel cage induction motor

RESULT

Thus the no load and blocked rotor test on a given three phase squirrel cage induction motor and

the equivalent circuit is drawn.

P

N

1Ø, 230V, 50Hz AC Supply

R2' X2'

RL' =R2' (1/s-1)

R1 X1

X0 R0

I0

Iw I



REGULATION OF THREE PHASE ALTERNATOR BY EMF AND MMF METHODS.

AIM

To predetermine the regulation of a given three phase Alternator by EMF and MMF method and also draw the vector diagrams.

NAME PLATE DETAILS

( '"# " ) "

FUSE RATING

125% of rated current (Full load current) For DC shunt motor:

For Alternator:

APPARATUS REQUIRED

S.NO. NAME OF THE


1. 2. 3. 4. 5. 6. 7. 8.

Ammeter Ammeter Ammeter Voltmeter Voltmeter Rheostat Rheostat

Tachometer

MC MC MI MI MC

Wire Wound Wire Wound

-

(0-2 A) (0-10 A) (0-10 A)

(0-600V) (0-50V)

(500Ω, 1.2A)

(300Ω, 1.7A) -

1 1 1 1 1 2 1 1



CIRCUIT DIAGRAM FOR REGULATION OF THREE PHASE ALTERNATOR BY EMF & MMF METHOD

(Open circuit and Short circuit tests)

T

P

S

T

S

Fuse

V

220V DC SUPPLY

L F A

3 POINT STARTER

D

P

S

T

S

250, 2A

M

F

FF

A

AA

(0-10) A MI (0-600) V

MI

XX X

R

B Y N

A

(0-2) A MC

A

Fuse

Fuse

Fuse

Fuse

Fuse

Fuse

220V DC SUPPLY

D

P

S

T

S

350, 1.5A

79



FORMULAE USED

EMF Method 1. Armature Resistance Ra = 1.6 Rdc in ohms.

Here, Rdc is the resistance in DC supply.

2. Synchronous impedance Zs = (from the graph)

3. Synchronous impedance Xs = (Zs² - Ra²) in ohms.

4. Open circuit voltage Eo= (V cosø + Isc Ra) ² + (V sinø - Isc Xs) ² in Volts.

(For lagging power factor)

5. Open circuit voltage Eo= (V cosø + Isc Ra) ² + (V sinø - Isc Xs) ² in Volts

(For leading power factor)

7. Open circuit voltage Eo= (V + Isc Ra) ² + (Isc Xs) ² in Volts

(For Unity power factor)

6. Percentage regulation =

PRECAUTION

• The motor field rheostat should be kept in the minimum resistance position.

• The Alternator field Potential divider should be in the maximum voltage position.

• Initially all Switches are in open position.

PROCEDURE FOR BOTH EMF AND MMF METHOD

• Connections are made as per the circuit diagram.

• Give the supply by closing the DPST Switch.

• Using the Three Point starter, start the motor to run at the synchronous speed by varying the motor field rheostat.

• Conduct an Open Circuit Test by varying the Potential Divider for various values of Field Current and tabulate the corresponding Open Circuit Voltage readings.

• Conduct a Short Circuit Test by closing the TPST switch and adjust the potential divider to set the rated Armature Current, tabulate the corresponding Field Current.

• Conduct a Stator Resistance Test by giving connection as per the circuit diagram and tabulate the Voltage and Current readings for various resistive loads.

Open circuit voltage (E1 (ph)) Short circuit current (Isc)

Eo –Vrated Vrated X 100 (both for EMF & MMF method)



PROCEDURE TO DRAW THE GRAPH FOR EMF METHOD

• Draw the Open Circuit Characteristics curve (Generated Voltage per phase Vs Field Current).

• Draw the Short Circuit Characteristics curve (Short Circuit Current Vs Field Current).

• From the graph find the open circuit voltage per phase (E1 (Ph)) for the rated Short Circuit Current (Isc).

• By using respective formulae find the Zs, Xs, Eo and percentage Regulation.

PROCEDURE TO DRAW THE GRAPH FOR MMF METHOD

• Draw the Open Circuit Characteristics curve (Generated Voltage per phase Vs Field Current).

• Draw the Short Circuit Characteristics curve (Short Circuit Current Vs Field Current).

• Draw the line OL to represent If' which gives the rated generated voltage (V).

• Draw the line LA at an angle (90 ± ) to represent If'' which gives the rated full load current (Isc) on short circuit ((90 + ) for lagging power factor and (90-) for leading power factor).

• Join the points O and A and find the field current (If) by measuring the distance OA that gives the Open Circuit Voltage (Eo) from the Open Circuit Characteristics.

• Find the percentage Regulation by using suitable formula.

Tabulation for Regulation of three phase Alternator by EMF and MMF methods

Open circuit test

Field Current

(If)

Open Circuit Line Voltage (V0L)

Open Circuit Phase Voltage (V0 (Ph))

S.No.

Amps Volts Volts



Short circuit test

Regulation of three phase Alternator by EMF and MMF methods

Model Graph for EMF Method

Field Current (If)

Short Circuit Current (120 to 150 % of rated current)

(ISC)

S.No.

Amps Amps

OCC

E1 (ph)

Field Current (If ) in Amps

Short

Cir

cuit

Curr

ent

(IS

C)

in A

mps

Open

Cir

cuit

Volt

age

(V0

(P

h))

in V

olt

s

SCC



Regulation of three phase Alternator by EMF and MMF methods

Model Graph for MMF Method

SCC

OCC

E0 (ph)

Lead.

Field Current (If ) in Amps

Short

Cir

cuit

Curr

ent

(IS

C)

in A

mps

Open

Cir

cuit

Volt

age

(V0

(P

h))

in V

olt

s

O L

A

A

A

E0 (ph)

Unity

E0 (ph)

Lag.

Lead. Lag.

Unity

90- 90+



Resultant Tabulation for Regulation of three phase Alternator by EMF and MMF methods

Regulation curve of Alternator (EMF, MMF and Vector diagram)

RESULT

Thus the regulation of three phase alternator by EMF and MMF methods and the regulation curves are drawn.

Percentage of Regulation

EMF Method MMF Method

S.No. Power

Factor Lagging Leading Unity Lagging Leading Unity

1.

0.2

-

-

2.

0.4

-

-

3.

0.6

-

-

4.

0.8

-

-

5.

1.0

Lagging pf

Leading pf

+ %

Reg

ula

tio

n

- %

Reg

ula

tio

n

From EMF method

From MMF method

Unity pf



STABILITY ANALYSIS OF LINEAR SYSTEM

AIM

To analysis the stability of the given linear system using Bode Plot, Nyquist Plot and Root Locus.

APPRATUS REQUIRED


1

2

Computer

MATLAB Software

-

-

-

-

1

1

THEORY

POLAR PLOT

The polar plot of a sinusoidal transfer function ( )G jω on polar coordinates as ω is varied from zero to

infinity. Thus the polar plot is the locus of vectors ( )G jw and ( )G jw as ω is varied from zero to infinity. The

polar plot is also called Nyquist plot.

NYQUIST STABILITY CRITERION

If ( ) ( )G s H s contour in the ( ) ( )G s H s plane corresponding to Nyquist contour in s-plane encircles the

point 1 0j− + in the anti – clockwise direction as many times as the number of right half s-plane of ( ) ( )G s H s .

Then the closed loop system is stable.

ROOT LOCUS

The root locus technique is a powerful tool for adjusting the location of closed loop poles to achieve

the desired system performance by varying one or more system parameters.

The path taken by the roots of the characteristics equation when open loop gain K is varied from 0 to

∞ are called root loci (or the path taken by a root of characteristic equation when open loop gain K is varied

from 0 to ∞ is called root locus.)

FREQUENCY DOMAIN SPECIFICATIONS

The performance and characteristics of a system in frequency domain are measured in term of frequency

domain specifications. The requirements of a system to be designed are usually specified in terms of these

specifications.



The frequency domain specifications are

1. Resonant peakr

M .

2. Resonant Frequencyr

ω .

3. Bandwidth.

4. Cut – off rate

5. Gain margin

6. Phase margin

RESONANT PEAKr

M

The maximum value of the magnitude of closed loop transfer function is called the resonant peakr

M . A large

resonant peak corresponds to a large over shoot in transient response.

RESONANT FREQUENCY r

ω

The bandwidth is the range of frequency for which the system gain is more than 3 dB− . The frequency at

which the gain is 3 dB− , called cut off frequency. Bandwidth is usually defined for closed loop system and it

transmits the signals whose frequencies are less than cut-off frequency. The bandwidth is a measured of the

ability of a feedback system to produce the input signal, noise rejection characteristics and rise time. A large

bandwidth corresponds to a small rise time or fast response.

CUT-OFF RATE

The slope of the log-magnitude curve near the cut off frequency is called cut-off rate. The cut-off rate

indicates the ability of the system to distinguish the signal from noise.

GAIN MARGIN g

K

The gain marging

K is defined as the reciprocal of the magnitude of open loop transfer function at phase cross

over frequency. The frequency at witch the phase of open loop transfer function is 180 is called the phase

cross over frequencypc

ω .

PHASE MARGIN γ

The phase margin γ is that amount of additional phase lag at the gain cross over frequency required to bring

the system to the verge of instability, the gain cross over frequencygc

ω is the frequency at which the

magnitude of open loop transfer function is unity (or it is the frequency at which the db magnitude is zero).



PROCEDURE

• Enter the command window of the MATLAB.

• Create a new M – file by selecting File – New – M – File.

• Type and save the program.

• Execute the program by either pressing F5 or Debug – Run.

• View the results.

• Analysis the stability of the system for various values of gain.

PROBLEM

Obtain the Bode Plot, Nyquist Plot and Root Locus of the given open loop T.F is 2

3

2( )

2H s

s s+=

+

Using Bode Plot

num = [0 0 2] den = [1 3 2] bode (num,den) grid title (‘BODE DIAGRAM’) % To Find out Gain Margin

sys = tf (num, den) bode (sys) Margin (sys) [ gm, ph, wpc, wgc ] = margin (sys).

Using Nyquist Plot

num = [0 0 2] den = [1 3 2] nyquist (num,den) grid title (‘Nyquist Plot’)

Using Nyquist Plot

num = [0 0 2] den = [1 3 2] rlocus (num,den) grid title (‘Root Locus Plot’)

RESULT

Thus the stability of the given linear system using Bode Plot, Nyquist Plot and Root Locus was

analyzed.



DIGITAL SIMULATION OF LINEAR SYSTEM

AIM

To simulate the time response characteristics of second order linear system using

MATLAB.

APPRATUS REQUIRED


1

2

Personal Computer

MATLAB Software

-

-

-

-

1

1

THEORY

The desired performance characteristics of control system are specified in terms of time

domain specification. Systems with energy storage elements cannot respond instantaneously and

will exhibit transient responses, whenever they are subjected to inputs or disturbances.

The desired performance characteristics of a system pf any order may be specified in

terms of the transient response to a unit step input signal.

The transient response of a system to unit step input depends on the initial conditions.

Therefore to compare the time response of various systems it is necessary to start with standard

initial conditions. The most practical standard is to start with the system at rest and output and

all time derivatives there of zero. The transient response of a practical control system often

exhibits damped oscillations before reaching steady state.

The transient response characteristics of a control system to a unit step input are

specified in terms of the following time domain specifications.

1. Delay time d

t

2. Rise time r

t

3. Peak time p

t

4. Maximum overshoot p

M

5. Settling time s

t

1. Delay Time

It is the taken for response to reach 50% of the final value, for the very first time.



2. Rise Time

It is the time taken for response to raise from 0 to 100% for the very first time. For under

damped system, the rise time is calculated from 0 to 100%. But for over damped system it is the

time taken by the response to raise from 10% to 90%. For critically damped system, it is the

time taken for response to raise from 5% to 95%.

Rise time r d

tπ θω−

=

Where, 211

tanξξ

θ

−− =

and

Damped frequency of oscillation 21ndξω ω −=

3. Peak Time

It is the time taken for the response to reach the peak value for the very first time. (or) It is the

taken for the response to reach the peak overshoot p

t .

Rise time p d

tπ

ω=

4. Peak Overshoot (Mp)

It is defined as the ration of the maximum peak value measured from final value to the final

value.

Let final value ( )c e=

Maximum vale ( )c tp

=

Peak Overshoot, p

M

( ) ( )

( )

c t c ep

c e

−=

21% 100M e

p

πξ

ξ

−

−= ×

5. Settling Time

It is defined as the time taken by the response to reach and stay within a specified error. It is

usually expressed as % of final value. The usual tolerable error is 2% or 5% of the final value.

Settling Time 4

s nt

ξω= (For 2% error).

Settling Time 3

s nt

ξω= (For 5% error).



PROCEDURE

• Enter the command window of the MATLAB.

• Create a new M – file by selecting File – New – M – File.

• Type and save the program.

• Execute the program by either pressing F5 or Debug – Run.

• View the results.

• Analysis the time domain specifications of the system.

PROBLEM

Obtain the time domain specifications of the given open loop T.F is 2

2

100( )

100H s

s s+=

+

MATLAB PROGRAM FOR UNIT IMPULSE PRSPONSE

num = [ 0 0 100 ]

den = [ 1 2 100 ]

impulse (num, den)

grid

title (‘ unit impulse response plot’)

MATLAB PROGRAM FOR UNIT STEP PRSPONSE

num = [ 0 0 100 ]

den = [ 1 2 100 ]

step (num, den)

grid on

title (‘unit step response plot’)

RESULT

Thus the time response characteristic of second order linear system was verified using

MATLAB.



DESIGN OF P, PI, PID CONTROLLER

AIM

To design P, PI, and PID controllers for first order systems using MATLAB.

APPARATUS REQUIRED

1. Controller and system kit.

2. Patch chords.

3. Computer and Interference chord.

THEORY

Proportional Controller

1. The Proportional Controller is a device that produces the control signal, u (t) which is

Proportional to the input error signal e (t).

In P – controller, u (t) e (t).

Therefore u (t) = Kp c (t).

Where Kp – Proportional gain or constant.

2. The Proportional plus Integral Controller (PI – Controller) produces an output signal

consisting of two terms one on proportional to error signal and the other proportional to

the integral of error signal

In PI – Controller, u (t) [e (t) + | e (t) dt]

Therefore, u (t) = e (t) + Kp / Ti | e (t) dt

Where Kp – Proportional gain or constant,

Ti – Integral Time.

3. The PID Controller produces an output signal consisting of three terms one on

proportional to error signal and the another one proportional to the integral of error

signal and the third one is proportional to derivative of error signal.

In PID Controller, u (t) [e (t) + | e (t) + d /dt ((e (t))]

Therefore, u (t) = e (t) + Kp / Ti | e (t) dt + Kp Td d /dt ((e(t))]

Where Kp – Proportional gain or constant,

Ti – Integral Time.

Td – Derivative Time.


Type 0 First Order System with P – Controller

Computer CH 0 Computer CH 1

Step Input

(FG)

P Controller

Level Shifter

Level Shifter


Type 0 First Order System with PI - Controller


Step Input

(FG)

PI Controller

Level Shifter

Level Shifter


Type 0 First Order System with PID - Controller


Step Input

(FG)

PID Controller

Level Shifter

Level Shifter



Procedure

Type – 0 First Order System with P – Controller

1. Connections are given as per the circuit diagram.

2. Set Proportional Band = 80, Integral Time = 64000 and Derivative Time = 0.

3. Measure the performance specifications.

Type – 0 First Order System with PI – Controller


2. Set Proportional Band = 80, Integral Time = 30 and Derivative Time = 0.


Type – 0 First Order System with PI – Controller


2. Set Proportional Band = 80, Integral Time = 30 and Derivative Time = 0.1.


Transfer Function for P, PI, and PID Controller:

P – Controller: Transfer Function = Kp

PI – Controller: Transfer Function = Kp [1 + 1 / Ti S]

PID Controller: Transfer Function = Kp [1 + 1 / Ti S + Td S]

TABULAR COLUMN

S. No Time Domain Specification P controller PI controller PID controller



Model Graph

RESULT

Thus the design of P, PI and PID controller was done.



DESIGN OF LAG AND LEAD COMPENSATOR

AIM

To design and implement the suitable lag and lead compensator for a given linear system

to improve the performance.

APPARATUS REQUIRED

1. Transfer function and compensator

2. Computer interface chord

3. Patch chords

THEORY

LAG COMPENSATOR

A compensator having the characteristics of a Lag network is called a lag

compensator. If a sinusoidal signal is applied to a lag network, then in steady state the output

will have a phase lag with respect to input.

Lag compensation results in a large improvement in steady state performance but

results in slower response due to reduced bandwidth. The attenuation due to the lag compensator

will shift the gain cross over frequency to a lower frequency point where the phase margin is

acceptable.

The general form of lag compensator transfer function is given by:

G(S) = (S+T) / (S+P) = (S + 1/T) / S + 1/BT Where, T > 0 and B >1

LEAD COMPENSATOR

A compensator having the characteristics of a Lead network is called a Lead

compensator. If a sinusoidal signal is applied to the lead network, then in steady state the output

will have a phase lead with respect to input.

Lead compensation increases the bandwidth, which improves the speed of

response and also reduces, whereas there is a small change in steady state accuracy. Generally,

Lead compensation is provided to make an unstable system as a stable system.

A Lead compensator is basically a high pass filter so it attenuates high frequency

noise effects. If the pole introduced by the compensator is not cancelled by a zero in the system,

then lead compensation increases the order of the system by one.

The general form of Lead compensator transfer function is given by:

G(S) = (S+T) / (S+P) = (S + 1/T) / S + 1/aT Where, T > 0 and a<1

PROCEDURE



Type II Order System Performance

Without Lag Compensator


2. Switch on the power supply.

3. Apply step input.

4. Set Pb = 100%

5. Measure the time domain specification of the II order system from the waveform.

With Lag Compensator




4. Set Pb = 100%

5. Measure the time domain specification of the II order system from the waveform.

6. Compare the performance with and without lag compensator.

TABULAR COLUMN

S. No Time Domain Specification Without Lag With Lag

PROCEDURE



Type II Order System Performance

Without Lead Compensator




4. Set Pb = 100%.

5. Measure the time domain specification of the I order system from the waveform.

With Lead Compensator




4. Set Pb = 100%

5. Measure the time domain specification of the I order system from the waveform.

6. Compare the performance with and without Lead compensator.

TABULAR COLUMN

S. No Time Domain Specification Without Lead With Lead



Model Graph (Lead Compensator)

Model Graph (Lead Compensator)

RESULT: Thus the lag and lead compensator of the given system is implemented and the

performance was compared.



TRANSFER FUNCTION OF SEPARATELY EXCITED

DC SHUNT GENERATOR

AIM

To determine the transfer function of the given Separately Excited DC Shunt generator.

NAME PLATE DETAILS

FUSE RATING

Motor: 125% of full load current (rated current)

Generator: 125% of full load current (rated current)

APPARATUS REQUIRED


1

2

3

4

5

6

7

8

Ammeter

Ammeter

Ammeter

Voltmeter

Voltmeter

Rheostat

Rheostat

Single Phase Variac

MC

MC

MI

MC

MI

Wire wound

Wire wound

-

(0-10A)

(0-2A)

(0-300mA)

(0-300V)

(0-300V)

250, 2A

350, 1.5A

230V/ (0-270V)

1

1

1

1

1

1

1

1



FORMULAE

1.Generated EMF Constant (Kg) = Eg / If in Volts / Amps (From the Graphs)

2. Field Resistance (Rf) = Vf / If

3. Effective Resistance (Reff) = VL/ IL in Volts / Amps (From the Graphs)

Where, VL = Change in load voltage in volts

IL = Change in load current in amps

4. Load Resistance (RL) = PL / IL 2

Where, RL = Load Resistance in Ohms

PL = Power of Load in Watts

IL = Total Load current in Amps

5. Field Inductance Lf

Where, Xf= (Zf2 –Rf

2)

Xf= 2f Lf

Lf= Xf / 2f

f = frequency of applied source in hertz

6.Transfer function

Eg(s) Ef(s) = (No Load)

Vt (s) / Ef(s) = (Load)

PRECAUTION

1. The motor field rheostat should be kept at minimum resistance position.

2. The motor armature rheostat should be kept at maximum resistance position.

3. At the time of starting, the motor should be in no load condition.

(Kg / Rf )

(1+ (Lf / Rf) S) (1+ (Reff / RL))

(Kg / Rf )

(1+ (Lf/Rf) S)



PROCEDURE

To find out Generated EMF Constant (Kg)


2. The motor is made to run at the rated speed.

3. The generated emf is noted for various values of field current.

4. The voltage across the field winding is also measured

5. From the OCC curve Back Emf constant is calculated.

To find out Field Impedance (Zf)


2. Using single phase variac the supply voltage is varied.

3. The corresponding reading of field current is noted for different values of applied voltage.

4. From the noted readings the field Impedance is calculated.

RESULT

Thus the transfer function of separately excited DC shunt generator is determined.



TRANSFER FUNCTION OF ARMATURE AND FIELD CONTROLLED DC SHUNT MOTOR

AIM

To determine the transfer function of the given armature and field controlled DC shunt motor.

NAME PLATE DETAILS

FUSE RATING:


APPRATUS REQUIRED


1

2

3

4

5

6

7

8

9

10

11

Ammeter

Ammeter

Ammeter

Voltmeter

Voltmeter

Voltmeter

Rheostat

Rheostat

Rheostat

Tachometer

Single Phase Variac

MC

MC

MI

MC

MC

MI

Wire wound

Wire wound

Loading

Digital

-

(0-15A)

(0-2A)

(0-10A)

(0-300V)

(0-50V)

(0-300V)

250, 2A

50, 5A

10A, 230V

-

230V / (0-270V)

1

1

1

1

1

1

1

1

1

1



FORMULAE

1. Inertia Constant (J) =(Vav * Iav) / (Nav * N)×(60/2) 2 ×((t1* t2) /(t1-t2)) Kg-m2

Where, Vav (V1+V2) / 2

Iav (I1+I2) / 2

Nav (N1+N2) / 2

N Small Change in Speed (i.e) N1~N2

t1Time for fall of speed from 1500 rpm to 750 rpm in no load condition

in seconds.

t2 Time for fall of speed from 1500rpm to 750rpm in load condition in

Seconds

2. Viscous Friction Co-Efficient (f) =(2 /60) 2 ×(J /2) ×(N12~N2

2) in N-m / rad /Sec

Where, J Inertia Constant in Kg-m2

Angular displacement in rad / Sec

= (2 Nav /60)

3. Back EMF Constant (Kb) =(Va-IaRa) / (2 N/60) in N-m / Amps

4. Torque T = (S1~S2) × (R+ t/2) × 9.81 in N-m.

Where, R- Radius of the Break drum in m.

t- Thickness of the Belt in m.

S1, S2- Spring balance reading in Kg.

5. Motor Gain Constant (Km) = KT / (Ra × f )

Where KT = KT' × (Current through the Armature / Rated Current of the Motor)

KT'= T / Ia (From the Graphs)

6. Motor Time Constant (a) = La / Ra.

Where, Xa= (Za2 -Ra

2)

Xa= 2f La

La= Xa / 2f

7. Transfer function Q(s) / E(s) =

[KT / (Ra × f )]

S [1+ (La/Ra) S] [1+ (J/f) S]+ [KT Kb /(Ra × f)]



THEORY

Ra = Armature resistance in ohms.

La= Armature inductance of the winding in Henry.

Ia= Armature current in Amps.

If = Field current in Amps

E= Applied voltage in Volts.

Eb=Backemf in Volts.

Tm =Torque developed by the motor in N-m

=Angular displacement of motor shaft in radian.

J= Equivalent of moment of inertia of motor and load referred to motor shaft in kg-m2

f=Equivalent viscous friction coefficient of motor and load referred to motor shaft in N-m / rad / Sec.

Air gap flux is proportional to the field current because the DC motor should operate in linear magnetization curve for servo application.

(i.e) If Kf If Where, Kf is the Proportionality constant

The torque developed by the motor is proportional to the product of armature current and air gap flux.

(i.e) Tm Ia

Ia Kf If

= K1 Ia Kf If

We know that If is constant for armature controlled motor.

(i.e) Tm = (K1 Kf If ) Ia

Tm = KT Ia Where, KT is the motor torque constant

Back emf of the emf of motor is proportional to the speed.

(i.e) Eb d ()/ dt



Eb = Kb d ()/ dt ------------------------- 1 Where, Kb is the back emf constant in volt / rad /sec

Loop equation of armature circuit

Va = La d (Ia)/dt +RaIa+Eb ------------------ 2

Torque equation is

J d2/dt2 +f d/dt = Tm

= KT Ia --------------3

Taking Laplace transform of Equations 1,2, & 3

From Eq (1) Eb(s) = Kb S (s)------------ 4

From Eq (2) La S Ia(s) +Ra Ia(s) = V(s) - Eb(s)

(La S +Ra) Ia (s) = (V(s) - Kb S (s))

Ia (s) = (V(s) - Kb S (s) / (La S +Ra)

From Eq (3) J S2 (s) +f S (s) = Tm(s)

(J S2 +f S) (s) = Tm(s) = KT× Ia (s)

(J S2 +f S) (s) = KT× Ia (s)

(J S2 +f S) (s) = KT× (E(s) - Kb S (s) / (La S +Ra)

(JS2 +f S) (s) = KT E(s) - KTKb S (s)

(La S +Ra) (La S +Ra)

(JS2 +f S) (s) + KT Kb S (s) = KT E(s)




(JS2 +f S) (La S +Ra) + KT Kb S (s) = KT E(s)


(s) = KT

E(s) (JS2 +f S) (La S +Ra) + KT Kb S

(s) = KT

E(s) S (JS +f ) (La S +Ra) + KT Kb

(s) = KT

E(s) S f Ra (1+(J/f) S) (1+(La/ Ra )S ) + KT Kb

(s) = KT / f Ra

E(s) S (1+(J/f) S) (1+(La/ Ra) S) + KT Kb/ f Ra

PRECAUTION

1. The motor field rheostat should be kept at minimum resistance position.

2. The motor armature rheostat should be kept at maximum resistance position.

3. At the time of starting, the motor should be in no load condition.

PROCEDURE

To find out Inertia Constant (J)


2. The DC supply is given by closing the DPST switch.

3. The DPDT switch is thrown into position 1,2.

4. The motor is made to run at the rated speed by adjusting the field rheostat.

5. The DPDT switch is brought to the original position 0,0’. The time taken for falling of

speed from 1500 to 750 rpm is noted.

6. Once again the DPDT switch is thrown into position 1,2. Then the motor is made to run at

the rated speed

7. Then the DPDT switch is changed into position 1’, 2’.

8. Then J and f is calculated by using the formula.



To find out Torque Constant (KT)



3. The field current is kept constant.


5. The various values of Ia spring balance readings are noted

6. Torque is calculated and plotted from the graph by adjusting the slope, torque constant KT is determined.

To find out Back Emf Constant (Kb)

1.Connections are given as per the circuit diagram.


3. At rated speed the supply voltage and armature value readings are noted.

4. The Back Emf constant is calculated.

To find out Armature resistance (Ra)



3. By adjusting the loading rheostat the various values of Ia and Va are noted.

4. The armature resistance is calculated by the application of formula.

To find out Armature inductance (La)


2. Using single phase variac the supply voltage is varied.

3. The corresponding reading of Ia are noted for different values of applied voltage

4. Then Za and La are calculated by using the formula.

RESULT

Thus the transfer function of the given armature and field controlled DC shunt motor is determined.

Documents

51355420 Lab Manual for e e Cs