REFERENCE MANUAL EE0311 MEASUREMENTS & CONTROL …webstor.srmist.edu.in/web_assets/srm_mainsite/files/files/Measurement... · 6 Calibration of single phase energy meter direct loading

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EE0311-Measurements & Control System Lab 1

REFERENCE MANUAL

EE0311 – MEASUREMENTS & CONTROL SYSTEMS LAB

DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING FACULTY OF ENGINEERING & TECHNOLOGY

SRM UNIVERSITY, Kattankulathur – 603 203

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LIST OF EXPERIMENTS

Sl.No. Name of the Experiments Page No.

1 Measurements of Inductance using Maxwell’s bridge

2 Measurements of Inductance using Anderson’s bridge

3 Measurements of capacitance Schering’s bridge

4 Measurements of resistance using whetstone bridge

5 Measurements of resistance using Kelvin’s bridge

6 Calibration of single phase energy meter direct loading

7 Calibration of single energy meter Phantom loading

8 Calibration of three phase energy meter direct loading

9 Measurements of power factors

10 Study of synchro transmitter & receiver pair

11 Speed torque characteristics AC servo motor

12 Transfer function field controlled DC motor

13 Design and implementation of Lag, Lead compensator

14 Transfer function of armature controlled DC motor

15 Digital simulation of the above controller using MATLAB

software

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Exp. No.1

MAXWELL’S CAPACITANCE BRIDGE

Aim

To measure the

i) Inductance of a coil

ii) Q factor of the coil using Maxwell’s bridge

Apparatus Required

Sl.No. Apparatus Range Quantity

1 Maxwell’s bridge kit -- 1

2 Inductive coil -- 1

3 Headphone -- 1

Theory

In this bridge, an inductance is measured by comparison with a standard variable

capacitance

Under balanced condition

32

44

411

1)( RR

RCj

RLjR

R1R4 + j L1R4 = R2R3 + j R2R3C4R4

Separating the real and imaginary parts,

R1 = 4

32

R

RR

and L1 = R2R3C4

The expression for Q factor of the coil is, Q = L1 / R1 = C4R4

Formula Used

L1 = Unknown inductance – Henry

R2 = Non inductive resistance – ohms

Rm = Multiplier resistance – ohms

C1 = 0.1F

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Procedure

Connection to be made as per the circuit diagram

The balance condition is obtained by adjusting capacitance in the bridge

The balanced condition is checked with a help of headphone

All the values in the bridge are noted down

MAXWELL’S BRIDGE

L1 – Unknown inductance

R1 – Effective resistance of inductor,

C4 – Variable standard capacitor

R2, R3, R4 – Known non-inductive resistance

Phasor Diagram

E3 = E4 = I1 R3 = I4 R4 = IC / C4

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Tabulation

Maxwell’s bridge method

Sr.

No.

Given Inductance

‘L’

Capacitance

‘C’

Resistance

‘Rm’

Resistance

R2’

L = PRC

Unit Henry F K K mH

1 600 0.6 1000 1000 600

2 520 0.5 1000 1000 500

3 550 0.6 1000 1000 600

Model calculation

P = 1000

R = 1000

C = 0.655 x 10-6

F

L = PRC

= 1000 1000 0.6 10-6

= 0.6

= 600 mH

Result

Thus the inductance of the given coil is found by Maxwell’s bridge

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ANDERSON’S BRIDGE

Aim

To determine the self inductance of the given coil by Anderson bridge.

Apparatus Required


1 Anderson bridge kit -- 1

2 Oscillator -- 1

3 Known Inductive box -- 1

4 Head phone -- 1

5 Patch card -- 6

Theory

It is modification of the Maxwell’s inductance – Capacitance Bridge. In this method, the

self-inductance is measured in terms of a standard capacitor. This method at balance/

I1 = I3 and I2 = IC + I4

I1R3 = IC x 1 / jC

IC = I1jCR3

Writing other balance equations,

I1(r1+R1+jL1) = I2R2+ICr

and IC (r + 1/jC) = (I2-IC) R4

Substituting the value of IC in the above equations and by equating real and imaginary parts,

R1 = 1

4

32 rR

RR

And L1 = ))(( 4224

4

3 RRRRrR

RC

Formula Used

R1 = (R2R3/R4) – r1

L1 = (C R3/R4)[r (R4+R2)+R2R4]

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ANDERSON’S BRIDGE

Phasor Diagram

Procedure

Connection to be made as per the circuit diagram.

With a particular value of ‘C’ the balanced condition is obtained by adjusting the

value of resistance.

All the values in the bridge are noted down

Repeat it with different values of ‘C’ and calculate every time the value of ‘L’.

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Tabulation

Sr.

No.

Given Inductance

‘L’

Capacitance

‘C’

Resistance

‘Rm’

Resistance

R2’

L =

(RQ+m(S+R)

Unit Henry F K K mH

1 68 0.05 1060 6500 71

2 45 0.05 1010 4050 45.7

Model calculation

P = 1000

R = 1000

Q = 1000

L = C [PQ = [R+S] m)

L = 5 106 [1000 1000 + (1000 +1060) 6500]

= 71.95 103

= 71 mH

Model Calculation

R = 1000, Q = 1000 Q

L = C [RQ + (R+S) M)

= 0.005 10-6 [1000 1000 + (1000+1060) 6500]

= 71.95

= 71 MH

Result

Thus the values of inductance and resistance are measured by Anderson’s bridge.

Resistance of the coil =

Inductance of the coil =

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SCHERING’S BRIDGE

Aim

To determine the (a) unknown capacitance and resistive loss in the capacitor and (b)

dissipation factor of the capacitor.

Apparatus Required


1 Schering’s bridge kit - 1

2 Oscillator - 1

3 Standard capacitance - 1

4 Headphone - 1

5 Unknown capacitance - 1

6 Patch card - 6

Theory

Schering bridge is widely used for capacitance and dissipation factor measurement. It is

extensively used in the measurement of capacitance.

At balance,

(r1 + 1 / jCx) (R4 / (1 + jC4R4) = 1 / j C2 x R3

r1 R4 – jR4 / Cx = -jR3 / C2 + R3R4C4 / C2

Equating the real and imaginary parts,

R1 = R3C4 / C2

Cx = C2 (R4 / R3)

Dissipation factor, D1 = Tan = C1r1

C4 R4

Formula Used

Cx = C2 (R4 / R3)

Where, C2 = Standard capacitor

R3, R4 = Non-inductive resistance

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SCHERING’S BRIDGE

Cx – Unknown capacitance

C4 – variable Capacitor

R3, R4 – Non inductive resistance

Phasor Diagram

Procedure

The trainer is switched ‘ON’ and the unknown capacitance is connected in the

terminals Cx.

Initially the resistance R3 is kept some value and by varying the value of resistance R4

the balanced condition is obtained.

The balanced condition is checked with the help of head phone.

All the values are noted down.

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Tabulation

Sr.

No.

R3 (1) C2 R4 (2) Cx

Obs Value

Set Value

Unit K F F F

1 100 0.05 800 0.4 0.4

2 10 0.05 80 0.4 0.4

3 100 0.05 600 0.3 0.3

4 10 0.05 60 0.3 0.3

Model calculation

R4 = 40 20 = 800

R3 = 100

C2 = 0.05F

C1 = 3

42

R

RC

cx = c2 (R4/R3)

= 0.4 F

Result

The value of unknown capacitance is found out using Schering’s bridge

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MEASUREMENT OF RESISTANCE USING WHEATSTONE BRIDGE

Aim

To measure the given medium resistance using Wheatstone bridge.

Apparatus Required


1 Wheatstone bridge kit -- 1

2 Unknown resistance -- 1

3 Galvanometer -- 1

4 Patch card -- 6

Theory

It is used for the measurement of medium resistances. Very high degrees of accuracy can

be achieved with the Wheatstone bridge. It has four resistive arms, consisting of resistances R1,

R2, R3 and R4 together with a battery source and a null detector usually a galvanometer or other

sensitive current meter. The current through the galvanometer depends on the potential

difference between points C and D. The bridge is said to be balanced when there is no current

through the galvanometer or when the potential difference across the galvanometer is zero.

For bridge balance we can write,

I1 R1 = I2 R2 (1)

For galvanometer current to be zero, the following conditions also exist:

41

31RR

EII

(2)

And 32

42RR

EII

(3)

Combining the above three equations

321

2

41

1

RR

R

RR

R

R2 R4 = R1R3

From which,

2

31

4R

RRR

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Formula Used

Unknown resistance 2

31

R

RRRx

Where 2

3

R

R= ratio arm.

Procedure

The unknown resistance is connected to the kit. Ratio arm is set to some value.

By adjusting the resistance R1 the galvanometer is made to indicate null position or

zero, indicating balanced condition.

The values of resistance are noted using multimeter.

The unknown resistance is calculated from these values.

WHEASTONE BRIDGE METHOD

Tabulation

Sr.No. Value marked R2 Rm Unknown

resistance Rx

Unit

1 1000 1000 1000 1000

2 2000 1000 1000 2200

3 3100 1000 1000 3300

4 3400 1000 1000 3700

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Model calculation

R = (P/Q) S

P = 1000

Q = 1000

(i) S = 1000

S = 1000

1000x 1000 = 1000

(ii) S = 2000

R = 1000

1000 x 2000 = 2000

(iii) S = 3000

R = 1000

1000x 3000 = 3000

Result

Thus the value of the medium resistance is measured using Wheatstone bridge.

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KELVIN’S DOUBLE BRIDGE

Aim

To measure unknown value of low resistance by balancing the Kelvin’s double bridge.

Apparatus Required


1 Kelvin’s double bridge -- 1

2 Galvanometer -- 1

3 Patch cards -- 3

4 Unknown resistance -- 1

Theory

It is a modification of Wheatstone bridge. In the figure P and Q are the first set of ratio

arms. P and Q are the second set of ratio arms and is used to connect the galvanometer to a point

d at the appropriate potential between points m and n to eliminate the effect of connecting lead of

resistance r between the resistance Rx and the standard resistance S. The ratio p/q is made equal

to P/Q. Under balanced conditions there is no current through the galvanometer.

Eab = Eand

Eab = acEQP

P

and

)(

)(

rqp

rqpSIRE xac

And

)( rqp

prIRE xand

When Eab = Eand

q

p

Q

P

rqp

qr

Q

SRRx

If P/Q = p/q, then Q

SPRx

.

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Formula Used

Unknown resistane of Kelvin’s double bridge

R = PS / Q in ohms

Procedure

The trainer is energized and the power supply +5V is checked

A Galvanometer is connected externally to the trainer.

The unknown resistance ‘R’ is connected in the trainer.

The value of P/Q = p/q = 0.1 ratio

The value of S is adjusted for proper balance and the value of ‘S’ is noted and R is

calculated from the formula

Unknown resistance = R = PS / Q in

Tabulation

Sr.

No.

P Q S Measured

value

R=P S/Q

Set value Rx

Unit K K Ohms Ohms

1 1 1 10 10 10

2 1 1 10 90 100

P, Q : First set of ratio arm

p , q : Second set of ratio arm

Rx : Unknown resistance

S : Standard resistance

R : Resistance of connecting lead

G : Galvanometer

E : Internal Battery

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KELVIN’S DOUBLE BRIDGE

Model Calculation

ohmsX

Q

PXSR 10

1000

101000

Result

The unknown value of resistance is found out using Kelvin’s bridge.

R = 10 ohms

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CALIBRATION OF ENERGY METER ; 1-PHASE

Aim

To calibrate a single phase energy meter by

(i) Direct loading

Apparatus Required


1 Wattmeter 230V, 5A UPF 1

2 Energy meter

3 Voltmeter 0-230V 1

4 Ammeter 0-10A 1

5 Resistive load 10 A 1

Precautions

At the time of switching on the supply, no load must be included

DPST switch is kept open at the time of starting

Procedure

Connection are made as the circuit diagram

By observing the precaution, both the current coils and the pressure coil are supplied

with the rated voltage – in this case 230V.

Now the load is applied gradually till the rated current

All the meter reading are noted down.

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DIRECT LOADING

Direct Load & Phantom Loading

Sr.No. Voltmeter

Reading

V

Ammeter

Reading

I

Wattmeter

M.F 4

Revolution

N

Time Taken

Sec / T

1 220 2 100 2 29

2 220 3.8 200 2 14

3 220 5.7 400 2 9

4 220 7.5 500 2 7

True Energy

ET

Energy Recorded by the EM

EM

Percentage Error

3.22 3.33 3.416

3.11 3.33 7.07

3.0 3.33 11

3.11 3.33 7.07

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Calculation

Power measured by wattmeter is P = Wattmeter read x multiplication fator

True Energy, ET = P x t . . . . wh

Energy recorded by the energy mete is

EM = energy meter constant x N . . . . . .Wh

Percentage Error = (EM – ET) x 100%

Result

Thus the single phase energy meter was calibrated by Direct Load

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CALIBRATION OF ENERGYMETER : 3-PHASE

Aim

To calibrate the given 3-phase energymeter with a standard wattmeter using direct

loading.

Apparatus Required


1 Ammeter 0-10A MI 1

2 Voltmeter 0-600V MI 1

3 Wattmeter 600V, 10A UPF 1

4 Energy meter

Precautions

At the time of switching on the supply, no load must be included.


At the time of switching on the supply, the variac must be in the minimum potential

position.

Procedure

TPST is closed and supply is given

Variac is adjusted to apply rated voltage to energy meter

Load is gradually applied and the number of revolutions of energy meter, disc and

meter readings are taken.

The graph is drawn for energy recorded Vs % error.

Theory

Calibration of all instruments is important once it affords the opportunity to check the

instrument against a known standard and to find error and accuracy. Polyphase or 3-phase

energymeters in a ‘n’ conductors system requires (n-1) measuring elements for measurement of

total energy. Thus a 3-phase 4 wire system requires a 3 element energy system. Polyphase

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energymeters may be multidisc type each element divides a separate disc. In the single disc type

meter all elements drive the same disc.

Circuit Diagram

Tabular Column

V

(v)

I

(A)

MF

1

Time for 1

revolution

Wattmeter x Time

Readings (kw-sec)

420 2 900 1 31

420 3.8 1600 1 14

420 5.8 2200 1 8

True Energy Energy Meter

(Em)

% error

7.75 4.16 -46%

6.72 4.16 -33%

5.88 4.16 -29%

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Calculation

Power measured by wattmeter is P = wattmeter read x multiplication factor

True Energy, ET = P x t . . . . wh

Energy recorded by the energy mete is

EM = energy meter constant x N . . . . . .Wh

Percentage Error = (EM – ET) x 100%

Result

Hence given 3-phase energy meter was calibrated.

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MEASUREMENT OF POWER FACTOR USING POWR FACTOR METER

Aim

To measure the power factor of the given circuit power factor meter.

Apparatus Required

1-phase power factor meter

Precautions

At the time of switching on the supply, no load must be included


Procedure

Connections are made as per the circuit diagram

By observing the precaution load is applied till the rated current

The value of voltage, current and power factor are noted down

Experiment is done for both inductive and capacitive loads.

Circuit Diagram

POWER FACTOR METER

INDUCTIVE LOAD

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Tabular Column

Inductive Load

Voltage

(V)

Current

(A)

Power Factor

(Lagging)

228 1.1 0.95

228 1.25 0.93

228 1.4 0.97

228 1.5 0.85

228 1.6 0.82

CAPACITIVE LOAD

Capacitive Load

Voltage

(V)

Current

(A)

Power Factor

(Lagging)

230 0.25 0.74

230 0.5 0.85

230 0.6 0.93

230 0.75 95

230 0.85 0.97

230 0.95 0.98

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SYNCHRO TRANSMITTER & RECEIVER PAIR

A synchro is an electromagnetic transducer commonly used to convert an angular

position of a shaft into an electric signal.

The basic synchro is usually called a synchro transmitter. Its construction is similar to

that of a three phase alternator. The stator (stationary member) is of laminated silicon steel and

is slotted to accommodate a balanced three phase winding which is usually of concentric coil

type (Three identical coils are placed n the stator with their axis 120 degree apart) and is Y

connected. The rotor is a dumb bell construction and wound with a concentric coil. An AC

voltage is applied to the rotor winding through slip rings. Ref. Fig. No.1A.

Let an AC voltage Vr (t) = Vr sin Wct … (1) be supplied to the rotor of the synchro

transmitter. Thisvoltage causes a flow of magnetizing current in the rotor coil which produces a

sinusoidally time varying flux directed along its axis and distributed nearly sinusoidal, in the air

gap along stator periphery. Because of transformer action, voltages are induced in each of the

stator coils. As the air gap flux is sinusoidally distributed, the flux linking any stator coil is

proportional to the cosine of the angle between rotor and stator coil axis and so is the voltage

induced in each stator coil.

The stator coil voltages are of course in time phase with each other. Thus we see that the

synchro transmitter (TX) acts like single phase transformer in which rotor coil is the primary and

the stator coils form three secondaries.

Let Vs1 N, Vs2 N and Vs3 respectively be the voltages induced in the stator coils S1, S2

and S3 with respect to the neutral. Then for the rotor position of the synchro transistor shown in

fig.No.1 where the rotor axis makes an angle 0 with the axis of the stator coil S2.

Let Vs1N = KVr sin Wct cos (0+120) (2)

Vs2N = KVr sin Wct cos (0) (3)

Vs3N = KVr sin Wct cos (0+240) (4)

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The three terminal voltages of the stator are

Vs1s2 = Vs1N – Vs2N

= 3 KVr sin (0=240) sin Wct (5)

Vs2S3 = Vs2N – Vs3N

= 3 KVr sin (0+120) sin Wct (6)

= 3 KVr sin (0) sin Wct (7)

When 0 is zero from equation (2) and (3) it is seen that maximum voltage is induced in the stator

coil s2 while it follows from equation (7) that the terminal voltage Vs3s1 is zero. This position

of rotor is defined as the electrical zero of the Tx and is used as a reference for specifying the

angular position of the rotor.

Thus it is seen that the input to the synchro transmitter is the angular position of its rotor

shaft and the output is a set of three single phase voltages given by equation (5), (6) and (7). The

magnitudes of these voltage are functions of a shaft position.

The classical synchro systems consists of two units.

1. Synchro transmitter (Tx)

2. Synchro rceiver (Tr)

The synchro receiver is having almost the same constructional features. The two units

are connected as shown in figure No.2. Initially the winding S2 of te stator of transmitter is

positioned for maximum coupling with rotor winding. Suppose its voltage is V. The coupling

between S1 and S2 of the stator and primary (Rotor) winding is a cosine function. Therefore the

effective voltages in these winding are proportional to cos 60 degrees or they are V/2 each. So

long as the rotors of the transmitters and receivers remain in this position, no current will flow

between windings because of voltage balance.

When the rotor of Tx is moved to a new position, the voltage balance is disturbed.

Assume that the rotor of Tx is moved through 30 degrees, the stator winding voltages will be

changed to zero, 0.866V and 0.866V respectively. Thus there is a voltage imbalance between

the windings causes currents to 1 flow through the close circuit producing torque that tends to

rotate the rotor of the receiver to a new position where the voltage balance is again restored.

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This balance is restored only if the receiver turns through the same angle as the transmitter and

also the direction of the rotation is the same as that of Tx.

The Tx Tr pair thus serves to transmit information regarding angular position at one point

to a remote point.

System Description and Operation

The system set up is made up of synchro transmitter and synchro receiver on a single

rigid base provided with suitable swithes and anodized angular plates. The system also contains

a step down transformer for providing excitation to the rotors. Suitable test points for rotor (R1

and R2) and stator (S1, S2 and S3) for both Tx and Tr are provided.

Operating Instructions

Experiment No.1 : Study of synchro transmitter

In this part of the experiment we can see how, because of the transformer action, the

angular position of the rotor of synchro transmitter is transformed into a unique set of stator

voltages.

Procedure:

1. connect the mains supply to the system with the help of cable provided. Do not

connected any patch cords to terminals marked “S1, S2 and S3”

2. Switch on mains supply for the unit.

3. Starting from zero position, note down the voltage between stator winding terminals i.e

Vs1s2, Vs2s3 and Vs3s1 in a sequential manner. Enter readings in a tabular form and

plot a graph of angular position of rotor voltages for all three phases.

4. Note that zero position of the stator rotor coinsides with Vs2s1 voltage equal to zero

voltage. Do not disturb this condition.

Experiment No.2 : Study of synchro transmitter and receiver pair.

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Procedure

1. Connect mains supply cable.

2. Connect S1, S2 and S3 terminals of transmitter to S1, S2 and S3 of synchro receiver by

patch cords provided respectively.

3. Switch on SW1 and SW2 and also switch on the mains supply.

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4. Move the pointer i.e rotor position of synchrono transmitter Tx in steps of 30 degrees and

observe the new rotor position. Observe that whenever Tx rotor is rotated, the Tr rotor

follows it for both the directions of rotations and their positions are in good agreement.

5. Enter the input angular position and output angular position in the tabular form and plot a

graph.

Precautions

1. Handle the pointers for both the rotors in a gentle manner

2. Do not attempt to pull out the pointers

3. Do not short rotor or stator terminals

FRONT PANEL VIEW OF SYNCHRO TX AND TR

Note: 1) Connect S1, S2, S3 of synchro transmitter to S1, S2, S3 of synchro receiver

respectively by mans of patch cords.

2) SW1 & SW2 are switches for rotor supply (excitation) of synchro TX &

TR.

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TOP VIEW OF SYNCHRO TRANSMITTER & RECEIVER

SYNCHRO TRANSMITTER ROTOR POSITION VERSUS STATOR VOLTAGES FOR

THREE PHASES

(Vsls3, Vsls2, VS2S3)

Sr.No. Position rotor

degrees

Stator / Vs3S1 Terminal VS1S2 Voltages (RMS)

VS2S3

1 00 0.1 60.3 59.8

2 30 33.8 34.5 68.6

3 60 58.9 1.1 60.7

4 90 69.1 33.7 34.9

5 120 60.1 59.1 0.4

6 150 36.2 68.9 32.6

7 180 0.9 60.3 59.3

8 210 33.9 34.8 68.9

9 240 59.1 0.3 59.6

10 270 68.8 33.5 34.9

11 300 59.7 60 0.4

12 330 33.5 69.2 35.1

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TYPICAL RESULTS FOR

Sr.

No.

Angular position in degrees synchro

transmitter I/P

Angular position in degrees synchro

receiver O/P

1 0.0 0.5

2 30.0 30.5

3 60.0 61.0

4 90.0 89.0

5 120.0 119.0

6 150.0 148.0

7 180.0 178.0

8 210.0 209.0

9 240.0 240.0

10 270.0 269.0

11 300.0 299.0

12 330.0 329.0

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SPEED TORQUE CHARACTERISTICS OF AC SERVO MOTOR

Introduction

An AC servo motor is basically a two phase induction motor except for certain special

design feature. A two phase induction motor consisting of two stator windings oriented 90

degrees electrically apart in space and excited by ac voltage which magnitude and 90 degrees.

Generally voltages of equal magnitude and 90 degrees phase difference are applied to the two

stator phases thus making their respective fields 90 degrees apart in both time and space, at

synchronous speed. As the field sweeps over the rotor, voltages are induced in it producing

current in the short circuited rotor. The rotating magnetic field interacts with these currents

producing a torque on the rotor in the direction of field rotation.

The shape of the characteristics depends upon ratio of the rotor reactance (X) to the rotor

resistance (R). In normal induction motors X/R ratio is generally kept high so as to obtain the

maximum torque close to the operating region which is usually around 5% slip.

A two phase servo motor differs in two ways from normal induction motor.

1. The rotor of the servo motor is built with high resistance so that its X/R ratio is small and

the torque speed characteristics is as shown in the figure (2).

Curve (3) is nearly linear in contrast to highly non linear characteristics with large X/R.

It must emphasized that if a conventional induction motor with high X/R ratio is used for

servo applications, then because of the positive slope for part of the characteristics, the

system using such a motor becomes unstable.

The motor construction is usually squirrel cage or drag cup type. The diameter of the

rotor is kept small in order to reduce intertia and thus to obtain good accelerating

characteristics. Drag cup construction is used for a very low intertia operations.

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2. In servo applications, the voltages applied to the two stator windings are seldom

balanced. On of the phases known as the phase known as the control phase with respect

to the voltage supplied to the reference windings and it has a variable magnitude and

polarity. (fig.2). The control winding voltage is supplied from a servo amplifier. For low

power applications, AC servo motors are preferred because they are light weight, rugged

and there are no brush contacts to maintain.

Description of the set up

The motors which is required to be tested is mounted on a small but sturdy pedestal. The

motor is having extension of shafts on both the sides.

Speed variation and speed measurement

The reference winding of the motor is excited from a fixed voltage of 100 volts. The

control winding voltage is obtained through an R-C combination. The voltage available to

control winding is varied by the control of resistance R. The capacitance is used to generate a

phase shift. By varying the magnitude of the control voltage, it is possible to vary the speed of

the AC servo motor. The secondary of the transformer T1 provided the reference winding and

control winding voltage.

On one of the sides of the shaft, a metallic disk with 20 holes (1/4” dia) is mounted. A

photo transistor and light source arrangement is located on the two sides of the disc; so that the

light beam is regularly interrupted by the hole – No- hole arrangement of the disc. The photo

transistor conducts when light is incident on it and acts almost as an open circuit when no light is

falling on it.

In the process the cct generates a train of pulses. The number of pulses per second is

directly proportional to the revolutions persecond. It means for 1500 RPM disc speed, the disc

would be completing 25 revolutions per second and with 20 holes on the disc, 500 pulses would

be generated by the photo pick up in the second. Thus for a sped of 750 rpm, 250 pulses would

be developed by the photo pick up. These pulses are wave shaped by amplifier and a Schmitt

trigger cct. Finally they are fed to a monostable cct which produces constant width and constant

height pulses. Consequently the meter deflection is proportional to the number of pulses per

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second and hence to the rpm of the motor under test. There is a preset in services with the meter

which works as a calibrating control.

A full wave output of a rectifier produces a fixed frequency of 100Hz (within + or – 1%

accuracy) and the same is used as a standard frequency for effecting calibration on the speed

indication. The preset marked “PR1” is to be adjusted for 20% of F.S.D or to 300 rpm. The

switch SW4 is thrown back to normal mode after carrying out calibration check up.

Torque Measurement

In order to measure torque produced by the AC servo motor, we must have an

arrangement to produce a variable load on the AC servo motor. The ac servomotor is

mechanically coupled to a small dc machine (a permanent magnet dc motor or generator) on the

remaining side of the extended shaft. A variable dc current is required to be passed on through

the dc motor. The polarity of the current is such as to produce an opposite torque as a result of

its interaction with the field of the permanent magnet.

In can be proved that the electrical power developed by the AC servo motor is given by

the product of back emf generated by the dc machine and current we are forcing through the

armature by means of a variable resistance and the constant voltage source. By varying the

resistance, the current is changing and the opposite torque is also changing. We have to use the

following formula to find the torque in gm-cm.

cmgmNpi

pT

2

6010019.1 4

where Eb = Back E.M.F

Ia = Armature current

When P = power in watts

= Eb x Ia

N = R.P.M

It P is in milliwatt, proper substitution must be made in the result.

In this formula, Eb can be found by measuring the generated emf across the armature

terminal for a given speed. As the field is constant the output emf (hence back emf) is

proportional to the shaft speed, with armature circuit open circuited, we can run the machine as a

dc generator and find slope (volt/rpm) for the given dc machine.

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Ia is measured by ammeter which is connected in series with the power supply and the

variable resistance (LOAD CONTROL). This method does not take into account the no load

torque developed by the ac servomotor. To measure the torque developed at no load (i.e torque

just required to rotate speed measuring disc, rotor of ac servomotor, rotor of dc motor) the ac

servomotor is switched off. Now the dc machine run as the motor with the help of the dc power

supply, speed bring controlled by variable resistance. Again we have to effect the measurement

of Ia for a given speed. From the product of Eb (back emf developed by the motor) and armature

current taken, we can find the mechanical power developed at the motor shaft. Again we must

use the formula

60

2 NTpiP

Ni

PTorque

29

6010019.1 4

For various speeds, we can note down the no load torque required to be developed by motor.

This torque is negligible and may not be taken into account for normal testing.

Speed torque characteristics of AC servo motor.

Study all the controls carefully on the front panel.

1. Keep the switch SW3 in upward position, indicating that the armature circuit of dc

machine is not connected to auxiliary power supply (12 volts), switch SW2 should also

be in off position.

2. Ensure P1 and P2 are in fully anticlockwise position.

3. Now, switch on SW1 and also switch on SW2. You can observe that AC servomotor will

start rotating and the speed will be indicated by the meter M1 on the front panel. (It is

assumed that calibration procedure is already carried out for speed measurement).

4. With SW3 in OFF condition, vary the speed of the AC servomotor by moving P1 in

clockwise direction and note the emf generated by the dc machine (Now working as dc

generator or tacho). Enter the results in Table No.1 (Use a dc voltmeter in the range 0 to

2 volts or so).

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Table 1 : To plot speed vs Back emf characteristics

Sr. No. Speed R.P.M Back E.M.F Volts

1 320 -0.409

2 500 -0.585

3 700 -0.835

4 900 -1.057

5 1100 -1.29

6 1300 -1.52

Rotor dimensions for AC servo motor :-

Density of Material d = 7.9 gm/cm3

5. Now switch SW3 in off condition, switch ON SW2 and keep the pot P1 in minimum

position. You can observe that the ac servo motor starts moving with speed being

indicated by the RPM indicator. You can measure the reference winding voltage (about

100 volts ac and control winding voltage (which is variable by P1). Note the speed of ac

servomotor. Now switch on SW3 and start loading ac servo motor by controlling pot P2

in a slow fashion. Note down corresponding values on Ia and N. Enter these values in

Table.2.

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Table No.2 (Speed torque characteristics)

TYPICAL READINGS FOR AC SERVO MOTOR SPEED – TORQUE

CHARACTERISTICS

Controls Voltage Vc = 20 volt

Sr.

No.

Ia

mA

Speed N

RPM

Eb

Volt.

Pmw = Eb x Ia

Millwatt

Torque

Gm-cms

1 200 1300 1.3 260.0 19.46

2 400 1175 1.175 470.0 30.92

3 500 1050 1.05 525.5 48.65

4 600 975 0.97 585.0 58.38

5 700 800 0.80 560.0 68.00

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Sr.

No.

Ia

mA

Speed N

RPM

Eb

Volt.

Pmw = Eb x Ia

Millwatt

Torque

Gm-cms

1 200 1400 1.4 280.00 19.46

2 300 1350 1.35 405.00 29.19

3 400 1300 1.3 520.00 38.92

4 600 1200 1.2 720.00 58.38

5 700 1175 1.17 822.5 68.11


Sr.

No.

Ia

mA

Speed N

RPM

Eb

Volt.

Pmw = Eb x Ia

Millwatt

Torque

Gm-cms

1 0.05 850 -0.15 -0.0075 -0.858

2 0.15 780 0.66 0.099 12.350

3 0.20 700 1.24 0.248 34.47

4 0.25 620 1.77 0.4425 69.449

5 0.35 550 2.57 0.899 159.053

6. Now you may set control winding voltage to a new value of 30 volts after switching of

SW3. Again repeat the process as indicated in step No.5 i.e. Table 2 for a new value of

control winding voltage.

7. Plot the speed torque characteristics for various values of control winding voltages.

Study their nature.

Precautions

1. Before switch on, P1 and P2 should be always brought to most anticlockwise position.

2. Controls P1 and P2 should be operated in a gentle fashion.

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MAINTENANCE INSTRUCTION FOR AC SERVOMOTOR SPEED TORQUE

CHARACTERISTICS

1. Check for loose or broken connections and transformer voltages, fuses etc.

2. For photoelectric pick up, the lamp (6 volts, 0.06 amps) should be glowing. Check for

loose connection or blown lamp.

3. +5 volt DC should be present for photo electric pick up circuit measurable at the

connector.

4. Check for (500 Ohm 3 Watt) load control potentiometer & 10 Kilo Ohm / 3 Watt speed

control potentiometer.

5. For speed indicator, throw the internal DPDT switch marked cal / read, in cal position.

The meter should indicate 300 rpm if no indication is available check for IC 741, IC555

on speed indicator PCB DPDT switch should be in read position, for normal operation.

6. Check for proper coupling to the small DC tachogenerator.

Figure – 1

Schematic Diagram of Two Phase Induction Motor

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Figure – 2

Torque – Speed Characteristics of Induction motor

Characteristics (3) = AC Servomotor

Fig. No.(4) Study of AC Servo Speed – Torque Characteristics

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Block Diagram for AC servomotor Speed Torque Characteristics

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TYPICAL TORQUE CALCULATION OF POINT ‘A’ ON GRAPH 2

EC = 70 volt

Ia = 170 milli Amp. = 0.17 amp.

Speed ‘N’ = 850 RPM

For speed 850 RPM., Eb – 960 milli volt = 0.96 volt

Therefore power ‘p’ = Eb x Ia = 0.96 x 0.17 = 0.1632 watt

Therefore

Npi

pTTorque

2

6010019.1''

4

850142.32

6010019.11632.0''

4

T

T = 18.68 Gm Cm.

Therefore point ‘A’ (18,68,850), which is plotted on graph 2.

ANALYSIS OF AC SERVOMOTOR SPEED-TORQUE CHARACTERISTICS

We observed that the torque – speed curves are not straight lines. Therefore a linear

differential equation cannot be used to represent the exact motor characteristics. Sufficient

accuracy may be obtained by approximating the characteristics by straight lines. The following

analysis is based on this assumption.

(Reference : - feedback control system analysis & synthesis by J.J.D’AZZO & H.Houpis . Page

No.48)

The torque generated is a function of both the speed W & the control winding voltage ec.

In terms of partial derivatives, the torque equation is

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),( wetec

Te

e

Tcc

c

(1)

By approximating torque – speed curves by parallel straight lines, the partial derivative

coefficients of eq (1) are constants which can be evaluated from the graph.

KwT

ke

Tc

c

& (2)

for a load consisting of inertial & damping, the load torque required is,

TL = JDW = BW (3)

Where D is operator

Since the generated load & torque must be equal, from equations (1) & (3) we have,

Kcec + Kww = JDw + Bw (4)

Rearranging terms,

JDw + (B-Kw)w = Kcec (5)

In terms of (position), this equation can be written as,

JD26 + (B-Kw) DQ = Kcec (6)

In order for the system to be stable, the coefficient (b-Kw) must be positive. Observation

of the motor characteristics shows that Kw - W

T

is negative, therefore stability requirement is

satisfied even if ‘B’ is assumed to be negligible.

From speed torque characteristics of this motor, near the operating point ‘Q’

We have,

V

cmgm

e

TK

tconswc

c10

9

tan

(7)

= 0.9gm-cm/V0H

and rpm

cmgm

w

TK

tconsec

w50

3

tan

= -0.0063 gm-cm / rad / sec

therefore if equation (7) values for Kc & Kw are used in equation (6) we have,

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JD2Q + (B+0.0063) DQ =

V

cmegm c9.0 (8)

Where values for ‘J’ and ‘B’ can be inserted if ‘B’ is negligible, only ‘J’ value need be

introduced.

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TRANSFER FUNCTION OF FIELD CONTROLLED DC MOTOR

Aim

To determine the transfer function of a field controlled DC motor.

Apparatus Required

Sl. No. Apparatus Type & Range Quantity

1 Ammeter (0-10A) MC

(0-2A) MC

(0-2A0 MI

1

1

1

2 Voltmeter (0-300V) MC

(050) MC

1

2

3 Rheostat 300 / 1.2A

100 / 3A

1

1

Formula

The transfer function of a field controlled DC motor is

)}1)(1{()(

)(

mf

m

f STST

K

E

Tm = Mechanical time constant of rotor = J/B

J = Moment of Inertia of rotor = Kg m2 / rad – sec

Lf = Field inductance (H)

Km = Determined Using Load Test

T = R x 9.8 X (S1 ~ S2) N-M

Tf = Time constant of field circuit Lf / Rf

Procedure

I) To determine motor gain constant – Km (Load test):-

1. Motor field rheostat is kept at minimum position

2. Supply is given and the motor is started

3. Adjust the motor field rheostat and bring the motor to rated speed

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4. Voltmeter, ammeter and spring balance readings are noted

5. Readings are taken for different field event keeping armature current cut

II) Retardation Test:-

1. Connections are given as per the circuit diagram

2. Motor sis started on no load

3. Motor field rheostat is adjusted to bring the motor slightly above the rated speed

4. Using DPDT switch supply is cut off and motor is allowed to retard

5. Different values of speed changes to the corresponding time are noted

6. Now motor is started as usual and brought to rated speed

7. DPDT switch is thrown off such that supply to armature is cut off, but a known

resistance R is connected to the armature and the motor is allowed to retard.

8. Time taken of 5% fall in speed, voltmeter voltmeter and current readings are

noted.

9. Similarly time taken for 5% fall in speed without R is obtained.

To find Rf:

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To find Lf:

Model Graph:

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To find Ra:

LOAD TEST

3 Point Starter

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Fuse rating = 1.25 x 10 15A

Name plate details

Rated power = 3 Hp

Rated voltage = 220V

Rated current = 10A

Rated speed = 1500 rpm

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Load Test:

Sl.

No.

V

(Volts)

If

Ia kept

emf)

N

(rpm)

Spring balance readings Torque

T=9.81 R X S1 ~ S2 N-m S1

(Kg)

S2

(Kg)

S1 ~ S2 (Kg)

1 200 0.4 1498 0 0 0 0

2 200 0.5 1438 1 0 1 1.147

3 200 0.54 1390 3 1 2 2.295

4 200 0.6 1360 6 1.5 4.5 5.164

5 200 0.65 1354 8 2 6 6.886

Retardation Test:

Without load resistance With load resistance

N (rpm) Time (s) I (A) V (volts) N (rpm) t (sec)

1600-1500 1.42 2.8 175 1600-1500 0.79

1500-1400 1.45 2.7 170 1500-1400 0.89

1400-1300 1.74 2.65 160 1400-1300 0.82

To find Rf :

1 Connections are given as per the circuit diagram

2 By varying rheostat different ammeter and voltmeter readings are obtained.

Sl.No. V (volts) I (A) Rf = V/If ()

1 11 0.32 343.75

2 130 0.4 325

3 170 0.5 340

4 200 0.6 333.33

Average 333.52

Age : 333.52

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To fine Lf:

1 Connections are given as per the circuit diagram

2 The variac is adjusted to obtain different voltages and currents

Sl. No. V (volts) If (mA) Zf (Vf/If () Xf Lf

1 60 13 4.615103 4602.70 14.65

2 100 20 5.0103 4988.13 15.87

3 140 27 5.185103 5174.13 16.46

4 180 33 5.45103 5436.66 17.31

5 220 39 5.64103 5630.01 17.92

Average 5167.04 16.44

Model Calculation

Obtain sf

tI

TK

from T – If curve

dT

dNis calculated from N-t curve obtained from Retardation test without R

)(1

1

tt

tPP

where P1

power consumed in the load resistor during retardation test

)(2

1)(

2

1 2

2

2

12211 aa RIRIIVIV

t = Time taken for speed reduction during retardation test without load R

t’ = Time taken for speed reduction during retardation test with load R.

Now, P = 0.0109 JN dt

dN

J can be determined now.

21 loglog

12

NNm

ttT

obtained from speed time curve

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Find B = mT

J

BR

KK

f

tm

Substituting the values for different constants in the general formula for TF, we get the transfer

function of the given M/C

Result

Hence the transfer functions of the field controlled DC motor was found to be

)}893.141)(565.01{(

094.2

)(

)(

SSE f

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TRANSFER FUNCTION OF LAG, LEAD NETWORK

Aim

To obtain the transfer function of a lag, lead network

Apparatus Required


1 Resistor 1K

470

1

1

2 Capacitor 0.1f 1

3 Function Generator -- 1

4 CRO -- 1

Description

Compensation is essentially a compromise between steady state accuracy and relative

stability.

a) Load Compensation: There are many ways to realize continuous time lead

compensators of which one is an electrical RC network. Lead compensators

essentially yields an appreciable improvement in transient response and a small

change in steady state accuracy. It way accentuate high frequency noise effects. A

lead compensator is basically a high pass filter i. high frequencies are passed.

b) Lag Compensation: This yields an appreciable improvement in steady state accuracy

at the expense of increasing the transient response time. It will suppers the effect of

high frequency noise effects. It permits a high gain at low frequencies which

improves steady state performance. In lag compensation we use attenuation

characteristic at high frequencies rather than the phase lag characteristic. Lag

compensation increases the low frequency gain and thus improves the steady

accuracy of the system, but reduced the speed of response due to reduced bandwidth.

Procedure

1. The connections are given as per the circuit diagram

2. Using function generator, input is given and the output is observed at the CRO

3. For different values of frequencies, the values of a, b and output voltage are

determined.

4. The graph is drawn by taking frequencies along X-axis and magnitude and phase

along Y-axis.

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Lead Compensating Network

Lag Compensating Network

Model Graphs (Bode Plot)

1) Lead Network Note : Use semi log graph sheets

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2) Lag Network

Tabulations

Lead Network

Sl.

No.

Frequency Input

Voltage

(V)

Output

Voltage

(V0)

a b = sin-1

(a/b) deg

Gain = 20

log

(V0/Vi)db

1 11 42=8 5.60.5=3.0 1 2.8 20.92 -9.11

2 10.1=0.1k 42=8 50.5=3.0 0.2 2.6 4.41 10.1

3 11.5=1.5k 42=8 6.20.5=3.1 1.4 3.2 25.94 8.23

4 12=2k 42=8 70.5=3.5 1.8 3.6 30.0 7.18

5 13=3k 42=8 4.21=64 1 2.2 27.03 5.59

6 101=10k 3.82=7.6 6.41=64 1.2 3.4 20.66 1.49

7 1001=100k 3.62=7.2 6.81=6.8 0.6 3.6 9.59 0.96

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Lag Network

Sl.

No.

Frequency Input

Voltage

(V)

Output

Voltage

(V0)

a b = sin-1

(a/b) deg

Gain = 20

log

(V0/Vi)db

1 0.08k 4.21 30.5 1.4 2.2 39.52 -8.93

2 0.1k 4.21 30.5 1.4 2 44.42 -8.943

3 1k 4.21 40.1 2 2.2 65.38 -20.42

4 2k 4.21 2.20.1 1.8 2.2 54.9 -25.61

5 5k 4.21 2.250mV 1.2 2.2 33.05 -31.63

6 10k 4.21 2.250mV 0.2 2.2 5.21 -31.63

7 20k 4.21 2.250mV 0.2 2.2 7.83 -31.63

Formula

1. Lead network transfer function =

TS

ST

1

1

where = R2 / R1 + R2,

T = R1 C1

2. For lag network transfer function =

TS

TS

1

1

1

where

2

21

R

RR

T = R2 C2

Result

The transfer function of lead and lag networks were determined and was found to be

For lead network =

00003195.01

00015.01319.0

For lag network =

63.6797

59.21276319.0

S

S

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TRANSFER FUNCTION OF ARMATURE CONTROLLED DC MOTOR

Aim

To obtain the transfer function of armature controlled DC motor

Apparatus Required


1 Rheostat 50 / 5A

300 / 1.2A

1

1

2 Ammeter (0-10A) MC

(0-200mA) MI

1

1

3 Voltmeter (0300V) MC

(0-30V) MI

2

1

4 1-phase Variac -- 1

Formula

Transfer function = ])1)(1[()(

)(

bama

a

a KKSTST

K

sV

s

BR

KK

a

t

a

where Kt is the slope of T – Ia curve (motor gain constant)

radKgm

dt

dNN

PJ

tt

tPP /

0106.0

.'

' 2

21 loglog

12

N

e

N

e

m

m

ttT

T

JB

b

a

a

a KR

LT = back emf constant volt / rpm from no load test curve

Procedure

I Load Test

1. The supply is switched on and the motor is started with a 3-point starter

2. Motor field rheostat is adjusted and the motor is brought to rated speed

3. Speed, Ammeter, Voltmeter and spring balance readings are noted down

4. Motor is loaded gradually till rated current and corresponding readings are

noted down.

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Retardation Test

Model Graphs

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Load Test

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To find Ra

To find La

II Retardation Test

1. Motor is started on noload using 3-point starter

2. Adjust motor field rheostat and run motor at speed slightly greater than rated

speed.

3. Using DPST switch cut off the supply and allow the motor to retard

4. Various values of speed changes to corresponding time are taken.

5. Motor is started again and brought to the rated speed

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6. DPST switch is used to cut off armature supply but a known resistance is added

to armature circuit & motor is allowed to retard.

7. Time for 5% fall on speed & corresponding voltmeter, ammeter readings are

noted down.

Tabulations

Load Test

Sl.

No.

V

(volts)

I

(A)

Spring balance readings Speed

(rpm)

T

(N-m) S1

(Kg)

S2

(Kg)

S1 ~ S2

(Kg)

1 220 1 2 2 0 1490 0

2 220 1.5 1.5 3.5 2 1475 0.229

3 220 2 1.6 4.6 3 1440 2.410

4 220 2.5 2 6 4 1430 4.017

5 220 3 2 7.4 5.4 1425 5.968

6 220 3.5 2 8.4 6.4 1420 6.088

7 220 4 2 9 7 1415 7.142

8 220 4.5 2 10 8 1410 8.248

No Load Test

Sl. No. Speed (rpm) V (volts) Ia (A) Eb (V)

1 1500 215 0.26 206.04

2 1400 208 0.242 198.068

3 1250 180 0.184 178.096

4 1100 164 0.162 162.152

8. Time for 5% fall in speed without R is noted

III To find Ra:


2. By varying the rheostat, different values of V and I are noted

3. From these above values, the value of Ra is computed

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IV To find La:


2. By varying the 1 phase variac, different values of V and I are noted

3. From these values, the values of Z are obtained. From Z and Ra, the value of Xa

(and hence La) are computed.

To find Ra:

Va(V) Ia (A) Ra = Va / Ia ()

8 3.1 2.58

10 3.5 2.857

12 4.0 3.0

13 4.5 2.88

Average 2.831

To find La:

Va(V) Ia (A) Za = Va / Ia () Xa () La (H)

40 1 40 39.89 0.126

88 2 44 43.90 0.139

134 3 44.64 44.57 0.141

112 2.5 44.8 44.71 0.1423

Average 0.137H

Retardation Test:

(Without load R) With load R

N (rpm) Time (s) N (rpm) V (volts) I (A) Time, T(s)

1600-1500 1.3 1600-1500 200 2.5 0.7

1500-1400 1.8 1500-1400 180 2.4 1.8

1400-1300 2.2 1400-1300 165 2.3 2.2

Model Calculation:

Find Kb and Kt from Eb Vs N and TVs Ia graphs

Find La from Ra and Xa measurements

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Determine dN / dt, the slope of NVs Time graph

)(2

1)(

2

1' 2

2

2

12211 aa RIRIIVIVP from retardation test values with load

t1 = Time in ‘sec’ for retardation of the machine with resistive load

t = Time in ‘sec’ for retardation of the machine without resistive load

find

dt

dNN

PJ

ttT

NNm

0109.0

,loglog 21

12

wheremT

JB

tt

tPP

''

BR

KK

a

t

a

. Obtain transfer function by substitution of constants.

Result

Hence the transfer function of the given armature controlled DC motor was found to be

}67.5)783.51)(0412.01{(

61.38

)(

)(

SSsR

s

a

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STABILITY ANALYSIS OF LINEAR SYSTEMS

Aim

To analyze the stability of the linear systems using Bode / Root locus / Nyquist plot,

using MATLAB Software tool.

Theory

Bode Plot:

The bode plot is the frequency response plot of the transfer function of a system. A bode

plot consists of two graphs. One is a plot of the magnitude of a sinusoidal transfer function

versus log w, the other is a plot of the phase angle of sinusoidal transfer function versus log w.

The bode plot can be drawn for both open loop and closed loop transfer function.

Usually the bode plot is drawn for open loop system. The standard representation of the

logarithmic magnitude of open loop transfer function of G(jw) is 20 where the base of the

logarithm is 10. The nit used in this representation of the magnitude is the decibel, usually

abbreviated db. The curve are drawn on semi log paper, using the log scale (abscissa) for

frequency and the linear scale (ordinate) for either magnitude (in decibels) or phase angle (in

degrees).

The main advantage of the bode plot is that multiplication of magnitudes can be

converted into addition. Also a simple method for sketching an approximate log magnitude

curve is available.

Determination of phase and gain margin from bode plot

The gain margin in db is given by the negative of db magnitude of G(jw) at the phase

cross-over frequency, wpc. The wpc is the frequency at which phase of G(jw) is 1800. If the db

magnitude of G(jw) at wpc is negative then gain margin is positive and vice versa.

Let gc be the phase angle of G(jw) at gain cross over frequency wgc. The wgc is the

frequency at which the db magnitude of G(jw) is zero. Now the phase margin, is given by, =

1800+ gc. If gc is less than – 1800 then phase margin is positive and vice versa.

Nyquist Stability Criterion

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If the G(S) H(S) contour in the G(S) H(S) plane corresponding to Nyquist contour in the

s-plane encircles the point (-1+j0) in the anticlockwise direction as many times as the number of

halfs-plan poles of G(S) H(S), then the closed loop system is stable.

In examining the stability of linear control systems using the Nyquist stability criterion,

the following three situations.

1. There is no encirclement of -1+j0 point. This implies that the system is stable if there are

no poles of G(S) H(S) in the right half s-plan. If there are poles on right half s-plane then

the system is unstable.

Bode Diagram

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Frequency (rad/sec)

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2. An anticlowise encirclement or (or encirclements) of -1+j0 point. In this case the system

is stable if the number of anticlociwise encirclement is same as the number of poles of

G(S) H(S) in the right half s-plane. If the number of encirclement is not equal to number

of poles on right half s-plane then the system is unstable.

3. There is a clockwise encirclement (or encirclement) of the -1+j0 point. In this case the

system is always unstable.

Procedure

1. Write programs for the given transfer function

2. Simulate it using MATLAB software

3. Observe the graph

4. Calculate the theoretical values for the time domain specifications and compare with the

observed values.

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Programme & Plots

%Root locus;

% G is the transfer function

s=tf(‘s’)

G=75*(1+0.2*s)/(s*(s^s+16*s+100));

rlocus(G);

axis equal;

% Nyquist plot

s=tf(‘s’);

G=75*(1+0.2*s)/(s*(s^s+16*s+100));

nyquist(G);

axis equal;

% Bode plot

s=tf(‘s’);

G=75*(1+0.2*s)/(s*(s^s+16*s+100));

bode(G);

axis equal;

Result

The response of the given transfer using Bode plot, Nyquist Plot & Root locus obtained

using the MATLAB. The theoretical values and practical values are compared.

Documents

REFERENCE MANUAL EE0311 MEASUREMENTS & CONTROL …webstor.srmist.edu.in/web_assets/srm_mainsite/files/files/Measurement... · 6 Calibration of single phase energy meter direct loading