CONTROL SYSTEMS LAB MANUAL - anuraghyd.ac.in€¦ · eee deptartment control systems lab manual...

EEE Deptartment Control Systems Lab Manual

Anurag College of Engineering

CONTROL SYSTEMS LAB

MANUAL



LIST OF CONTROL SYSTEM LAB EXPERIMENTS

1. TRANSFER FUNCTION OF D.C.SHUNT GENERATOR

2. CHARACTERISTICS OF MAGNETIC AMPLIFIER

3. SPEED-TORQUE CHARACTERISTICS OF SERVOMOTOR.

4. TIME RESPONSE OF SECOND ORDER SYSTEM.

5. LAG-LEAD COMPENSATORS

6. SIMULATION OF TRANSFER FUNCTION USING OP-AMP.

7. STATE SPACE MODEL OF TRANSFER FUNCTION USING MATLAB

8. VERIFICATION OF ROOT LOCUS USING MATLAB.

9. TRANSFER FUNCTION MODEL FOR STATE SPACE USING MATLAB



1. TRANSFER FUNDTION OF DC GENERATOR

AIM:

To determine the transfer function of dc generator.

NAME PLATE DETAILS:

Rated voltage =

Rated current =

Speed =

Output Power =

APPARATUS:

Dc motor –generator set, motor starter, field rheostat, rheostat as potential

differentiator for excitation of generator, ammeters –MC&MI, voltmeters–MC&MI,

tacho generator, variac, connecting wires.

CIRCUIT DIAGRAM:

MC- Mechanical coupling

Fig(i)



Fig(ii)

Fig (iii)

THEORY:

The transfer function of a dc generator is derived as follows

dt

(t)dIL(t)IR(t)V

(t)IK(t)V

fffff

fgg

Vg(t) generated voltage

Kg generator constant

If(t) field current



Applying L.T with initial conditions as zero

]sL[R

(s)V(s)I

(s)]IsL[R(s)V

(s)sI L(s)IR(s)V

(s)IK(s)V

ff

ff

ffff

fffff

fgg

Kg=generated EMF constant

Block diagram representation for the above two equations

Vf(s) If(s) Vg(s)

]sL[R

KFunctionTransfer

ff

g

In this equation, the values of Kg, Rf & Lf have to be obtained.

PRECAUTIONS:

1. The motor should run at rated speed while conducting OCC test.

2. During the conduct of field impedance and resistance drop tests only the field

windings should be energized.

PROCEDURE:

1. Connect the circuit as per the circuit diagram shown in fig (i).Ensure that the

motor field rheostat and the P.D in the generator field circuit should be minimum.

2. Start the motor with the help of a starter and adjust the speed of the motor to the

rated value by varying the field rheostat.

3. Vary the P.D in the generator circuit in small steps and note down the field

current of the generator (If) and generator emf (Eg) and tabulate it in table (i).

4. To determine Kg ,magnetization characteristics Eg Vs If of a separately excited dc

generator has to be plotted as shown in fig(iν) and use the straight line position to

determine Kg= Eg / If.

Kg

1

[Rf+sLf ]



5. The field resistance of the generator Rf is determined by the field resistance drop

test as shown in figure in fig(iii)Vary the P.D in steps ,note down the Ammeter

and voltmeter values and tabulate it in table(ii).

6. To determine inductance Lf of a generator first the impedance Zf has to

determined by field impedance drop test as shown in fig (ii).

7. Vary the variac in fig (ii). Note down the ammeter and voltmeter values and

tabulate it in table (iii).

OCC Characteristic:

Field Current If(A) Generated Voltage Eg(V)

Table (i)

Field resistance drop test:

Sl.No Vf (V) If (A) Rf=Vf/If (Ω)

Average Rf = Ω

Table (ii)

Field Impedance drop test:

Sl.No Vf (V) If (mA) Zf=Vf/If (Ω)

Average Zf = KΩ

Table (iii)



CALCULATIONS

Field resistance Rf =1.2* Rf avg Ω

Impedance Zf = KΩ

][(s)V

)(VT.F

FunctionTransfer

K

graph From

f2

X

]R[ZX

f

g

g

f

212

f

2

ff

ff

g

f

g

f

sLR

Ks

I

E

L

MODEL GRAPH:

Fig (iν)

RESULT:

The transfer function of dc generator was determined by conducting OCC test on the

given dc generator and the T.F of the system is found to be

f

Lf

RgK

T.F



2. Magnetic Amplifier AIM:

To Study the control characteristics of a Magnetic Amplifier

APPARATUS:

1. Magnetic Amplifier having laminated core.

Ammeters D.C (0-100ma), Ammeters A.C (0-500ma) are arranged in unit itself

2. Patch cards

3. Low Bulb

THEORY:

1. Magnetic amplifier is a device consisting of saturable reactors, rectifiers and

conventional transformers, used to secure control or amplication.

2. The load current in magnetic amplifier is cotrolled by a D.C.magnetizing current.

3. A large current value is controlled by a small current value; hence such type of

circuits is termed as current amplifiers.

4. To control the load current, a saturable reactor is used.The reactance of the reactor

depends upon magnetic coupling and magnetism induced depends upon the

D.C.control current.

5. The load current is controlled by using magnetic property and hence the term

magnetic amplifier.

6. The most common basic saturable reactor which is used in magnetic amplifier

circuits consists of a three legged closed laminated core with coils wound on each

leg.

7. The coils wound on central limb are called as control winding and coils wound on

outer limbs are called as load winding.

8. Due to D.C.current in the control winding, the degree of magnetization in the core

is changed.

9. Hence the flux density changes, i.e.reactance of the core by changing the

D.C.current in the control winding.

10. If the load winding is connected in series with the load, one can control the

current in the load by changing reactance of the coil with the help of D.C.control

current.



CIRCUIT DIAGRAMS:

SERIES CONNECTED MAGNETIC AMPLIFIER:

Fig (i)

PARALLEL CONNECTED MAGNETIC AMPLIFIER:

Fig(ii)

SELF-SATURATED MAGNETIC AMPLIFIER:

Fig (iii)



PROCEDURE:

SERIES CONNECTION:

1. Connected the circuit as per the circuit diagram shown in fig (i).

2. Keep the slide switch on ‘D’ position which will be indicated by an indicator after

circuit is switched on

3. Keep control switch knob at its extreme position which ensure zero control

current at starting.

4. With the help of patch cards connect the following terminals on the front panels

of the unit

a) Connect AC to A1

b) Connect B1 to B2

c) Connect B2 to L

5. Connect a 100w fluorescent lamp in the holder and switch on the unit.

6. Now gradually increase the control current by rotating control current setting

knob clockwise in steps and note down control current and corresponding load

current and tabulate it in table (i).

7. Plot the graph of load current Vs control current.

B.PARALLEL CONNECTION:

1. Connect the circuit as per the circuit diagram shown in fig (ii)

2. Keep slide switch in position ‘D’ which will be indicated by an indicator after unit

is switched on.

3. Keep control current setting knob at its extreme left position which ensures zero

control current at starting.

4. With the help of plug in links, connect following terminals on the front panel of

the unit.

a) Connect AC to A1

b) Connect A1 to A2

c) Connect B1 to B2

d) Connect B2 to L



5. Connect 100 watt fluorescent lamp in the holder provide for this purpose and

switch on the unit

6. Now gradually increase control current by rotating control current setting knob

clockwise in steps and note down control current and corresponding load current

and tabulate it in table (ii).

7. Plot the graph of load current vs control current.

C. SELF SATURATED CONNECTION:

1. Connect the circuit as per the circuit diagram shown in fig(iii).

2. Keep slide switch in position ‘E’ which will be indicated by an indicator, after

unit is switched on.

3. Keep control switch knob at its extreme position which ensures zero control

current at staring.

4. With the help of patch cards connect the following terminals on the front panel of

the unit.

a) Connect Ac to C1

b) Connect A3 to B3

c) Connect B3 to L

5. Connect a 100W fluorescent lamp in the holder provide for this purpose and witch

on the unit.

6. Now gradually increase control current by rotating control current setting knob

clockwise in steps and note down control current and corresponding load current

and tabulate it in table (iii).

7. Plot the graph of load current Vs control current.

PRECAUTIONS:

1. For series and parallel connections of the magnetic amplifier the switch should be in D

mode.

2. For self saturation connection the switch is thrown to position E.



TABULAR COLUMNS:

SERIES CONNECTION:

Sl.No Ic (mA) IL (mA)

Table (i)

PARALLEL CONNECTION:


Table (ii)

SELF SATURATION CONNECTION:


Table (iii)

MODEL GRAPHS:

SERIES CONNECTION:



PARALLEL CONNECTION:

SELF SATURATION CONNECTION:

OBSERVATIONS:

1. In series connection of the magnetic amplifier the load current is zero owing to

high reactance.

2. In parallel connection the load current is not zero, even though the control current

is zero due to low reactance.

RESULT:

The magnetic amplifier control characteristics were studied and drawn.

3. SPEED- TORQUE CHARACTERISTICS DC SERVO MOTOR



AIM:

To draw the speed - torque characteristics of a dc-servomotor.

APPARATUS:

Dc Servo Motor

Multimeter (Or) Voltmeter

Connecting Wires

CIRCUIT DIAGRAM:-

THEORY:

Servo motors are used in automatic control systems. When the objective of the

system is to control the position of an object then the system is called servo system.

The dc motor can be controlled by varying either the field current (or) the

armature current. Dc servo motor gives high efficiency than from ac servo motor of same

size. The types of dc servo motors are the series ,shunt and permanent magnet (PM)motor



.the ease of controllable speed along with linear torque speed control curve makes the PM

motor ideal for servo mechanism applications

PRECAUTIONS:

1. The speed control knob is always in the most anti clock wise position before

switching on the position.

2. In order to increase the armature voltage, rotate the knob in the clock wise

direction in a gentle fashion.

3. In order to increase the load on the motor, adjust the knob K in a gentle fashion.

PROCEDURE:

1. Adjust T1 to 40gm with the help of knob K.

2. Ensure the pot P1 is in maximum position, switch on the supply.

3. Connect the voltmeters across the terminals of armature and field.

4. Adjust P1 so that Va =10v and P2 such that V f =20v.

5. Note down T1and T2 and speed values in tabular column.

6. Keeping Va=10v, adjust T1 up to 150gm in steps of readings.

7. Now for Va =15, 20, 25 and 30v repeat step 6.

8. From the table plot the speed –torque characteristics.

9. Repeat the above step for various values of Vf by controlling P2 .

TABULAR COLUMNS:

FIELD CONTROL: Va= Vf1= Where K=rg

T1(gm)

T2(gm) (T1-T2)XK

(mN-m)

Ia(amp) (N)rpm



Va= Vf2=

T1(gm) T2(gm) (T1-

T2)K(mN-m)

Ia(amp) N(rpm)

Va= Vf3=

T1(gm) T2(gm) (T1-T2)K(mN-

m)

Ia(amp) N(rpm)

ARMATURE CONTROL:

Va1= Vf=

T1(gm) T2(gm) (T1-T2)K(mN-m) Ia(amp) N(rpm)

Va2= Vf=


Va3= Vf=




MODEL GRAPHS:

ARMATURE CONTROL

Va1>Va2>Va3

Vf3>Vf2>Vf1

CONCLUSIONS:

1. In armature control the speed of the servo motor is increased with increase in

armature voltage.

2. The speed of the servomotor decreases with the increase in field voltage.

RESULT:

The speed- torque characteristics of a dc servo motor is plotted for both armature control

and field control.

4. TIME RESPONSE OF SECOND ORDER SYSTEM



AIM:

1. To obtain the time response of second order system

2. To determine time domain specifications.

APPARATUS:

Decade resistance box

Decade inductance box

Decade capacitance box

Function generator

CRO probes

Connecting wires.

.

CIRCUIT DIAGRAM:

Fig (i)

THEORY:

The time response of second order system is defined as the response of the system as the

function of time. Apply the KVL to the circuit,



)(1

)(

)(11

)(

)(1

)()()(E

equations above the to transformLaplace Applying

)(1

)(

)(1)(

)(

2

i

sICs

sE

sIsRCLCsCs

sE

sIcs

sLsIsRIs

dttic

tE

dtticdt

tdiLtRitE

o

i

o

i

212

d

21

2

22

2

n

2

22

o

1frequency natural damping

2R ratio damping

where

1

1

2

i.e,

functionsfer order tran second standardith function w transfer above theComparing

01

isEquation sticCharacteri

1

1

1

1

)(

)(E T.F

n

n

n

nn

i

LC

LC

LC

ss

LCsLRs

LCsLRs

LC

sRCLCssE

s

PROCEDURE:

1. Connect the circuit as per the circuit diagram shown in fig (i).

2. A square wave of amplitude 1V and frequency of 100Hz is given as input to the

circuit by using a function generator.

3. Connect the CRO probes across the capacitor terminals.

4. The various time domain specifications are measured from the output waveform



PRECAUTIONS:

i) Set the R, L and C values before switch on the supply.

ii) Set the input signal voltage equal to 1V and frequency as 100HZ

THEORITICAL CALCULATIONS:

For the given R, L and C parameters

21

2

2

12

1-

r

s

d

p

p

n

1

1tan

)(t Time Rise

Error 5% 3

Error 2% 4

tTime Settling

7.01t TimeDelay

tTimePeak

)(

)()(M shoot,over peak Maximum

2L

R ratio Damping

1

nd

d

n

n

n

d

p

n

where

for

for

c

ctc

LC



MODEL GRAPH:

PRACTICAL OBSERVATIONS:

Max % peak over shoot, %Mp =

Delay time, td =

Rise time, tr = Peak time, tp =

Settling time, ts =

TABULAR COLUMN:

Time domain specifications Practical observations Theoretical

calculations

Max % peak over shoot, %Mp

Delay time, td

Rise time, tr

Peak time, tp

Settling time, ts



OBSERVATIONS:

1. In the output response tolerance errors can not be observable.

2. Settling time in the output response can be observed only at the 5%

tolerance.

RESULT:

The response of second order system was obtained and time domain specifications were

obtained from the response.

The time domain specifications are :

% Mp=

td =

tr =

tp =

ts =

5. LAG COMPENSATOR

AIM:

To study the electrical lag compensator network experimentally and to draw bode plots

for improvement of steady state and transient behavior of system.

APPARATUS:

1. CRO with 2 channels

2. frequency generator to supply a variable frequency sinusoidal source

3. lag compensator kit (R1=20kΩ,R2=25kΩ& C=0.2nf)

4. 1:1 CRO probes -2 Nos

CIRCUIT DIAGRAM:



Fig (i)

THEORY:

Some kind of corrective subsystems introduce in a system to force the plant to meet the

desired specifications. These sub systems are known as compensators. Desired

specifications mean transient response and steady state error. In general, there are two

situations in which compensator are required to stabilize it as well as to achieve a specific

performance. In the 2nd case the system is stable. But the compensation is required to

obtain the desired performance. The lag compensation is required to improve the steady

state behavior of the system of a system while nearly preserving its transient response.


The general form of the T.F of lag compensator is

1 1

s

1s

)(

c

c

c

cc

p

Z

ps

zssG

From the electrical lag- network



s

s

C

RRs

s

CRRRRs

CRs

R

CRRsCRR

CRsC

sCRR

sCR

sE

sE

sCRR

sCR

sE

sE

i

i

o

1

1

R

1)(R 1

11

1

1

)(R

R

1)(1)(

1R

1)(

1

)(

)(

1

1

)(

)(

2

221

2212

2

21

2

2121

22

21

20

21

2

The sinusoidal T.F of the lag- network is

)()(1

1)(

jGjG

j

jjG ccc

REPRESENTATION OF S- PLANE:

Zc Pc

-1/ τ -1/ τ β

PROCEDURE:



1. Connections are made as per the circuit diagram shown in fig (i). Apply a variable

frequency of constant amplitude through frequency generator to input terminals of

the lag compensation network.

2. Connect both the input and output terminals of CRO and record the input and

output sinusoidal signals on the CRO screen.

3. For every value of input frequency, record corresponding lagging phase angle Ф

from the CRO.

4. τ and β values are calculated from the known values R1,R2&C.and determine

Gc(jω)for every value of ω.

5. Gc (jω) is converted into polar form and bode plots are sketched.

TABULAR COLUMN:

S.NO Frequency(Hz) A B Xo Yo Gain=

20log(B/A)

Ф=

Sin-1(-Xo/A)

CALCULATIONS:

1

2

221

n

CR

RRR

MODEL GRAPH:



RESULT:

The electrical lag compensator network was studied experimentally and the bode plot is

plotted.

5. LEAD COMPENSATOR

AIM:

To study the electrical lead compensatory network experimentally and to draw bode plots

for improvement of steady state and transient behavior of system or plant

APPARATUS:

5. CRO with 2 channels

6. frequency generator to supply a variable frequency sinusoidal source

7. lag compensator kit (R1=20kΩ,R2=25kΩ& C=0.2μf)

8. 1:1 CRO probes -2 Nos

CIRCUIT DIAGRAM:



Fig (ii)

THEORY:

A lead compensator speeds up the transient response and increases the margin of stability

of system .it also helps to increase the system error constant through to a limited extent.


The general form of the T.F of lag compensator is



)()(1

1)(G

isnetwork lag a offunction transfer sinusoidal The

1

1

,1,1

1

1

1

1R

1R

)1(1)(

)(E

network-lead Electrical the

1,1

1

)(

c

1212

1221

1

212121

121

1212

12

112

20

jGjGj

jj

s

s

CRRRRs

s

CRRRRs

CRs

CRRRRsCRR

CRsCR

RCsRRR

CsR

CsRCsRR

R

sE

s

For

PZs

s

Ps

ZssG

cc

i

cc

c

cc

REPRESENTATION OF S- PLANE:



Pc Zc

-1/ τ α -1/ τ

PROCEDURE:

6. Connections are made as per the circuit diagram shown in fig (ii).

7. Apply a variable frequency of constant amplitude is applied through frequency

generator to input terminals of the lead compensation network.

8. Connect both the input and output terminals of CRO and record the input and

output sinusoidal signals on the CRO screen.

9. For every value of input frequency, record corresponding phase angle Ф from the

CRO.

10. τ and α values are calculated from the known values R1, R2&C.and determine

Gc(jω)for every value of ω.

11. Gc(jω) is converted into polar form and bode plots are sketched.

TABULAR COLUMN:

S.NO Frequency(Hz) A B Xo Yo Gain=

20log(B/A)

Ф=

Sin-1(-Xo/A)

CALCULATIONS:



1

1

212

n

CR

RRR

MODEL GRAPH:

RESULT:

The electrical lead compensator network was studied experimentally and the bode plots

are plotted.

6. SIMULATION OF TRANSFER FUNCTION USING OP-AMPS

AIM:

To simulate the transfer function using Op-Amps, by using the circuits Integrator,

Non inverting amplifier and summing amplifier.

APPARATUS:

Op- Amps IC -741 -3 NO’S

Capacitor 0.1μF -1 No.

Resistor 10 KΩ -5 No’s



2 KΩ- 2 No.’s

100KΩ- 1 No.

Function Generator, CRO & probes, connecting wires.

THEORY:

1. Op-amp is a operational amplifier, which performs arithmetic operations.

2. Op-amp pin configuration contains 8-pins, generally it is IC 741

3. In 741 second and third pins are inverting and non-inverting pins, it is operated in

conduction mode by giving biasing voltages - VEE and VCC to the 4th and 7th pins

respectively.

4. It is a high gain amplifier.

5. In inverting mode the phase shift between input and output is 1800, where as in

non-inverting mode the input and output signals are in phase.

6. In integrator circuit output is integration of input signal.

CIRCUIT DIAGRAM:

Fig (i)

PROCEDURE:

1. Connect the circuit as per the circuit diagram shown in fig (i).

2. A square wave input is given to both the integrator and non inverting amplifier

circuits.



3. +Vcc and –Vee are applied as +10v and -10v at 7 and 4 pins respectively for

every circuit shown in the circuit diagram.

4. Individual out puts V01 and V02 of integrator and non inverting amplifier are

summed by using a summing amplifier which is shown in figure.

5. The output waveform of integrator, non-inverting amplifier and summing

amplifier are observed and plotted on the graph

THEORITICAL CALCULATIONS:-.

For the integrator circuit,

)01.1(

10

)1(1

R

R-

1

f

1sCsR

K

CsRT

ff

For the Non- inverting amplifier,

.01s)(1

10-2

TT

amplifier summingFor

21

21

12

T

RRT f

MODEL GRAPH:



RESULT:

The transfer function of the op-amp was simulated.

7. STATE SPACE TO TRANSFER FUNCTION

USING MATLAB

AIM:

To determine the transfer function for the given state space representation.



0D 1141C

0

0

1

B

010

001

2105

A

PROGRAM:

The program to convert state space representation to transfer function

A= [-5 -10 -2; 1 0 0; 0 1 0];

B= [1; 0;0];

C=[1 4 11];

D=[0];

[num ,den]=ss2tf (A, B, C, D)

THEORY:

This experiment is done to convert the state space representation into transfer function

model by using MATLAB.

D

A-SI

A]B-C.Adj[SI Function Transfer

0D 1141C

0

0

1

B

010

001

2105

A



2105

114S

1]B-C.Adj[SI .

2105)01()(105)S(S

10

01

2105

A -SI

114

1

1141).(.

1

).(

10551

25

2)210(

)(

10522

55)210(

1

A)-(SI ofmatrix

10

01

2105

A-SI

23

2

232

2

2

2

2

2

2

2

2

2

SSS

S

DASI

FT

sssSS

S

S

S

SSS

S

BASIAdjC

S

S

BASIAdj

SSS

SSS

SSS

ASIAdj

SSS

SSSS

SS

Cofactor

S

S

S

RESULT:

num = 0 1 4 11

den = 1 5 10 2

Hence the transfer function was verified for the given state space representation.

T.F= (S2+4S+11 / S3+5S2+10S+2)



8. PLOTING OF ROOT LOCUS

AIM:

To obtain root locus plot for a given transfer function 1/ (s2-4s+8) by using MATLAB.

PROGRAM: num= [1];

den= [1 -4 8];

rlocus (tf (num, den))

THEORY:

The root locus technique is used for stability analysis. Using the root locus

the range of values of K, for a stable system can be determined. It is also easier to study

the relative stability of the system from the knowledge of location of closed loop poles.

The root locus can be plotted in S-plane by verifying system parameters over the

complete range of values. The roots corresponding to a particular value of the system

parameter can then be located on the locus ors the value of the parameter for a desired

root locus can be determined from root locus.

PROCEDURE:

From the command window open new .M file. Write a program and

save it on to the desktop and come back to the command window. Now type .M file

name and observe the root locus.

THEORETICAL CALCULATIONS:

Given transfer function = 84

12 ss

Characteristic equation is 0842 ss

The roots are (2-j2) & (2+j2)



MODEL GRAPH:

RESULT:

The root locus plot for a given transfer function was verified in MATLAB.

9. STATE SPACE REPRESENTATION OF TRANSFER FUNCTION

USING MATLAB

AIM:

To determine the state space representation for the given transfer function

PROGRAM:

The program to convert transfer function in to state space representation

num = [a b c];

den = [1 p q r];

[A B C D] = tf2ss (num, den)

THEORY:

This experiment is done to convert the state space representation into transfer function

model by using MATLAB.



State space representation

DuCxy

BuAxx

*

is the state space representation of a physical system. The function tt2ss (num, den)

converts the given transfer function into state space representation.

CONVERTION OF T.F INTO STATE SPACE MODEL:

T.F = )(

)(23

2

sU

sY

qsrpss

cbsas

Let,

321

*

1

2

2

3

3

*

12

3

12

*

2

2

23

*

3

)(

)(

x

rxqxpxxtU

rydt

dyq

dt

ydp

dt

ydtU

xdt

yd

xxdt

yd

xxdt

dy

Y

)(

0

0

1

010

001

)(

3

2

1

*

3

*

2

*

1

2

*

3

1

*

2

321

*

1

tu

x

x

xrqp

x

x

x

xx

xx

tUrxqxpxx

Comparing with equation



)(]0[

)(

)(

)(

0

0

1

B

010

001

3

2

1

321

2

2

2

*

tU

x

x

x

cbaY

cxbxaxtY

cydt

dyb

dt

ydatY

cbsastY

rqp

A

then

BuAxx

Comparing with

Y=CX+DU

[0]D cbaC

There fore

[0]D

0

0

1

B

010

001

cbaC

rqp

A

RESULT:

[0]D

0

0

1

B

010

001

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CONTROL SYSTEMS LAB MANUAL - anuraghyd.ac.in€¦ · eee deptartment control systems lab manual...

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