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CHRISTU JYOTI INSTITUTE OF TECHNOLOGY & SCIENCE
Colombonagar,Janagoan,Warangal
ANDHRA PRADESH-506167
2013-14 1st Semester
LABORATORY MANUAL
of
CONTROL SYSTEMS AND SIMULATION
Prepared by
T.Bhargavi
Associate Professor
for
III B.Tech EEE
DEPARTMENT OF
ELECTRICAL & ELECTRONICS ENGINEERING
1
INDEX
Page No
List of experiments as per university
3
List of experiments to be conducted for this
semester
Cycle indicate schedule and the batch size
4
5
7
Guidelines For Laboratory Notebook
Laboratory Practice Safety Rules
Sl. No
9
Experiment Name
1.
Time response of Second order System
10-12
2.
3.
4.
Characteristics of Synchros
Effect of feedback on DC Servo motor.
Transfer function of DC motor
13-17
18-19
5.
6.
Characteristics of Magnetic Amplifier
Lag and lead compensation- magnitude and phase plot.
25-28
29-33
7.
Effect of P, PD ,PI ,PID controller on a second order
system
Characteristics of AC servo motor
PSPICE simulation of Op-Amp based integrator and
differentiator circuits
Stability analysis (Bode, Root Locus, Nyquist) of linear
34-36
8.
9.
10.
20-24
37-40
41-42
43-46
time invariant system using matlab
Additional Experments
11.
Characteristics of Dc Servo Motor
47-49
Time-Domain Analysis Of A Given Circuit Using
Matlab
50-52
12.
2
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY
III Year B.Tech EEE ISem
Academic year 2013-2014
L T/P/D C
0 -/3/- 2
1
(55603)CONTROL SYSTEMS AND SIMULASTION LAB
The following experiments are required to be conducted as compulsory experiments.
Any eight of the following experiments are to be conducted
1. Time response of Second order System
2. Characteristics of Synchros
3. Programmable logic controller – study and verification of truth tables of Logic Gates,
Simple Boolean expressions and application of speed control of motor.
4. Effect of feedback on DC Servo motor.
5. Transfer function of DC motor
6. Effect of P, PD ,PI ,PID controller on a second order system
7. Lag and lead compensation- magnitude and phase plot.
8. Transfer function of DC generator
9. Temperature controller using PID
10. Characteristics of Magnetic Amplifier
11. Characteristics of AC servo motor
Any two Simulation experiments to be conducted.
1. PSPICE simulation of Op-Amp based integrator and differentiator circuits.
2. Linear system analysis (Time domain analysis, Error analysis) using MATLAB.
3. Stability analysis (Bode, Root Locus, Nyquist) of linear time invariant system using
MATLAB.
4. State Space model for classical transfer function using MATLAB verification.
3
Experiments Conducted by the Department:1. Time response of Second order System
2. Characteristics of Synchros
3. Effect of feedback on DC Servo motor.
4. Transfer function of DC motor
5. Effect of P, PD ,PI ,PID controller on a second order system
6. Lag and lead compensation- magnitude and phase plot.
7. Characteristics of Magnetic Amplifier
8. Characteristics of AC servo motor
9. PSPICE simulation of Op-Amp based integrator and differentiator circuits.
10. Stability analysis (Bode, Root Locus, Nyquist) of linear time invariant system using
MATLAB.
Additional Experments
1. Characteristics of Dc Servo Motor
2. Time-Domain Analysis Of A Given Circuit Using Matlab
4
LABORATORY PRACTICE
SAFETY RULES
SAFETY is of paramount importance in the Electrical Engineering Laboratories.
2.Electricity NEVER EXECUSES careless persons. So, exercise enough care and attention
in handling electrical equipment and follow safety practices in the laboratory. (Electricity
is a good servant but a bad master).
3.Avoid direct contact with any voltage source and power line voltages. (Otherwise, any such
contact may subject you to electrical shock)
4.Wear rubber-soled shoes. (To insulate you from earth so that even if you accidentally
contact a live point, current will not flow through your body to earth and hence you will be
protected from electrical shock)
5.Wear laboratory-coat and avoid loose clothing. (Loose clothing may get caught on an
equipment/instrument and this may lead to an accident particularly if the equipment
happens to be a rotating machine)
6.Girl students should have their hair tucked under their coat or have it in a knot.
7.Do not wear any metallic rings, bangles, bracelets, wristwatches and neck chains. (When
you move your hand/body, such conducting items may create a short circuit or may touch a
live point and thereby subject you to electrical shock)
8.Be certain that your hands are dry and that you are not standing on wet floor. (Wet parts of
the body reduce the contact resistance thereby increasing the severity of the shock)
9.Ensure that the power is OFF before you start connecting up the circuit.(Otherwise you will
be touching the live parts in the circuit)
10.Get your circuit diagram approved by the staff member and connect up the circuit strictly
as per the approved circuit diagram.
11.Check power chords for any sign of damage and be certain that the chords use safety
plugs and do not defeat the safety feature of these plugs by using ungrounded plugs.
12.When using connection leads, check for any insulation damage in the leads and avoid
such defective leads.
13.Do not defeat any safety devices such as fuse or circuit breaker by shorting across it.
Safety devices protect YOU and your equipment.
14.Switch on the power to your circuit and equipment only after getting them checked up
and approved by the staff member.
15.Take the measurement with one hand in your pocket. (To avoid shock in case you
accidentally touch two points at different potentials with your two hands)
16.Do not make any change in the connection without the approval of the staff member.
17.In case you notice any abnormal condition in your circuit ( like insulation heating up,
resistor heating up etc ), switch off the power to your circuit immediately and inform the
staff member.
18.Keep hot soldering iron in the holder when not in use.
19.After completing the experiment show your readings to the staff member and switch off
the power to your circuit after getting approval from the staff member.
After completing the load-test, suck out the water in the brake-drum using the plastic
bottle with nozzle and then dry off the drum with a sponge which is available in the
laboratory.(The water, if allowed to remain in the brake-drum, will corrode it)
ammeters and watt-meters in case of over load, an under-rated fuse may not allow one
even to start the experiment)
20. Some students have been found to damage meters by mishandling in the following ways:
Keeping unnecessary material like books, lab records, unused meters etc. causing meters
to fall down the table.
Putting pressure on the meter (specially glass) while making connections or while talking
or listening somebody.
STUDENTS ARE STRICTLY WARNED THAT FULL COST OF THE METER WILL BE
RECOVERED FROM THE INDIVIDUAL WHO HAS DAMAGED IT IN SUCH A MANNER.
Copy these rules in your Lab Record. Observe these yourself and help your friends to observe
I have read and understand these rules and procedures. I agree to abide by these rules and
procedures at all times while using these facilities. I understand that failure to follow these rules and
procedures will result in my immediate dismissal from the laboratory and additional disciplinary
action may be taken.
5
GUIDELINES FOR LABORATORY NOTEBOOK
The laboratory notebook is a record of all work pertaining to the experiment. This record should be
sufficiently complete so that you or anyone else of similar technical background can duplicate
the experiment and data by simply following your laboratory notebook. Record everything directly
into the notebook during the experiment. Do not use scratch paper for recording data. Do not trust
your memory to fill in the details at a later time.
Organization in your notebook is important. Descriptive headings should be used to separate and
identify the various parts of the experiment. Record data in chronological order. A neat, organized
and complete record of an experiment is just as important as the experimental work.
1. Heading:
The experiment identification (number) should be at the top of each page.Your name and date
should be at the top of the first page of each day's experimental work.
2.Object:
A brief but complete statement of what you intend to find out or verify in the experiment
should be at the beginning of each experiment
3.Diagram:
A circuit diagram should be drawn and labeled so that the actual experiment circuitry could
be easily duplicated at any time in the future. Be especially careful to record all circuit changes
made during the experiment.
4.Equipment List:
List those items of equipment which have a direct effect on the accuracy of the data. It may
be necessary later to locate specific items of equipment for rechecks if discrepancies develop in the
results.
5.Procedure:
In general, lengthy explanations of procedures are unnecessary. Be brief. Short
commentaries along side the corresponding data may be used. Keep in mind the fact that the
experiment must be reproducible from the information given in your notebook.
6.Data:
Think carefully about what data is required and prepare suitable
data tables. Record instrument readings directly. Do not use calculated results in place of
direct data; however, calculated results may be recorded in the same table with the direct data.
Data tables should be clearly identified and each data column labeled and headed by the proper units
of measure.
7.Calculations:
Not always necessary but equations and sample calculations are often given to illustrate
the treatment of the experimental data in obtaining the results.
8.Graphs:
Graphs are used to present large amounts of data in a concise visual form. Data to be
presented in graphical form should be plotted in the laboratory so that any questionable data
points can be checked while the experiment is still set up. The grid lines in the notebook can be
used for most graphs. If special graph paper is required, affix the graph permanently into the
notebook. Give all graphs a short descriptive title. Label and scale the axes. Use units of
measure. Label each curve if more than one on a graph.
9.Results:
The results should be presented in a form which makes the interpretation easy. Large
amounts of numerical results are generally presented in graphical form. Tables are generally used
for small amounts of results. Theoretical and experimental results should be on the same graph or
arrange in the same table in a way for easy correlation of these results.
10.Conclusion:
This is your interpretation of the results of the experiment as an engineer. Be brief and
specific. Give reasons for important discrepancies.
6
EXPERIMENT NO.1
TIME RESPONSE OF SECOND ORDER SYSTEM
AIM :To study the Time Response of a Second Order series RLC System to determine the parameters of L
& C from unit step input.
APPARATUS :1.
2.
3.
4.
Second Order System study unit.
CRO
Multimeter
Connecting Leads
BLOCK DIAGRAM :-
CIRCUIT DIAGRAM :-
THEORY :The transfer function which relates input voltage and capacitor voltage is
VC(S) / Vi(S) = 1/ (LC S2 + RC S + 1)
The characteristic equation is
LC S2 + RC S + 1= 0 (or)
S2 + (R/L) S + 1 (L/C) = 0
By comparing with a standard characteristic equation we get,
δ = (R/2) √(C/L)
and
ωn = 1 / √(LC)
Where
δ = Damping Ratio
7
ωn = Undamped natural frequency
PROCEDURE :
Connections are given as per the block diagram.

Adjust the input square wave such that the magnitude of the wave is 1V (p-p).
(Check the square wave in CRO by placing CRO in Channel 1 mode).

observe the time response on the CRO (Channel 2) by varying the resistance by changing the
knob provided on the front panel.

Set the resistance to a fixed value (say 650 Ω). Use millimeter to measure the resistance and
take the corresponding values of Peak Time (TP), Peak Over Shoot (µP) (i.e. Max Peak
Value -1) using trace papers.

Calculate Damping Ratio (δ), Undamped Natural Frequency (ωn) from the following
formulae
[
δ = ln (µP) / √(∏2 + ln (µP)2
ωn = ∏ / TP √(1- δ2)

Calculate the parameters L & C of RLC system using the following formulae
δ = (R/2) √(C/L)

ωn = 1 / √(LC)
and
Now calculate Settling Time (TS), and Damped Frequency (ωd) using the following
formulae
TS = 4 / (δ ωn)
------ (2% Settling Time)
ωd = ωn √(1- δ2)

Repeat Step 4 to 7 for different values of Resistances and tabulate the readings.

Find out average L & C values.
TABLE :Sl.
No.
Resistance
Maximum
Peak
(µP) in V
Peak
Time
(TP) in
ms
Damping
Ratio
(δ)
Undamped
natural
frequency
(ωn) in Hz
1
2
MODEL GRAPH :-
8
L in H
C in μF
Damped
Frequency
(ωd) in Hz
Settling
Time
(TS) in
Ms
RESULT :Studied the Time Response of a Second Order series RLC System and determined the parameters of
L, C and verified the Settling Time (TS) from unit step input.
For R=650Ω, Obtained values of L=
R=800 Ω, Obtained values of L=
& C=
&C=
9
EXPERIMENT NO.2
CHARACTERISTICS OF SYNCHRO
AIM :
1. Study of the operation of a Synchro as a transmitter.
2. Study of the operation of Synchro transmitter and Synchro receiver pair.
3. Study of the operation of Synchro as a torque synchro.
APPARATUS :
1.
2.
3.
4.
5.
Synchro Transmitter
Synchro control Transformer,
Voltmeter (0-200V)
Weights
Connecting Wires
APPARATUS DESCRIPTION :
1.
Synchro Transmitter
a. The structure of most of the synchro Transmitter is similar to that of a
conventional three phase F.H.P.Motor. The stator of a synchro is a cylindrically
slotted and laminated magnetic structure, usually bearing a three phase Y
connected windings which is the secondary of the synchro (Except the differential
& control transformer) in most of the cases the stator laminations are skewed one
slot pitch to eliminate slot lack and the resulting angular errors. The stator
windings is not a three phase winding in usually meaning of the term since all
induced voltages are in time phase.
2.
Syncro Control Transformer
a. In this rotor of control transformer is a cylindrical in shape so air gap is uniform.
This is required to obtain equal impedance throughout the revolution and also it
increases fan out. Output voltage is proportional to cosine of angular
displacement between both the rotor.
3.
Voltmeter
a. An M.I.Voltmeter is used to measure the voltage.
4.
Connecting Wires
a. They are used connect various components of circuit.
CIRCUIT DIAGRAMS :
10
THEORY
The rotor of a Synchro Transmitter is a salient pole dumbbel shaped magnetic structure housing the
primary winding of the transmitter. Voltage is applied to this winding through the sliprings and
brushes. The stator has the secondary coils wound in its skewed slots distributed around its
periphery. Although the stator windings are distributed, they act as if they were positioned at 1200
apart.
Let an Ac voltage Vr(t) = Vr Sinwct be applied to the rotor of the Synchro transmitter. This
voltage causes a flow of magnetizing current in the rotor coil which produces a sinusoidally time
varying flux directed along its axis and distributed nearly sinusoidally in the air gap along the 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 the rotor and stator coil axes and so is the voltage induced in each stator coil.
Let Vs1n Vs2n and Vs3n respectively be the voltages induced in the stator coils S1, S2, S3 with
respect to the neutral. Then, for the rotor position of the synchro transmitter. Where the rotor axis
makes an angle with the axis of the stator coils S2.
Vs1n =
KVrCos(wt +120)Sinwct
Vs2n =
KVrCos(wt ) Sinwct
Vs3n =
KVrCos(wt +240)Sinwct
Vs1s2 =
Vs1s2 =
Vs1n - Vs2n
k3 KvrSin( wt+240) Sinwct
Vs2s3 =
k3 KvrSin( wt+120) Sinwct
Vs3s1 =
k 3 KvrSin(wt ) Sinwct
when wt =
0
Vs1s3 =
0 is known as Electrical Zero
PROCEDURE :
Experiment (a)
1. Connect the supply to R1 and R2 of the transmitter through patch cords.
2. Measure the voltage across S1 and S2, S2 and S3, S1 and S3 respectively at various
positions of the rotor.
11
3. The voltage V/st can be plotted and it can be observed that the three voltages are
symmertrical and displaced by 1200.
Experiment (b)
1. Rotor of the Synchro transmitter to be connected to same supply through patch cords.
2. Stators of the both the Synchros are to be connected as shown in the figure.
3. For various positions of the rotor of the Synchro transmitter, voltage across the rotor of the
receiver can be measured and plot a graph.
4. The voltage signals from the receiver will be sinusoidal.
Experiment (c)
1. Rotor of the both sysnchros are to be connected to same A.C.Supply.
2. Stator of the both synchros are to be connected as shown in Figure.
3. The rotor of the transmitter is rotated through some angle  the alingment in the receiver
will be distrurbed and torque will be exerted.
4. The torque can be measured using the pulley and weight arrangmenet on the receiver shaft.
With increase in the rotation of transmitter rotor, torque developed increases upto a limit.
To measure the torque zero position is to be obtained on both the rotors and rotor of the
transmitter is to be kept at some fixed position. (Hold the rotor manually) and weights are to
be put in two pans say W1 and W2 in such a way as to rotate the rotor of receiver at some
angle.
OBSERVATION:
Experiment (a)
S. No.
 (degrees)
1
0
2
30
3
60
4
90
5
120
6
150
7
180
8
210
9
240
10
270
11
300
12
330
V(S1-S2)
(volts)
V(S2-S3)
(volts)
Experiment (b)
Transmitter
(Rotor
Angle)
Receiver
(Voltage )
MODEL GRAPHS :
12
V(S3-S1)
(volts)
PRECAUTIONS :
1. Apply only 50V a.c
2. Measure output voltage on micro voltmeter using probe.
3. See the suppressed carrier modulated signal on CRO by rotating one of the rotors with some
change in velocity.
4. Check the continuity of connecting wires.
5. Weights should be properly placed.
RESULT :
The Synchro transmitter-control transformer pair gives a voltage signal at the rotor terminals of the
control transformer proportional to the angular difference between the transmitter and control
transformer shaft position.
QUESTIONS :
1. What are the principles of synchro pair?
2. Why the rotor of control transformer is made cylindrical in shape?
3. What is the difference between synchro motor and synchro control transformer?
4. What is Synchro Transmitter?
5. Synchros is a ___________
6. The input to synchro Transmitter is _____________
7. The magnitude of output voltage of the synchro transmitter is function of ___________
8. Synchro transmitter-Control transformer pair acts as _________
9. The rotor of control transformer is made up of __________
10. When the two rotors of synchro pair are at right angle, then the voltage induced in control
transformer is _________
11. The electrical zero of transmitter is __________
13
12. What is the advantage of synchro type transmission over potentiometer transmission is
_______
13. Synchro has an operating angle of _______
APPLICATIONS
Synchros is used as a error detector.
14
EXPERIMENT NO.3
DC POSITOIN CONTROL SYSTEM
AIM: To study the position control system by using DC signals.
APPARATUS: DC position control system units.
OPERATION WITH OUT FEEDBACK (SW1 In off position i.e., Tacho out)
(1). Now slowly advance the input potentiometer P1 in clockwise direction. The O/P potentiometer
along with load will be seen to be following the change in the input potentiometer.
(2). Keep the pot P1 at around 180 degrees position. P2 will be also in the same position.
(3). Now change the input pot in a step fusion by a 60 to 80 degrees. The O/P will be observed to
change in oscillatory mode before it settles in final position. The tendency for oscillations is found
to be dependent on the amplifier gain setting. For high gain there are too many oscillations where
as for low gain oscillations are reduced but with static error.
OPERATION WITH STABILIZING FEEDBACK:
1. Now put the SW1 in lower position.
2. SW2 must be in down position i.e., degeneration mode. Keep P4 in fully anti clock wise
direction.
0
3. Now take the pot P1 to 180 position and effect step input change in one of the directions, O/P
gain indicates oscillations is found to be dependent on the amplifier gain setting. For high gain
there are too many oscillations where as for low gain oscillations are reduced but with static
error.
OPERATION WITH STABILIZING FEEDBACK:
1. Now put the Sw1 in lower position.
2. Sw2 must be in down ward position i.e degeneration mode. Keep P4 in fully anti clock wise
direction.
0
3. Now take the pot P1 to 180 position and effect step input change in one of the directions, O/P
gain indicates oscillations.
4. Now advance the pot P4 in clock wise direction, the O/P now is observed to follow the I/P in a
smooth if P4 pot io too much advance. The o/p in a sluggish fashion indicating over damped
system.
5. Now put switch if P1 disturbed the pot P2 is found to oscillate continuously around the desired
position.
Table: 1
DEGENERATIVE:
S.No I/P
angular
degrees
position Output
angular With stabilizing
position degrees
No
oscillations
1
Table: 2
REGENERATIVE:
S.No I/P angular position
degrees
Remarks
Output
angular With
position degrees
stabilizing
Remarks
Oscillates
around 60
1
Table: 3
15
S.No
I/P angular position
degrees
Output angular With
position
stabilizing
degrees
out Remarks
No
oscillations
1
Result:
16
EXPERIMENT NO.4
TRANSFER FUNCTION OF DC MOTOR
AIM: - To determine the transfer function of armature controlled dc motor by performing load test
on dc motor and speed control by armature voltage control to plot characteristics between back
e.m.f. and angular velocity and armature current Vs torque.
APPARATUS: -
1) Armature controlled DC motor
2) Patch cards
3) Tachometer
FRONT PANEL DETAILS
AC, IN
: Terminals to connect 230V AC mains supply.
MCB
: 2 pole 16A MCB to turn ON / OFF AC supply to the controller.
Armature VA : Potentiometer to vary the armature voltage from 0 – 200V.
ON / OFF
: ON / OFF switch for arm voltage with self start.
0 – 200V DC : 0 – 200V variable DC supply for armature
0 – 230V AC “ 0 – 230V variable AC supply to final inductance eof field coil with NC lamp (AC
Voltage Controller)
CIRCUIT DIAGRAM:
1. LOAD TEST
2. ARMATURE VOTAGE CONTROL
THEORY
The speed of DC motor is directly proportional to armature voltage and inversely proportional to
flux in field winding. In armature controlled DC motor the desired speed is obtained by varying the
armature voltage.
Let
Ra = Armature resistance, Ohms
La = Armature Inductance , Henris
Ia = Armature current, Amps
Va = Armature voltage, Volts
Eb = Back emf,
17
Kt = Torque constant, N-m/A
T = Toque developed by motor, N=m
q = Angular displacmenet of shaft, rad
J = Moment of inertia of motor and load, Kg-m2/rad.
B = Frictional coefficient of motor and load, N-m/rad-sec.
Kb = Back emf constnat, V/(rad-sec)
By applying KVL to the equivallent circuit of armature, we can write,
IaRa + La (dIa/dt) + Eb = Va
Torque of DC motor proportional to the product of flux & current. Since flux is constant.
T α Ia
T = Kt Ia
The differential equation governing the mechanical system of motor is given by
J
d 2
d
B
T
2
dt
dt
The back emf of DC machine is proportional to speed of shaft.
Eb α dθ/dt;
Back emf, Eb = Kb(dθ/dt)
The Laplace transform of various time domain signals involved in this system are
L[Va] = Va(s); L[Eb]=Eb(s); L(T) = T(s); L[Ia] = Ia(s); L[θ]=[s]
on taking Laplace transform of the system differential
Ia(s) + La.s.Ia(s) + Eb(s) = Va(s)
(1)
T(s) = Kt Ia(s)
(2)
Js2θ (s) + Bsθ (s) = T(s)
(3)
Eb(s) = Kb sθ (s)
(4)
on equating equations (2) & (3)
KtIa(s) = (Js2+Bs) θ (s)
I a ( s) 
( Js 2  Bs)
 ( s)
Kt
equation (1) can be written as
(Ra+SLa) Ia(s) + Eb(s) = Va(s)
substitute Eb(s) & Ia(s) in above equation, we get
( Ra  SLa )
( JS 2  BS)
 (S )  Kb S (S )  Va (S )
Kt
 ( Ra  SLa )(JS 2  BS )  K b K t S 

  Va ( S )
Kt


.
the required transfer functions is q(s) / Va(s)
 (s)
Va ( s )

Kt
( Ra  sLa )( Js 2  Bs )  K b K t s
Kt
 Js 2 
sLa
( Ra (
 1) Bs1 
  Kb Kt s
Ra
 Bs 
Kt
Ra B
 ( s)

Va ( s) s[(1  sTa)(1  sTm)  Kb Kt / Ra B]

where , La/Ra = Ta = Electrical Time constant
and J/B = Tm = mechanical time constant
The parameters which determine the transfer function are Kt, Kb, Ri, La, B, J and these
parameters are found by conducting the following tests.
Brake Test
This test is conducted to find torque constant Kt and Back emf constant Kb.
18
It is a direct method and consists of applying a brake to water cooled pulley mounted on the motor
shaft. A belt is wound round the pulley and its two ends are attached to two spring balances S1 and
S2. The tension of the belt can be adjusted with the help of the wheels. Obviously, the force acting
tangentially on the pulley is equal to the difference between the readings of the two spring balances.
S1 and S2 spring balances in Kg.
R is the radius of the brake drum in meters.
N is the speed of the motor in rpm.
Torque T = (S1 – S2) R x 9.81 N-m.
The slope of plot between Eb Vs w gives Kb.
The slope of plot between Torque Vs Ia gives Kt.
SPEED CONTROL BY ARMATURE VOLTAGE CONTROL:
This test is conducted for determines B. The motor is run on no load with a suitable excitation by
connectivity it to a d.c. source. The only torque under no load condition at any constant speed is the
friction. Torque Bw only. The plot between torque and speed gives the B.
PROCEDURE:
I) LOAD TEST ON DC MOTOR: 1. Circuit connections are made as per the circuit diagram.
2. Connect 220V fixed DC supply to the field of DC motor and brake drum belt should be
lossened.
3. Start the motor by applying 0 = 220V variable DC supply from the controller till the motor
rotates at rated speed.
4. Note down meter readings which indicates no load reading.
5. Apply load in steps up to rated current of the motor and note down corresponding I, N, F1 &
F2 readings.
6. Switch off the armature DC supply using armature supply ON / OFF swich and then switch
OFF the MCB.
II) SPEED CONTROL BY ARMATURE VOLTAGE CONTROL:
1. Circuit connections are made as per the circuit diagram. „
2. Connect 220V fixed DC supply to the motor field. Keep the armature control pot at its
maximum position and switch at off position.
3. Switch ON the MCB, Switch on the armature control switch. Vary the armature voltage and
note down the speed and the corresponding meter readings.
4. Repeat the same for different armature voltages.
PRECAUTIONS:
1. Connect the polarities correctly and vary the knobs slowly. Avoid loose connections.
2. Take the readings without parallax errors.
OBSERVATION TABLE:
1.LOAD TEST:
S.No
Speed
(r.p.m)
IA(A)
F1
(Kg)
1
19
F2
(Kg)
T= (F1-F2)x6.5x9.81
N.M.
2. ARMATURE VOLTAGE CONTROL:
S.No
N
(r.p.m)
Ia (A)
V(v) Eb=V-IaRa
1
2
3
4
5
6
IDEAL GRAPHS:
MODEL CALCULATIONS:a).Motor Paramaters
DC motor – 0.5 HP / 220V / 1500 rpm
Arm resistance
Ra = 1.8Ω
Arm Inductance
La = 135mH
Field Resistance
Rf = 650Ω
Field inductance
Lf = 21 H
Moment of intertia J = 0.024 Kg/m2
Friction fo-efficient B = 0.8
TRANSFER FUNCTIONS :
K m1
s 

Va s  S  1
Kb
JR a
K m1 
, 
R aB  KbK t
K bK t
1)
2)
Ra
s  Km 2

; km 2 
TL s  S  1
R aB  KbK t
3)
I a s  K m 3 s m  1

Va s 
s  1
Km 3 
B
J
m 
R aB  KbK t
B
RESULT:
Transfer function of DC motor is calculated.
Kb=
kt=
20
W= 2  N/60
QUESTIONS
1. Why does the speed fall slightly when the D.C. shunt motor is loaded?
2. What will happen if the field current of the D.C. shunt motor gets interrupted?
3. What are the possible errors in the experiment?
4. How will you avoid the breaking arrangements getting heated?
5. Up to what capacity of motor can this type of test be done?
6. Why the motors are not operated to develop maximum power.
7. By applying which law, the direction of rotation of d.c. motor can be determined.
8. The transfer function dc motor with armature control is ____ system.
9. The transfer function dc motor with field control is ____ system.
10. What is order the of the transfer function of DC motor?
11. The motor time constant is given by; ___________
12. In armature control ________ is maintained constant.
13. Armature control is suitable for speeds ________________
APPLICATIONS
The dynamic and steady state performance of the system can be analyzed through this experiment.
21
EXPERIMENT NO.5
CHARACTERISTICS OF MAGNETIC AMPLIFIER.
Series Magnetic Amplifier.
AIM: - To study the characteristics of series magnetic amplifier.
APPARATUS: 1) R.P.S
2) D.M.M---2
3) Rheostat--- (200/ 1A) ---1
4) Connecting wires.
5) Magnetic amplifier kit.
APPARATUS DESCRIPTION
1. Magnetic Amplifier:
Consists of saturable reactor and silicon diode. The saturable reactor has a winding which is
excited with an AC voltage. The second wog is the control wog to which dc is supplied
causing core to saturate during the part of half cycle due to additional magnetization.
2. Ammeter:
To measure the current through windings.
3. DC regulated power supply:
To provide controlled DC voltage.
CIRCUIT DIAGRAM:
THEORY
Magnetic Amplifier consists of saturable reactor and silicon diode.
Saturable Reactor
The basic unit of magnetic amplifier in the saturable reactor. The saturable reactor has a load
winding which is excited with an AC voltage. The excited level in adjusted such that the variations
in flux in the core taken it‟s boundaries between the knee of the BH Curve.
The second winding is the control winding to which dc is supplied causing the core to
saturate during the part of the half cycle due to additional magnetizations.
When no dc is applied to the second winding. The core flux variation are within saturable
limit and hence the current drawn from AC supply by the load winding only be magnetizing current,
since DC voltage is applied at a particular instance in the half cycle.
Under these conditions the importance of the AC winding reduces almost zero. Hence, when a load
is connected in series with load winding, the entire supply.
Feed Back Winding
Introduced to provide negative to positive feedback when the feedback winding is connected in to
the load circuit such that flux produced by the load current passing through feedback winding assists
the flux of the control winding due to DC through it so that the total flux be comes larger than the
increasing the load current this action is called as positive feedback. The effect of positive feedback
is to increase the value of load current at a particular value control current from the without
feedback. Also due to positive feedback the characteristics curve becomes stepper, thus providing
increasing gain but less linearity decrease stability and slower response.
22
In the feedback winding connections are released then the flux due to this winding opposes the flux
of control winding. Thus the control current increases there by increasing the load current. The
feedback flux presents same of this action is called as negative feedback.
PROCEDURE:
1) Connections are made as per the circuit diagram.
2) Load winding LW1 and LW2 are connected in series.
3) Supply voltage is given to the control winding.
4) By varying the control winding voltage, note down the ammeter readings of Ic & Ie.
5) Plot the graph between Ie & Ic for different readings.
OBSERVATION TABLE:
S.No
1
Ic (mA)
IL(mA)
2
3
4
5
6
IDEAL GRAPH:
RESULT
Hence we have studied the characteristics of magnetic amplifier.
Parallel Magnetic Amplifier.
AIM: - To study the characteristics of parallel magnetic amplifier.
APPARATUS: 1) R.P.S
2) D.M.M---2
3) Rheostat--- (200/ 1A)---1
4) Connecting wires.
5) Magnetic amplifier kit.
CIRCUIT DIAGRAM:
23
PROCEDURE: 1) Connections are made as per the circuit diagram.
2) Load winding LW1 and LW2 are connected in parallel.
3) Supply voltage is given to the control winding.
4) By varying the control winding voltage, note down the ammeter readings of Ic & Ie.
5) Plot the graph between Ie & Ic for different readings.
OBSERVATION TABLE:
S.No
1
2
3
4
5
6
7
8
Ic (mA)
IL(mA)
IDEAL GRAPH: -
RESULT:
Hence we have studied the characteristics of magnetic amplifier.
PRECAUTIONS
1. Use the AC voltage available on the panes to excite the magnetic amplifier.
2. Make the use of voltage of 5 V to check the connections of the load winding, the voltage
induced in the control winding should be small.
3. Do not exceed the output winding and the maximum current permissible in the control
winding, load winding is rated at approximate 2 A.
4. Ensure that the load impedance is not less than that the limit permissible which is defined by
the limits on current as stated above.
QUESTIONS
1. What is the working principle of magnetic amplifier.
2. What are the advantage and disadvantages of magnetic amplifier.
3. What is exciting winding
4. What is controlling winding.
5. Define magnetomotive force.
6. Saturable reactors are made up of ___________materials
7. What is Bias winding.
8. What is the effect on gain and stability with negative feedback to magnetic amplifier.
9. What is the effect of positive feedback to magnetic amplifier
10. Magnetic amplifiers for switching purposes employ ____________feedback.
11. What do mean by single ended magnetic amplifier.
12. What is push-pull magnetic amplifier.
13. Write the applications of magnetic amplifier
14. A relay contact uses _______feedback in magnetic amplifier.
15. A pushpull amplifier with positive feedback may be used as___________
16. Define current gain and power gain referred to magnetic amplifier.
24
APPLICATIONS
1.
2.
3.
4.
5.
6.
Measurements of large DC currents.
Controlled device of AC & DC meters.
Alternator voltage regulations.
Relay amplifiers.
Measurements of low DC current.
Servo amplifier.
25
EXPERIMENT NO.6
LEAD, LAG COMPENSATION
AIM: - To determine the transfer function and phase angle to the simple phase lag, lead network
and lag lead network etc.
APPARATUS:
Function generator
Trainer Kit
CIRCUIT DIAGRAM:
1. PHASE LAG COMPENSATOR
PHASE LEAD COMPENSATOR:
3. LEAD – LAG COMPENSATOR
THEORY
Performance Specifications
a) Time-domain performance criterion: These are indicative of the performance of the closed-loop
system in terms of its time response, most commonly the unit step response. Referring to the unit
step response shown in figure the various time domain performance criteria are:
i) Delay time td defined as the time needed for the response to reach 50% of the final value.
ii) Rise time tr the time needed for the response to reach 100% of the final value for the first
time.
iii) Peak time tp, the time taken for the response to reach the first peak of the overshoot.
26
iv) Maximum Overshoot, Mp, given by
Mp 
c(t p )  c()
c ( )
x100 %
(Its value indicates the relative stability of the system)
v) Settling time ts, the time required by the system step response to reach and stay within a
specified tolerance band which is usually taken as +2% or +5%.
vi) Steady state error ess defined as
ess  lim[r (t )  c(t )]
t 
PROCEDURE:
A. Phase Lag compensator
1. Make the connections as shown in fig.
2. Select the components R – 10K; C = 0.1μf. Connect these components so as to rig up phase
circuit
θ = Tan-1 (WRC)
3. Switch on the line supply
4. Check calibration of phase angle by throwing SW2 in (cal) calibration position. If meter
does not indicate 1800. Adjust the calculate potentiometer circuit get 1800.
5. Keep SW3 in lag position.
6. Adjust the in put excitation to 3 volts r.m.s.
7. Now change the audio oscillator out put frequency in the range 20Hz to 100Hz and enter the
results in table.
8. Calculate the theoretical values of T(jw) and θ from the formulae given above
θ=Tan-1 (wT) – Tan-1 (wαT)
9. Plot the graph of T(jw) and θ against the frequency find out the corner frequency.
10. Connect the resistance of 10K & 1K across the output terminals of the lag network.
B. PHASE LEAD COMPENSATOR:
1.
2.
3.
4.
5.
Make connections as shown in fig.
Select the components R = 10KΩ, C = 0.1μF.
Connect these components so as to rig up phase lead circuit.
Switch on the supply
Check calibration of phase angle meter by throwing Sw2 in Cal. Position. If meter does not
indicate 1800, adjust cal. Potentiometer and get 1800 indication.
6. Keep theSW3 in lead position.
7. Repeat steps (5, 6, 7, 8) as the above.
27
8. We may connect a load of 1KΩ or 10kΩ across the network observe the effect of the load on
the frequency response and change in phase shift pattern.
C. LEAD – LAG COMPENSATOR
1.
2.
3.
4.
5.
Make the connections as shown in fig.
Select the components as R1 = 10KΩ, R2 = 10KΩ, C = 0.22μF.
Connect the components n the board so as to rig up to the lead components.
Repeat steps 3 & 4 as done in experiment.
Keep SW3 in load position repeat steps, otherwise we may evaluate the phase angle at 1/C;
w = 1/T;
t & Wm = 1/α.T.
ANALYSYS OF PHASE LEAD COMPENSATOR:
S1
ZC
T
ZC
GS   S 



1
ZC  0
1
S  PC
S
P
C
T ;


The T/F of the N/w
S  1



R
C
V0 S 
1 1


Vi S 
 R2 
 R1C1
S  
 R1  R2 

T = R1C1
R2
1
R1  R2
1
Wm  1
sin  m 
T 
1
1  jWmT
1
G jWm  

1  jWmT

PRECAUTIONS:
1. The components are to be connected with proper polarities.
2. Initially phase angle meter and voltmeter should be calibrated.
MODEL GRAPHS:
1. LEAD COMPENSATOR
2. LAG COMPENSATOR
28
3. LEAD – LAG COMPENSATOR
4.
OBSERVATION TABLE:
TABLE – 1: PHASE LEAD COMPENSATOR
Frequency
Indicated
Phase
Vo
angle
Vo/Vi
Calculated
Phase
angle
TABLE – 2: PHASE LAG COMPENSATOR
Frequency
Indicated
Phase
Vo
angle
Vo/Vi
TABLE – 3: PHASE LAG - LEAD COMPENSATOR
Frequency
Indicated
Phase
Vo
angle
Vo/Vi
29
Calculated
Phase
angle
PRECAUTIONS
1. Component are to be connected with proper polarity.
2. Initially phase angle meter and voltmeter should be calibrated.
RESULT
The bode plot : K = _______, 20 log K = ________, PM = ________
The lag compensator : PM = __________
The lead compensator : PM = __________
QUESTIONS
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Define phase margin
Define gain margin
Explain the purpose of Lag compensator
Explain the purpose of lead compensator
In of the following compensator the pole is placed near to the imaginary axis
Bode plot is ____________ plot
Define phase crossover frequency
Define phase crossover frequency
Phase angle can be measured from____________
If phase margin is positive & gain margin is negative ,comment on the stability.
Define compensators
For systems which are of type –2 or higher, which type of compensator is most suited.
30
EXPERIMENT NO.7
EFFECT OF P, PI, PID CONTROLLER ON
A SECOND ORDER SYSTEM
AIM :To study the steady state performance of an Analog P, PI & PID controller using simulated system.
APPARATUS :PID Controller
Patch Chords
BLOCK DIAGRAM :-
THEORY :A controller is a device introduced in the system to modify the error signal and to produce a control
signal. The controller modifies the transient response of the system.
Proportional Controller (P-Controller): The P-Controller is a device that produce a control signal u(t) which is a proportional to the input
error signal e(t).
U(t)
e(t)
U(t) = Kp e(t)
Kp = Proportional gain Constant
On taking Laplace Transformation of above eq.
U(s) = Kp E(s)
U(s) / E(s) = Kp
--- 1
--- 2
Eq. 1 & 2 gives the output of the P-Controller for input E(s) and transfer function of the PController respectively.
From Eq. 1, we can conclude that the P-Controller amplifies the error signal by an amount of Kp.
Also the Introduction of the controller on the system increases the loop gain by an amount of Kp.
Increase in loop gain improves the steady state tracking accuracy and relative stability and also
make the system less sensitive to parameter variations. The draw back in P-Controller is that it
leads to a constant steady state error.
Proportional plus Integral Controller (PI-Controller): -
31
The PI-Controller is a device that produces a output signal consisting of two terms one is
proportional to error signal and the other is proportional to the integral of error signal.
U(t)
[e(t) + ∫e(t) dt]
U(t) = Kp e(t) + (Kp/Ti) ∫e(t) dt
--- 1
Where Kp = Proportional gain Constant
Ti = Integral Time
On taking Laplace Transformation of above eq. with Zero initial conditions
U(s) = Kp E(s) + (Kp/Ti) (E(s)/s)
U(s) / E(s) = Kp (1+ 1/Tis)
--- 2
--- 3
Eq. 2 gives the output of the PI-Controller for input E(s) and eq. 3 is the transfer function of the PIController respectively.
The advantages of both P-Controller and I-Controller are combined in PI-Controller. The
Proportional action increases the loop gain and makes the system less sensitive to variations of
system parameters. The integral action eliminates or reduces the steady state error. The integral
control action is adjusted by varying the integral time.
Proportional plus Integral plus Derivative Controller (PID-Controller): The PID-Controller is a device that produces a output signal consisting of three terms one is
proportional to error signal and the second is proportional to the integral of error signal and third is
proportional to the derivative of the error signal.
U(t)
[e(t) + ∫e(t) dt + e(t) d/dt]
U(t) = Kp e(t) + (Kp/Ti) ∫e(t) dt + KpTd e(t) d/dt
--- 1
Where Kp = Proportional gain Constant
Ti = Integral Time Constant
Td = Derivative Time Constant
On taking Laplace Transformation of above eq. with Zero initial conditions
U(s) = Kp E(s) + (Kp/Ti) (E(s)/s) + KpTd E(s) s
--- 2
U(s) / E(s) = Kp (1+ 1/Tis + Tds)
--- 3
Eq. 2 gives the output of the PID-Controller for input E(s) and eq. 3 is the transfer function of the
PI-Controller respectively.
PROCEDURE :1. Make the connections as per the block diagram.
2. Set input DC amplitude to 1V.
3. Adjust I, D to Zero.
4.various values of P, measure Vf, Vi and Ve using meter provided on the kit and note down the
readings.
TABLE :P Controller (variable Proportionate gain)
Sl. No.
P
Vi
Vf
Ve
1
2
3
4
32
PI Controller (Const. Proportionate gain and Variable Integral gain)
P=3
Sl. No.
I
Vi
Vf
Ve
1
2
3
4
PID Controller (Const. Proportionate & Integral gain and Variable Differential gain)
P=
Sl. No.
I=
D
Vi
Vf
Ve
1
2
3
4
RESULT :Hence the steady state performance of an Analog P, PI & PID controller has been studied using
simulated system.
33
EXPERIMENT NO. 8
CHARACTERISTICS OF AC SERVOMOTOR
AIM :To study the Speed-Torque and Speed-Back emf characteristics of AC Servomotor.
APPARATUS :AC Servo Motor Kit
Patch Chords
Multimeter
BLOCK DIAGRAM :-
THEORY :1.
AC Servomotor :The motors that are used in automatic control systems are called Servomotors. When the
objective of the system is to control the position of an object then the system is called Servo
Mechanism. The servomotors are used to convert an electrical signal (control Voltage) applied
to them into an angular displacement of the shaft. Then can either operate in a continuous duty
or step duty depending on construction.
34
There are different varieties of servomotors available for control system applications. The
suitability of a motor for a particular application depends on the characteristic of the system, the
purpose of the system and its operating conditions. In general, a servomotor should have the
following features.
1.
2.
3.
4.
5.
6.
Linear relationship between the speed and electric control signal.
Steady state stability.
Wide rage of speed control.
Linearity of mechanical characteristics throughout the entire speed range.
Low mechanical and electrical inertial.
Fast Response.
Depending on the supply required to run the motor, they are broadly classified as DC
Servomotor and AC Servomotor.
An AC Servomotor is basically a 2-Ph induction motor except for certain special design
features. A 2-Ph servomotor differs in the following 2 ways from a normal induction motor
i. The rotor of the servomotor is built with high resistance, so that its X/R ratio is small
which results in linear speed-torque characteristics. But conventional induction motors
will have high value of X/R ratio which results in high efficiency and non-linear speedtorque characteristics.
ii. The excitation voltage applied to two stator windings should have a phase difference of
90˚.
2. Construction of AC Servomotor :The AC Servomotor is basically a 2-Ph induction motor with some special design features. The
stator consists of two pole pairs mounted on the inner periphery of the stator, such that their axes
are at an angle of 90˚ in the space. Each pole pair carries a winding. One winding is called
reference winding and the other is called control winding. The exciting current in the winding
should have a phase displacement of 90˚. The supply used to drive the motor is single phase and
so a phase advancing capacitor is connected tone of the phase to produce a phase difference of
90˚. The rotor construction is usually squirrel cage or drag cup type. The squirrel cage rotor is
made of laminations. The rotor bars are placed on the slots and short circuited at both ends by
end rings. The diameter of the rotor is kept small in order to reduce inertia and to obtain good
accelerating characteristics.
The drag cup construction is employed for very low inertia applications. In this type of
construction the rotor will be in the form of hallow cylinder made of aluminium. The
aluminium cylinder itself acts as short circuited rotor conductors.
The speed-Torque curves of AC Servomotor are non-linear except in the low speed region. In
order to drive a transfer function for the motor, some linearizing approximations are necessary.
A servomotor operates at high speeds, therefore the linear portions of speed-torque curves can
be extended out of the high speed region by use of dashed lines. But even with this
approximation, the resultant curves are still not parallel to each other. This means that for
constant speeds, except near Zero speed, the torque does not vary linearly with respect to input
voltage.
3. Transfer Function of AC Servomotor :Let
Tm = Torque developed by Servomotor
q = angular displacement by servomotor
ω = dθ /dt = Angular velocity
Tl = Torque required by load
J moment of inertia of load and rotor
B= Viscous frictional co-efficient of load and rotor.
K1 = slope of control phase voltage Vs torque characteristics
K2 = slope of speed torque characteristics
Torque developed by motor (Tm) = K1ec - K2 dθ /dt
Load Torque = J (d2θ/dt2) + B (dθ/dt)
35
At equilibrium, the motor torque is equal to load torque (Tm = Tl)
J (d2θ/dt2) + B (dθ/dt) = K1ec - K2 dθ /dt
On taking laplace transform of above eq. with zero initial conditions
J s2 θ(s) + Bs θ(s) = K1Ec (s) – K2S θ(s)
==>
(Js2 +Bs+K2s) θ(s) = K1Ec(s)
θ(s) / Ec(s)
= K1 / (Js2 +Bs+K2s)
= [K1 / (B+K2)] / [s (J/(B+K2))s +1]
= Km / (Tms + 1)
Where Km = K1 / (B+K2) = Motor gain constant
Tm = J/(B+K2) = Motor time constant
Hence the transfer function of AC Servomotor has derived.
PROCEDURE :1. Speed, Back emf (Eb) Characteristics :
Study all the front panel controls and features carefully

Initially keep load switch and servomotor switch in OFF position.

Before switching ON the instrument, keep load control potentiometer P1 and speed control
potentiometer P2 are in fully anti-clockwise (i.e. minimum ) position.

Now switch ON the instrument and also switch ON the servomotor. You can observe that
AC Servomotor will start rotating and the speed will be indicated by the rpm meter on front
panel.

With load switch OFF position, vary the speed of the AC servomotor by rotating speed
control potentiometer P2 in clockwise direction and note down the back emf (Eb) generated
by the DC machine at Tp terminals at different speed. Use digital millimeter to measure
back emf voltage. Tabulate these readings.

Plot the graph Back emf Speed Vs voltage (Eb)
2. Speed, Torque Characteristics :1. Initially keep load switch and servomotor switch in OFF position.
2. Before switching ON the instrument, keep load control potentiometer P1 and speed control
potentiometer P2 are in fully anti-clockwise (i.e. minimum ) position.
3. Now switch ON the instrument and also switch ON the servomotor. You can observe that
AC Servomotor will start rotating and the speed will be indicated by the rpm meter on front
panel.
4. By rotating P2, set control winding voltage (Vc) at 45V. Use digital millimeter to measure
control winding voltage. Note down the speed of Ac servomotor in table. Now keep P1 at
minimum position and switch ON the load switch to apply the load. Note down the back
emf voltage (Eb) from Tp Terminals. Note down the Eb and Ia values.
5. Repeat above step for different values (at least 3) of load control potentiometer. Note down
the corresponding value of Ia, Eb and speed.
36
6. Repeat the above two steps for Vc = 55V and 60V.
TABLE :1.
Speed, Back emf (Eb) Characteristics :Sl.
No.
Speed (N) in rpm
Back emf (Eb) in V
1
2
3
4
5
6
2.
Speed, Torque (T) Characteristics :-
Vc = 50 V
Sl. No.
Sped (N)
in rmp
Back emf
(Eb) in V
Current (Ia)
in A
Power (P) in W
(P = Eb x Ia)
Torque (T) in N-m
= (Px1.019x10-4x60) /
2N
1
2
3
Vc = 60 V
4
1
2
3
Vc = 70 V
4
1
2
3
4
MODEL GRAPHS :-
RESULT :The speed-torque characteristics of an AC Servomotor are studied and the graphs are drawn.
37
EXPERIMENT NO 9
SIMULATION OF TRANSFER FUNCTION USING OPERATIONAL AMPLIFIERS
AIM :To simulate and analyze the given Transfer Function using Operational Amplifiers.
APPARATUS :Simulation kit (Analog Computer & Power supply unit)
power Supply kit
DC Voltmeter (0-10V)
Patch Chords
CIRCUIT DIAGRAM :-
THEORY :Considr the Transfer Function
Y(s) / X(s) = (aS + d ) / (S2 + bS +c)
Y(s) is the output and X(s) is the input. In order to obtain a simulation diagram, above equation can
be written as
(S2 + bS +c) * Y(s) = (aS + d ) * X(s)
As the input X(s) should not be differential, the equation is divided by the highest power of S that
multiplies X(s), then the eq. becomes
Y(s) S + Y(s) b + Y(s) c / S = X(s) a + X(s) d / s
Y(s) S = - Y(s) b - Y(s) c / S + X(s) a + X(s) d / s
= - Y(s) b + X(s) a + 1/S [Y(s) c + X(s) d]
As X(s) is given and assuming Y(s) is available we get the computer set up for the Transfer
Function easily.
Let the forward Transfer Function of unit feedback system is
C(s) / E(S) = Gx(s) = K1 / S(1+S) (1+0.2S)
Here we need to study the I?O relationship for various gains of K1.
Equation for above unit feedback system is
38
0.2D3C + 1.2D2C + DC = K1E
Where E = error = R - C
------ 1
------ 2
Solving the highest order derivative system, we have
0.2D3C = K1E - 1.2D2C – DC
------ 3
By starting with equation 3, the three terms on the RHS connected as inputs to the integrator 1. The
output of the integrator (-0.2D2C) is fed to the integrator 2 and the output of this is 0.2D which is
fed to integrator 3 as input with a gain of 4 to give a output of -0.8C. Two of the inputs to integrator
1 are obtained from the integrator 1 and 2. The sign changer is required to obtain 0.25DC. Eq. 2
can be formed by means of adder 5 using the integrator 3 and R which is obtained from a separate
DC source. The output of adder 5 is negative, which is used to function as input to integrator 1.
PROCEDURE :1. Patch the Analog Computer set up as per circuit diagram (for Input gain of 4 to integrator 1,
use either R3 or R4 through input variable X of integrator 1)
2. Set the value of the gain K1 to 2.
3. For introduction of step input, apply positive voltage between terminals GND and S3 by
using any one of the four power supplies (0 – 10V) provided on the Power supply unit.
4. Set the step input (Vi) at 3V. Now switch on S3. Connect the output voltmeter (can also use
Recorder on the panel) to the output of Integrator 3.
5. Now press the start button and note down the integrator 3 output (Vo) using voltmeter.
6. Similarly adjust K1 = 1, 0.87, 0.5 and note down the voltmeter readings.
TABLE :Sl. No.
Gain of K1
Input (Vi)
Output (Vo)
Error (Vi-Vo)
1
2
3
4
RESULT :Simulation and analysis of Transfer Function using Op-Amps has been done.
39
EXPERIMENT NO.10
ROOT LOCUS PLOT & BODE PLOT USING MATLAB
AIM :To analyse frequency response of a system by plotting Root locus, Bode Plot using MATLAB
software.
APPARATUS :MATLAB 7 Software.
Personal Computer.
PROCEDURE :
1.
2.
3.
4.
5.
6.
Switch on Computer
Click on MATLAB icon.
Open Edit window to write the program.
After completion of program, run it by pressing F5.
Observe the output results.
Compare with theoretical values.
PROGRAM : 1
%Root Locus Plot
Clear all;
Clc;
Disp(„Transfer Function of given system is : \n‟);
num = input („Enter Numerator of the Transfer Function (ex: [1 1]) \ n‟);
Computer asks
“Enter Numerator of the Transfer Function (ex: [1 1]”
[Now enter the numerator (any value, Ex.:[1 4])]
den = input („Enter Denominator of the Transfer Function (ex: [1 1 2 1]) \ n‟);
Computer asks
“Enter Denominator of the Transfer Function (ex: [1 1 2 1])
[Now enter the Denominator (any value, Ex.: [1 2 3 4])]
G = tf(num,den);
Transfer Function :
s+4
-----------------------s^3 + 2s^2 + 3s + 4
Figure(1);
Rlocus(G);
OUT PUT :
Now you will get another window. By clicking on this window you can see the result plot as
shown.
40
Root Locus plot :-
PROGRAM : 2
%Bode Plot
Clear all;
Clc;
Disp(„Transfer Function of given system is : \n‟);
num = input („Enter Numerator of the Transfer Function (ex: [1 1]) \ n‟);
Computer asks
“Enter Numerator of the Transfer Function (ex: [1 1]”
[Now enter the numerator (any value, Ex.:[1 4])]
den = input („Enter Denominator of the Transfer Function (ex: [1 1 2 1]) \ n‟);
Computer asks
“Enter Denominator of the Transfer Function (ex: [1 1 2 1])
[Now enter the Denominator (any value, Ex.: [1 2 3 4])]
G = tf(num,den);
Transfer Function :
s+4
-----------------------s^3 + 2s^2 + 3s + 4
Figure(2);
bode(G);
%figure(3);
%margin(G); It can be used to get Gain Margin, Phase Margin etc
[Gm,Pm,Wpc,Wgc] = margin(G)
Disp(„Phase Cross Over Grequency is : \n‟);
Wpc
Disp(„Gain Cross Over Grequency is : \n‟);
Wgc
Disp(„Phase Margin in degrees is : \n‟);
Pm
Disp(„Gain Margin in db is : \n‟);
GM = 20*log10(Gm)
If (Wgc<Wpc)
Disp(„Closd loop system is stable‟)
elseif (Wgc>Wpc)
41
Disp(„Closd loop system is unstable‟)
else
Disp(„Closd loop system is Marginally stable‟)
end
OUT PUT :
Phase Cross Over Grequency is :
Wpc =
1.7321
Gain Cross Over Grequency is :
Wgc =
2.8009
Phase Margin in degrees is :
Pm =
-42.7323
Gain Margin in db is :
GM =
-12.0412
Closed loop system is unstable.
Bode plot :-
THEORITICAL CALCULATION
1. Phase Margin :
1. for a given Transfer Function G(s), get G(jω) by placing s= jω.
2. Separate Magnitude and Phase terms from G(jω).
3. Equate magnitude of G(jω) to ONE and get ω value, this ω is called Gain Cross Over
Frequency (ωgc)
4. Substitute ωgc in place of G(jω), get the phase angle (φ).
5. Now Phase margin (PM) = 180 + φ
2. Gain Margin :
1. For a given Transfer Function G(s), get G(jω) by placing s= jω.
2. Separate Magnitude and Phase terms from G(jω).
3. Equate imaginary part to ZERO and get ω value, this ω is called Phase Cross Over
Frequency (ωpc)
42
4. Substitute ωpc in real pat, get the corresponding gain (K).
5. Now Gain Margin (GM) = 20 log10 (1/K)
3. Gain Margin :
1. For a given Transfer Function G(s), place K in the numerator and get the characteristic
equation Q(s) = 1 + G(s).
2. Get Q(jω) by placing s = jω.
3. Separate imaginary and real terms from Q(jω).
4. Equate imaginary part to ZERO and get ω values, these values called Imaginary Cross Over
points.
5. Substitute ωpc in real pat and equate real part of G(jω) to ZERO and get the corresponding
gain (K).
6. This gain is called maximum Allowable Gain (Kmax) or Limiting value of the Gain for
stability.
TABLE –
Specification
Gain Margin (GM)
and Gain Cross Over
Frequency (Wgc)
Phase Margin (PM)
and Phase Cross Over
Frequency (Wpc)
Maximum
allowable
gain (Kmax)
Imaginary
Cross over
points
From MATLAB
Theoritical
RESULT :Root Locus Plot and Bode Plot of given Transfer Function has been plotted and verified with
theoretical calculations.
43
ADDITIONAL EXPERIMENTS
1.CHARACTERISTICS OF DC SERVO MOTOR
AIM :-
To study the effect of feedback on DC Servo Motor by its Torque-Speed characteristics
APPARATUS :-
DC Servo Motor Kit
Patch Chords
Multimeter
Connecting Leads
BLOCK DIAGRAM :-
THEORY :The types of DC Servo Motors are (i) Series Motor (ii) Shunt Motor (iii) Permanent Magnet Motor.
A DC Servo Motor can be controlled by varying either the field current or the armature current. DC
Servo Motors offers higher efficiency than that of AC Servo Motors of same size, but radio
interference is a problem in some applications.
Most of the DC Servo Motors used in low power applications are of the PM type. The ease of
controllable speed along with the linear torque-speed characteristics makes the DC Servo Motor
ideal for servo mechanism applications. The torque-speed curve is quite similar to that of the AC
Servo Motor. These motors are available in 6, 12 and 24 V models making them applicable to
solid-state circuitry. By comparison, the DC Servo Motor has some advantages over AC Servo
Motor. The DC Servo Motor inertia is greater than that of the AC Servo motor. This greater inertia
is due to the wound armature and commutator, which produces a heavier rotor. The DC Servo
Motor does not require any standby power whereas the AC Servo Motor continuously draws power
for its main (reference) winding.
Such DC Servo Motors are popular in compact systems such as pneumatic control and robotics
systems and in automatic control machines. DC Servo Motors in some modern servomechanism
may be one of the brush less types, which lend themselves to easy computer control Alone the same
lines, the stepping motor has become a valuable type to be used as a servo motor.
44
PROCEDURE :-

Before switch ON the instrument, please see that armature control potentiometer and field
control potentiometer are at minimum position so that the armature voltage applied to the
armature from zero volts onwards and field voltage applied to the field from 25V onwards.

Switch ON the instrument, observe that the field on indication LED glows, if not then
immediately switch OFF the instrument. Please note that for all DC motors field voltage to
be given initially before applying the armature voltage. Initially DC ammeter and RPM
meter indicates ZERO reading.

Adjust spring balance so that there is minimum load on the DC Servo Motor. Note that you
have to adjust the knob in the anti-clock wise direction to apply the load and clock wise
direction to release the load. You may fix knob at any particular place to apply a fixed load
on the DC Servo Motor.

Connect digital multi meters across the armature winding terminals and field winding
terminals to measure corresponding voltages.

Adjust armature control potentiometer so that Va = 10V and field control potentiometer so
that Vf = 20V.

Note down T1, T2, Armature Current (Ia) and Speed.

Keeping Va = 10V, Vf = 20V, adjust T1 up to 500 gm in suitable steps and note down the
readings as in step 6.

Now repeat the step 7 for Va = 15, 20 and 25 by keeping Vf at 20V.

You may repeat the steps 7 & 8 for Vf = 15V, 10V.
TABLE :Field Voltage (Vf) = 20 V
Va =15 V
Va =10 V
Sl. No.
T1
(gms)
T2
(gms)
T = T1 - T1
1
2
3
1
2
3
45
Torque = T * 3.5
Speed
(rpm)
Ia
(mA)
MODEL GRAPH :-
PRECAUTIONS :1. Potentiometers of Field control and Armature control must be always in minimum position (i.e.
extreme anti-clock wise direction) before switching ON the equipment.
2. Spring balance unit should be properly fixed to the main unit.
3. If field on indication LED is not glowing then immediately switch OFF the instrument and start
again.
RESULT :Hence the effect of Feedback on DC Servomotor has been studied with the help of Torque-sped
characteristics.
46
2.TIME-DOMAIN ANALYSIS OF A GIVEN CIRCUIT
USING MATLAB
AIM :To analyze the RLC circuit for its time-domain specifications and comparing with the theoretical
computations by using MATLAB.
APPARATUS :MATLAB 7 Software.
Personal Computer.
CIRCUIT DIAGRAM :
PROCEDURE :
Switch on Computer
Click on MATLAB icon.
Open Edit window to write the program.
After completion of program, run it by pressing F5.
Observe the output results.
Compare with theoretical values.
PROGRAM : 1
% II order series RLC Circuit Time-Domain specifications
Clear all;
Clc;
%Entering the parameters of RLC Circuit
R = input („Enter the Resistance of RLC Circuit (Ohm) \ n‟);


Now computer prompts like this
“Enter the Resistance of RLC Circuit (Ohm)”
Now enter the value for Resistance (any value – ex : 1)
L = input („Enter the Inductance of RLC Circuit (Henrey) \ n‟);


Now computer prompts like this
“Enter the Inductance of RLC Circuit (Henrey)”
Now enter the value for Inductance (any value – ex : 1)
C = input („Enter the Capacitance of RLC Circuit (farads) \ n‟);

Now computer prompts like this
“ Enter the Capacitance of RLC Circuit (farads)”
 Now enter the value for capacitance (any value – ex : 1)
%Modeling of the RLC Circuit
Num = 1;
Den = [L*C, R*C, 1];
Sys = tf(num,den);
Disp(„Transfer Function of Series RLC circuit is: „);
Sys
47
Transfer Function of Series RLC circuit is:
Transfer Function :
1
------------s^2 + s + 1
%Calculating Time Domain Specifications
[Wn,Zeta] = damp(sys);
Wn = Wn(1);
Zeta = Zeta(1);
Peak = exp(-(pi*Zeta)/sqt(1-Zeta^2))*100;
Tp = pi/(Wn* sqt(1-Zeta^2));
Ts = 4/(Zeta*Wn);
disp(„Time Domain Specifications of given RLC circuit are : \n‟);
Time Domain Specifications of given RLC circuit are :
disp(„Natural Frequency (rad/sec): „);
Wn
Natural Frequency (rad/sec):
Wn =
1.000
disp(„Damping Ratio : „);
Zeta
Damping Ratio :
Zeta =
0.500
disp(„Peak Over Shoot (%) : „);
peak
Peak Over Shoot (%) :
peak =
16.3034
disp(„Peak Time (sec) : „);
peak
Peak Time (sec) :
Tp =
3.6276
disp(„2% Settling Time (Sec) : „);
peak
2% Settling Time (Sec) :
Ts =
8
%Response step input
Figure(1);
Step(sys);
OUT PUT :
Now you will get another window. By clicking on this window you can see the result.
plot as shown
48
THEORITICAL CALCULATION
From the given RLC parameters, calculate Damping Ratio (Zeta or δ) and Natural Frequency (ωn) by
δ = (R/2) √(C/L)
and
Calculate Maximum Peak value (µP) by
µP = e^((- δ∏)/(1- δ2)1/2)
ωn = 1 / √(LC)
Calculate Peak Time (TP) by
2 1/2
P = ∏ / (ωn (1- δ ) )
Calculate Settling Time (Ts) by
Ts = 4 / δ ωn
TABLE –
Damping
Ratio
(Zeta or δ)
Natural
Frequency (ωn)
in rad/sec
Maximum
Peak value
(µP) in %
From
MATLAB
Theoretical
RESULT :-
Hence Time-Domain analysis of a given circuit has been studied.
49
Peak Time
(TP) in Sec
Settling
Time (Ts)
in Sec