Control Systems Laboratory Manual / II EEE, IV SEM
VELS UNIVERSITYSCHOOL OF ENGINEERING
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
LABORATORY MANUALCLASS SEMESTER SUBJECT : II YEAR EEE : IV :
CONTROL SYSTEMS LABORATORYAssistant Professor EEE Department
STAFF IN-CHARGE : V.Arivumani
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM
CONTROL SYSTEMS LABORATORY MANUAL
NAME CLASS SEMESTER ROLL NUMBER
: : : :
REGISTER NUMBER :
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM
INDEXS. No. Date Title of Experiment Page No. Marks
Signature
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM
SYLLABUS EE2257 CONTROL SYSTEM LABORATORY1. 2. 3. 4. 5. 6. 7. 8.
Determination of transfer function of DC Servomotor Determination
of transfer function of AC Servomotor. Analog simulation of Type -
0 and Type 1 systems Determination of transfer function of DC
Generator Determination of transfer function of DC Motor Stability
analysis of linear systems DC and AC position control systems
Stepper motor control system 9. Digital simulation of first order
systems 10. Digital simulation of second order systems P = 45 Total
= 45 DETAILED SYLLABUS 1. Determination of Transfer Function
Parameters of a DC Servo MotorAim To derive the transfer function
of the given D.C Servomotor and experimentally determine the
transfer function parameters Exercise 1. Derive the transfer
function from basic principles for a separately excited DC motor.
2. Determine the armature and field parameters by conducting
suitable experiments. 3. Determine the mechanical parameter by
conducting suitable experiments. 4. Plot the frequency response.
Equipment 1. DC servo motor 2. Tachometer 3. Multimeter 4. Stop
watch 2. : field separately excited loading facility variable
voltage source - 1 No : 1 No : 2 Nos : 1 No
0 0 3 2
Determination of Transfer Function Parameters of AC Servo
MotorAim To derive the transfer function of the given A.C Servo
Motor and experimentally determine the transfer function
parameters
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Control Systems Laboratory Manual / II EEE, IV SEM
Exercise 1. Derive the transfer function of the AC Servo Motor
from basic Principles. 2. Obtain the D.C gain by operating at rated
speed. 3. Determine the time constant (mechanical) 4. Plot the
frequency response Equipment 1. AC Servo Motor 2. Tachometer 3.
Stopwatch 4. Voltmeter : Minimum of 100w necessary sources for main
winding and control winding 1 No : 1 No : 1 No : 1 No
3.
Analog Simulation of Type-0 And Type-1 SystemAim To simulate the
time response characteristics of I order and II order, type 0 and
type-1 systems. Exercise 1. Obtain the time response
characteristics of type 0 and type-1, I order and II order systems
mathematically. 2. Simulate practically the time response
characteristics using analog rigged up modules. 3. Identify the
real time system with similar characteristics. Equipment 1. Rigged
up models of type-0 and type-1 system using analog components. 2.
Variable frequency square wave generator and a normal CRO - 1 No
(or) DC source and storage Oscilloscope - 1 No
4.
Determination of Transfer function of DC GeneratorAim To
determine the transfer function of DC generator Exercise 1. Obtain
the transfer function of DC generator by calculating and gain
Equipment 1. DC Generator 2. Tachometer 3. Various meters
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Control Systems Laboratory Manual / II EEE, IV SEM 4. Stop
watch
5.
Determination of Transfer function of DC MotorAim To determine
the transfer function of DC motor Exercise 1. Obtain the transfer
function of DC motor by calculating and gain Equipment 1. DC Motor
2. Tachometer 3. Various meters 4. Stop watch
6.
Stability Analysis of Linear SystemsAim To analyse the stability
of linear systems using Bode / Root locus / Nyquist plot Exercise
1. Write a program to obtain the Bode plot / Root locus / Nyquist
plot for the given system 2. Access the stability of the given
system using the plots obtained 3. Compare the usage of various
plots in assessing stability Equipment 1. System with MATLAB /
MATHCAD / equivalent software - 3 user license
7.
DC and AC position Control SystemsAim To study the AC and DC
position control system and draw the error characteristics between
set point and error. Exercise 1. To study various position control
systems and calculate the error between set point and output
position 2. To measure outputs at various points (between stages)
Equipment 1. AC and DC position control kit with DC servo motor. 2.
Power transistor 3. Adder
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Control Systems Laboratory Manual / II EEE, IV SEM
8.
Stepper Motor Control SystemAim To study the working of stepper
motor Exercise 1. To verify the working of the stepper motor
rotation using microprocessor. Equipment 1. Stepping motor 2.
Microprocessor kit 3. Interfacing card 4. Power supply
9.
Digital Simulation of First Order SystemAim To digitally
simulate the time response characteristics of first -order system
Exercise 1. Write a program or build the block diagram model using
the given software. 2. Obtain the impulse, step and sinusoidal
response characteristics. 3. Identify real time systems with
similar characteristics. Equipment 1. System with MATLAB / MATHCAD
(or) equivalent software - minimum 3 user license.
10.
Digital Simulation of Second Order SystemsAim To digitally
simulate the time response characteristics of second -order system
Exercise 1. Write a program or build the block diagram model using
the given software. 2. Obtain the impulse, step and sinusoidal
response characteristics. 3. Identify real time systems with
similar characteristics. Equipment System with MATLAB / MATHCAD
(or) equivalent software - minimum 3 user license.
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Control Systems Laboratory Manual / II EEE, IV SEM
LIST OF EXPERIMENTSFIRST CYCLE: 1. Determination of transfer
function of armature controlled DC servomotor. 2. Determination of
transfer function of field controlled DC servomotor. 3.
Determination of transfer function of AC servomotor.4.
Determination of transfer function of separately excited DC
generator.
5. Determination of transfer function of DC motor. 6. DC
position control system. SECOND CYCLE:7. Analog simulation of
Type-0 and Type-1 systems.
8. Digital simulation of first order systems. 9. Digital
simulation of second order systems10. Stability analysis of linear
systems.
11. Stepper motor control system.12. AC position control
system.
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Control Systems Laboratory Manual / II EEE, IV SEM
Expt. No:
Date: DETERMINATION OF TRANSFER FUNCTION OF ARMATURE CONTROLLED
DC SERVO MOTOR
AIM: To determine the transfer function of armature controlled
DC servo motor. APPARATUS / INSTRUMENTS REQUIRED: S. No 1. 2. 3. 4.
5. 6. 7. Description DC servo motor trainer kit DC servo motor
Rheostat Ammeter Voltmeter Stopwatch Patch cords Range 500/1A
(0-1)A (0-100) mA (0300) V (075) V Type Quantity 1 1 1 1 1 1 1 1 As
required
MC MI MC MI
THEORY: In servo applications a DC motor is required to produce
rapid accelerations from standstill. Therefore the physical
requirements of such a motor are low inertia and high starting
torque. Low inertia is attained with reduced armature diameter with
a consequent increase in the armature length such that the desired
power output is achieved. Thus, except for minor differences in
constructional features a DC servomotor is essentially an ordinary
DC motor. A DC servomotor is a torque transducer which converts
electrical energy into mechanical energy. It is basically a
separately excited type DC motor. The torque developed on the motor
shaft is directly proportional to the field flux and armature
current, Tm = Km Ia. The back emf developed by the motor is Eb = Kb
m.. In an armature controlled DC Servo motor, the field winding is
supplied with constant current hence the flux remains constant.
Therefore these motors are also called as constant magnetic flux
motors. Armature control scheme is suitable for large size motors.
ARMATURE CONTROLLED DC SERVOMOTOR:
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Control Systems Laboratory Manual / II EEE, IV SEM
FORMULAE USED: Transfer function of the armature controlled DC
servomotor is given as
(s) / Va(s) = Km / [s (1+sa)(1+sm ) + (Kb Kt /RaB)]where Motor
gain constant, Km = (Kt/RaB) Motor torque constant, Kt = T / Ia
Torque, T in Nm = 9.55 Eb Ia Back emf, Eb in volts = Va Ia Ra Va =
Excitation voltage in volts Back emf constant, Kb = Va / Angular
velocity in rad/ sec = 2N / 60 Armature time constant, a = La / Ra
Armature Inductance, La in H= XLa / 2f XLa in =(Za2 Ra2) Za in =
Va2 / Ia2 Armature resistance,Ra in = Va1 / Ia1 Mechanical time
constant, m = J / B Moment of inertia, J in Kg m2 / rad = W x (60 /
2 )2 x dt/dN N Stray loss, W in Watts = W x [ t2 / (t1-t2) ] Power
absorbed, W in watts = Va Ia t2 is time taken on load in secs t1 is
time taken on no load in secs dt is change in time on no load in
secs dN is change in speed on no load is rpm N is rated speed in
rpm
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Control Systems Laboratory Manual / II EEE, IV SEM
Frictional co-efficient, B in N-m / (rad / sec ) = W / (2N / 60
)2 W = 30 % of Constant loss Constant loss = No load i/p Copper
loss No load I/P = V ( Ia + If ) Copper loss = Ia2 Ra N is rated
speed in rpm
PROCEDURE: 1. To determine the motor torque constant Kt and Back
emf constant Kb: Check whether the MCB is in OFF position in the DC
servomotor trainer kit Press the reset button to reset the over
speed. Patch the circuit as per the patching diagram. Put the
selection button of the trainer kit in the armature control mode.
Check the position of the potentiometer; let it initially be in
minimum position. Switch ON the MCB. Vary the pot and apply rated
voltage of 220 V to the armature of the servomotor. Note the values
of the armature current Ia, armature voltage Va, and speed N. Find
the motor torque constant Kt and Back emf constant Kb using the
above values. Note: If the voltmeter and ammeter in the trainer kit
is found not working external meters of suitable range can be used.
OBSERVATIONS: Armature Voltage,Va (V) Armature Current,Ia (A)
Speed,N (rpm)
S. No.
CALCULATIONS:
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM DETERMINATION
OF TRANSFER FUNCTION OF ARMATURE CONTROLLED DC SERVO MOTOR PATCHING
DIAGRAM TO DETERMINE THE MOTOR TORQUE CONSTANT Kt AND BACK EMF
CONSTANT Kb
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM PROCEDURE: 2.
To determine armature resistance Ra: Check whether the MCB is in
OFF position in the DC servomotor trainer kit Patch the circuit as
per the patching diagram Put the selection button of the trainer
kit in the armature control mode. The field terminal is left
opened. Check the position of the potentiometer; let it initially
be in minimum position. Switch ON the MCB. Vary the pot and apply
rated voltage of 220 V to the armature of the servomotor. Note the
values of the armature current Ia, armature voltage Va. Find the
value of armature resistance Ra using the above values Note: If the
voltmeter and ammeter in the trainer kit is found not working
external meters of suitable range can be used. OBSERVATIONS:
Armature Voltage, Va1 (V) Armature Current, Ia1 (A) Armature
resistance, Ra ()
S. No.
CALCULATIONS:
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM DETERMINATION
OF TRANSFER FUNCTION OF ARMATURE CONTROLLED DC SERVO MOTOR PATCHING
DIAGRAM TO DETERMINE ARMATURE RESISTANCE Ra
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Control Systems Laboratory Manual / II EEE, IV SEM PROCEDURE: 3.
To find armature inductance, La Check whether the MCB is in OFF
position in the DC servomotor trainer kit Patch the circuit as per
the patching diagram Put the selection button of the trainer kit in
the armature control mode. The field terminal is left opened.
Switch ON the MCB. Note the values of the armature current Ia,
armature voltage Va. Find the value of armature inductance La.using
the above values Note: If the voltmeter and ammeter in the trainer
kit is found not working external meters of suitable range can be
used. OBSERVATIONS: S. No. Armature Voltage, Va2 (V) Armature
Current, Ia2 (mA) Armature impedance Za ()
CALCULATIONS:
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM DETERMINATION
OF TRANSFER FUNCTION OF ARMATURE CONTROLLED DC SERVO MOTOR PATCHING
DIAGRAM TO DETERMINE ARMATURE INDUCTANCE, La
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Control Systems Laboratory Manual / II EEE, IV SEM PROCEDURE: 4.
To determine moment of inertia J and frictional co-efficient B:
Check whether the MCB is in OFF position in the DC servomotor
trainer kit Patch the circuit as per the patching diagram Put the
selection button of the trainer kit in the armature control mode
and the DPDT switch in power circuit position. Check the position
of the potentiometer; let it initially be in minimum position.
Switch ON the MCB. Vary the pot and adjust the motor to run at
rated speed. Note the values of armature current Ia, armature
voltage Va, field current If, Speed N. Change the DPDT switch
position from power circuit side to load side, simultaneously
noting the time taken t1 of the motor to come to rest from rated
speed, using a stop watch. Set the potentiometer to minimum
position and change the DPDT switch to power circuit side Connect a
load of 500 Ohms in the load position Vary the pot and adjust the
motor to run at rated speed Change the DPDT switch position from
power circuit side to load side, simultaneously noting the time
taken t2 of the motor to come to rest from rated speed, using a
stop watch. Find the values of moment of inertia J and frictional
co-efficient B using the above values
OBSERVATIONS: S. No. Armature Voltage, Va (V) Armature Current,
Ia (A) Field Current, If (A) Speed, N (rpm)t1 (secs) t2 (secs)
CALCULATIONS:
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM DETERMINATION
OF TRANSFER FUNCTION OF ARMATURE CONTROLLED DC SERVO MOTOR PATCHING
DIAGRAM TO DETERMINE MOMENT OF INERTIA J , FRICTIONAL CO-EFFICIENT
B: ( t1 No load)
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM DETERMINATION
OF TRANSFER FUNCTION OF ARMATURE CONTROLLED DC SERVO MOTOR PATCHING
DIAGRAM TO DETERMINE MOMENT OF INERTIA J , FRICTIONAL CO-EFFICIENT
B: ( t2 load)
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Control Systems Laboratory Manual / II EEE, IV SEM
CALCULATIONS:
RESULT: The transfer function of armature controlled DC
servomotor is determined as
VIVA-VOCE QUESTIONS: 1. 2. 3. 4. 5. Define transfer function.
What is DC servo motor? State the main parts. What is servo
mechanism? Is this a closed loop or open loop system .Explain. What
is back EMF?
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Control Systems Laboratory Manual / II EEE, IV SEM Expt. No:
Date:
DETERMINATION OF TRANSFER FUNCTION PARAMETERS OF FIELD
CONTROLLED DC SERVO MOTOR AIM: To determine the transfer function
of field controlled DC servo motor. APPARATUS / INSTRUMENTS
REQUIRED: S. No 1. 2. 3. 4. 5. 6. 7. Description DC servo motor
trainer kit DC servo motor Rheostat Ammeter Voltmeter Stopwatch
Patch cords Range 500/1A (0-1)A (0-100) mA (0300) V (075) V Type
Quantity 1 1 1 1 1 1 1 1 As required
MC MI MC MI
THEORY: In a field controlled DC Servo motor, the electrical
signal is externally applied to the field winding. The armature
current is kept constant. In a control system, a controller
generates the error signal by comparing the actual o/p with the
reference i/p. Such an error signal is no enough to drive the DC
motor. Hence it is amplified by the servo amplifier and applied to
the field winding. With the help of constant current source, the
armature current is maintained constant. When there is change in
voltage applied to the field winding, the current through the field
winding changes. This changes the flux produced by field winding.
This motor has large Lf / Rf ratio, so time constant of this motor
is high and it cant give rapid responses to the quick changing
control signals. FIELD CONTROLLED MOTOR:
FORMULAE USED: Prepared by V.Arivumani, AP/EEE, Vels University,
Chennai 23
Control Systems Laboratory Manual / II EEE, IV SEM Transfer
function of field controlled DC servo motor is given as, where (s)
/ Vf (s) = Km / s (1+sTf) (1+sTm)
Motor gain constant Km = Ktf / Rf B Motor torque constant Ktf in
N-m / A = T / If Torque T in N-m = 9.55 Eb Ia / N Back EMF Eb in
volts = Va Ia Ra Va = Excitation voltage in volts Armature
resistance,Ra in = Va1 / Ia1 Field resistance,Rf in = Vf1 / If1
Field time constant Tf = Lf / Rf Field Inductance,Lf in H= XLf / 2f
XLf in = (Zf2 Rf2) Zf in = Vf2 / If2 Mechanical time constant Tm =
J / B Moment of inertia J in Kg m2 / rad = W x (60 / 2)2 x dt/dN N
Stray loss, W in watts = W x [ t2 / (t1-t2) ] Power absorbed, W in
Watts = Va Ia t2 is time taken on load in secs t1 is time taken on
no load in secs dt is change in time on no load in secs dN is
change in speed on no load is rpm N is rated speed in rpm
Frictional co-efficient, B in N-m / (rad / sec ) = W / (2N / 60 )2
W = 30 % of Constant loss Constant loss = No load i/p Copper loss
No load I/P = V ( Ia + If ) Copper loss = Ia2 Ra N is rated speed
in rpm
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Control Systems Laboratory Manual / II EEE, IV SEM PROCEDURE: 1.
To determine the motor torque constant Ktf : Check whether the MCB
is in OFF position in the DC servomotor trainer kit Press the reset
button to reset the over speed. Patch the circuit as per the
patching diagram. Put the selection button of the trainer kit in
the field control mode. Check the position of the potentiometer;
let it initially be in minimum position. Switch ON the MCB. Vary
the pot and apply rated voltage of 220V to the armature of the
servomotor. Note the values of the armature current Ia, armature
voltage Va, and speed N. Find the motor torque constant Kt f using
the above values. Note: If the voltmeter and ammeter in the trainer
kit is found not working external meters of suitable range can be
used. OBSERVATIONS: Armature Voltage,Va (V) Armature Current,Ia (A)
Speed,N (rpm)
S. No.
CALCULATIONS:
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM DETERMINATION
OF TRANSFER FUNCTION OF FIELD CONTROLLED DC SERVO MOTOR PATCHING
DIAGRAM TO DETERMINE THE MOTOR TORQUE CONSTANT Ktf
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Control Systems Laboratory Manual / II EEE, IV SEM PROCEDURE: 2.
To determine armature resistance Ra: Check whether the MCB is in
OFF position in the DC servomotor trainer kit Patch the circuit as
per the patching diagram Put the selection button of the trainer
kit in the armature control mode. The field terminal is left
opened. Check the position of the potentiometer; let it initially
be in minimum position. Switch ON the MCB. Vary the pot and apply
rated voltage of 220V to the armature of the servomotor. Note the
values of the armature current Ia, armature voltage Va. Find the
value of armature resistance Ra using the above values Note: If the
voltmeter and ammeter in the trainer kit is found not working
external meters of suitable range can be used. OBSERVATIONS:
Armature Voltage, Va1 (V) Armature Current, Ia1 (A) Armature
Resistance, Ra ()
S. No.
CALCULATIONS:
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM DETERMINATION
OF TRANSFER FUNCTION OF FIELD CONTROLLED DC SERVO MOTOR PATCHING
DIAGRAM TO DETERMINE ARMATURE RESISTANCE Ra
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Control Systems Laboratory Manual / II EEE, IV SEM PROCEDURE: 3.
To determine field resistance Rf: Check whether the MCB is in OFF
position in the DC servomotor trainer kit Patch the circuit as per
the patching diagram Put the selection button of the trainer kit in
the field control mode. The armature terminal is left opened. Check
the position of the potentiometer; let it initially be in minimum
position. Switch ON the MCB. Vary the pot and apply rated voltage
of 220V to the field of the servomotor. Note the values of the
field current If, field voltage Vf. Find the value of field
resistance Rf using the above values Note: If the voltmeter and
ammeter in the trainer kit is found not working external meters of
suitable range can be used. OBSERVATIONS: Field Voltage, Va1 (V)
Field Current, Ia1 (A) Field Resistance, Rf ()
S. No.
CALCULATIONS:
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Control Systems Laboratory Manual / II EEE, IV SEM DETERMINATION
OF TRANSFER FUNCTION OF FIELD CONTROLLED DC SERVO MOTOR PATCHING
DIAGRAM TO DETERMINE FIELD RESISTANCE RF
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Control Systems Laboratory Manual / II EEE, IV SEM PROCEDURE: 4.
To determine Field Inductance, Lf Check whether the MCB is in OFF
position in the DC servomotor trainer kit Patch the circuit as per
the patching diagram Put the selection button of the trainer kit in
the field control mode. The armature terminal is left opened.
Switch ON the MCB. Note the values of the field current If2, field
voltageVf2. Find the value of field inductance Lf.using the above
values Note: If the voltmeter and ammeter in the trainer kit is
found not working external meters of suitable range can be used.
OBSERVATIONS: S. No. Field Voltage, Vf2 (V) Field Current, If2 (mA)
Field Impedance Zf ()
CALCULATIONS:
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Control Systems Laboratory Manual / II EEE, IV SEM DETERMINATION
OF TRANSFER FUNCTION OF FIELD CONTROLLED DC SERVO MOTOR PATCHING
DIAGRAM TO DETERMINE FIELD INDUCTANCE, LF
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Control Systems Laboratory Manual / II EEE, IV SEM PROCEDURE: 5.
To determine moment of inertia J and frictional co-efficient B:
Check whether the MCB is in OFF position in the DC servomotor
trainer kit Patch the circuit as per the patching diagram Put the
selection button of the trainer kit in the armature control mode
and the DPDT switch in power circuit position. Check the position
of the potentiometer; let it initially be in minimum position.
Switch ON the MCB. Vary the pot and adjust the motor to run at
rated speed. Note the values of armature current Ia, armature
voltage Va, field current If, Speed N. Change the DPDT switch
position from power circuit side to load side, simultaneously
noting the time taken t1 of the motor to come to rest from rated
speed, using a stop watch. Set the potentiometer to minimum
position and change the DPDT switch to power circuit side Connect a
load of 500 Ohms in the load position Vary the pot and adjust the
motor to run at rated speed Change the DPDT switch position from
power circuit side to load side, simultaneously noting the time
taken t2 of the motor to come to rest from rated speed, using a
stop watch. Find the values of moment of inertia J and frictional
co-efficient B using the above values
OBSERVATIONS: S. No Armature Voltage, Va (V) Armature Current,
Ia (A) Field Current, If (A) Speed, N (rpm)t1 (secs) t2 (secs)
CALCULATIONS:
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Control Systems Laboratory Manual / II EEE, IV SEM
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Control Systems Laboratory Manual / II EEE, IV SEM DETERMINATION
OF TRANSFER FUNCTION OF FIELD CONTROLLED DC SERVO MOTOR PATCHING
DIAGRAM TO DETERMINE MOMENT OF INERTIA J , FRICTIONAL CO-EFFICIENT
B: ( t1 No load)
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM DETERMINATION
OF TRANSFER FUNCTION OF ARMATURE CONTROLLED DC SERVO MOTOR PATCHING
DIAGRAM TO DETERMINE MOMENT OF INERTIA J , FRICTIONAL CO-EFFICIENT
B: ( t2 load)
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Control Systems Laboratory Manual / II EEE, IV SEM
CALCULATIONS:
RESULT: The transfer function of field controlled DC servomotor
is determined as
VIVA-VOCE QUESTIONS: 1. What are the main parts of a DC servo
motor? 2. Name the two types of servo motor. 3. State the
advantages and disadvantages of a DC servo motor. 4. Give the
applications of DC servomotor. 5. What is servo mechanism? 6. What
do you mean by field controlled DC servo motor?
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Control Systems Laboratory Manual / II EEE, IV SEM Expt. No:
Date: DETERMINATION OF TRANSFER FUNCTION OF AC SERVO MOTOR AIM: To
derive the transfer function of the given AC Servomotor. APPARATUS
/ INSTRUMENTS REQUIRED: S. No 1. 2. 3. 4. 5. Description AC servo
motor trainer kit AC servo motor Ammeter Voltmeter Patch cords
Range (0-1) A (0-100) mA (0300) V (075) V Type MC MI MC MI Quantity
1 1 1 1 1 1 As required
THEORY: An AC servo motor is basically a two phase induction
motor with some special design features. The stator consists of two
pole pairs (A-B and C-D) mounted on the inner periphery of the
stator, such that their axes are at an angle of 90o in space. Each
pole pair carries a winding, one winding is called reference
winding and other is called a control winding. The exciting current
in the winding should have a phase displacement of 90o. The supply
used to drive the motor is single phase and so a phase advancing
capacitor is connected to one of the phase to produce a phase
difference of 90o.The rotor construction is usually squirrel cage
or drag-cup type. 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 hollow cylinder made of aluminium. The
aluminium cylinder itself acts as short-circuited rotor conductors.
Electrically both the types of rotor are identical.
WORKING PRINCIPLE :The stator windings are excited by voltages
of equal magnitude and 90o phase difference. These results in
exciting currents i1 and i2 that are phase displaced by 90o and
have equal values. These currents give rise to a rotating magnetic
field of constant magnitude. The direction of rotation depends on
the phase relationship of the two currents (or voltages). This
rotating magnetic field sweeps over the rotor conductors. The rotor
conductor experience a change in flux and so voltages are induced
rotor conductors. This voltage circulates currents in the
short-circuited rotor conductors and currents create rotor flux.
Due to the interaction of stator & rotor flux, a mechanical
force (or torque) is developed on the rotor and so the rotor starts
moving in the same direction as that of rotating magnetic
field.
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Control Systems Laboratory Manual / II EEE, IV SEM
GENERAL SCHEMATIC OF AC SERVOMOTOR:
FORMULAE USED: Transfer function, Gm (s) = Km / (1+ sm) Where
Motor gain constant, Km = K / FO + F K is T / C FO is T / N Torque,
T is 9.81 X R (S1 S2) R is radius of the rotor in m Frictional
co-efficient, F = W / (2N / 60)2 Frictional loss, W is 30 % of
constant loss in Watts Constant loss in watts = No load input
Copper loss No load i/p = V (IR+IC) V is supply voltage, V IR is
current through reference winding, A IC is current through control
winding, A Copper loss in watts = IC2 RC RC = 174 N is rated speed
in rpm Motor time constant, m = J / FO + F Moment of inertia J is
d4 L R / 32 d is diameter of the rotor in m ( Given d =39.5 mm) LR
is length of the rotor in m (Given L R =76 mm) is density = 7.8 X
102 gm / m
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Control Systems Laboratory Manual / II EEE, IV SEM
PROCEDURE: 1. 1. 2. 3. 4. 5. 6. DETERMINATION OF FRICTIONAL
CO-EFFICIENT, F Check whether the MCB is in OFF position. Patch the
circuit using the patching diagram. Switch ON the MCB Vary the
control pot to apply rated supply voltage Note the control winding
current, reference winding current, supply voltage and speed. Find
the frictional co-efficient using the above values
OBSERVATIONS: Supply Voltage V (V) Control winding Current Ic
(A) Reference Winding Current Ir (A) Speed N (rpm)
S. No.
CALCULATIONS:
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Control Systems Laboratory Manual / II EEE, IV SEM DETERMINATION
OF TRANSFER FUNCTION OF AC SERVO MOTOR PATCHING DIAGRAM TO
DETERMINE FRICTIONAL CO-EFFICIENT F:
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Control Systems Laboratory Manual / II EEE, IV SEM PROCEDURE: 2.
To determine the motor gain constant KmDETERMINATION OF FO FROM
TORQUE - SPEED CHARACTERISTICS:
1. 2. 3. 4. 5. 6.
Check whether the MCB is in OFF position. Patch the circuit
using the patching diagram. Set the control pot in minimum
position. Check whether the motor is in no load condition Switch ON
the MCB Vary the control pot and apply rated voltage to the
reference phase winding and control phase winding. Note down the no
load speed. 7. Apply load in steps. For each load applied note down
the speed and spring balance readings. ( Take 3 or 4 sets of
readings) 8. Reduce the load fully and allow the motor to run at
rated speed. 9. Repeat steps 7 and 8 for 75 % control winding
voltage. 10. Draw the graph between speed and torque, the slope of
the graph gives FO. OBSERVATIONS: Control voltage Vc1 = Spring
Balance Speed Torque values N T S1 S2 (Nm) (rpm) (kg) (kg) Control
voltage Vc2 = Spring Balance Torque Speed values T N S1 S2 (rpm)
(Nm) (kg) (kg)
S. No
MODEL GRAPH: TORQUE - SPEED CHARACTERISTICS
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Control Systems Laboratory Manual / II EEE, IV SEM
DETERMINATION OF K FROM TORQUE - CONTROL VOLTAGE
CHARACTERISTICS: 1. Check whether the MCB is in OFF position. 2.
Patch the circuit using the patching diagram. 3. Set the control
pot in minimum position. 4. Check whether the motor is in no load
condition 5. Switch ON the MCB 6. Vary the control pot and apply
rated voltage to the reference phase winding and control phase
winding. Note down the no load speed. 7. Load the motor gradually;
the speed of the motor will decrease. Vary the control pot and
increase the control winding voltage till the speed obtained at no
load is reached. Note down control voltage and spring balance
readings. 8. Repeat step 7 for various speeds and tabulate. (for
1000 rpm) 9. Plot the graph between torque and control winding
voltage. The slope of the graph gives the value of K. OBSERVATIONS:
Control Voltage Vc (V) Speed N1 = Spring Balance values S1 S2 (kg
kg Torque T Nm Speed rpm Speed N2 = Spring Balance values S1 S2 Kg
Kg Control Voltage Vc V
S. No
MODEL GRAPH: TORQUE - CONTROL VOLTAGE CHARACTERISTICS
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Control Systems Laboratory Manual / II EEE, IV SEM
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
44
Control Systems Laboratory Manual / II EEE, IV SEM DETERMINATION
OF TRANSFER FUNCTION OF AC SERVO MOTOR PATCHING DIAGRAM TO
DETERMINE MOTOR GAIN CONSTANT KM:
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Control Systems Laboratory Manual / II EEE, IV SEM
CALCULATIONS:
RESULT: The transfer function of AC servomotor is determined
as
VIVA-VOCE QUESTIONS: 1. What are the main parts of an AC
servomotor? 2. State the advantages and disadvantages of an AC
servo motor. 3. Give the applications of AC servomotor. 4. What do
you mean by servo mechanism? 5. What are the characteristics of an
AC servomotor?
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Control Systems Laboratory Manual / II EEE, IV SEM Expt. No:
DETERMINATION OF TRANSFER FUNCTION OF SEPARATELY EXCITED DC
GENERATOR AIM: To obtain the transfer function of separately
excited DC generator on no load and loaded condition. APPARATUS /
INSTRUMENTS REQUIRED: S. No Description Range Type Quantity
Date:
THEORY: Derivation of transfer function of separately excited DC
generator is as follows, Applying KVL to the field side, ef = Rf if
+ Lf (dif / dt) Applying KVL to the armature side, eg = Ra ia + La
(dia / dt) + RL ia VL = RL ia Also since eg if , let eg = Kg if
Taking Laplace transform of equation (1) we get Ef (s) = Rf If(s) +
sLf If(s) Ef (s) = If (s) [Rf + sLf] If (s) = Ef (s) / [Rf + sLf]
(5) (4) (2) (3) (1)
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Control Systems Laboratory Manual / II EEE, IV SEM
Taking Laplace transform of equation (2) we get Eg (s) = Ra
Ia(s) + sLa Ia(s) + RL Ia(s) Eg (s) = Ia(s) [Ra + sLa + RL] Taking
Laplace transform of equations (3) and (4) we get VL(s) = RL Ia( s)
Therefore, Ia( s) = VL(s) / RL Eg(s) = Kg If(s) Substituting.
equations (7) and (8) in equation (6) we get Kg If(s) = [Ra + sLa +
RL] [VL(s) / RL] Substituting the value of If (s) in the above
equation we get Kg Ef (s) / [Rf + sLf] = [Ra + sLa + RL] [ VL(s) /
RL] Hence transfer function, VL(s) / Ef (s) = Kg RL / {[Rf + sLf]
[Ra + sLa + RL]} For unloaded condition, Ia = 0 Therefore transfer
function VL(s) / Ef (s) = Kg / [Rf + sLf] For loaded condition Lf =
(Zf2 Rf2) / 2f La = (Za2 Ra2) / 2f Transfer function VL(s) / Ef (s)
= Kg RL / [Rf (Ra + RL) (1+sf) (1 + sa)] where f = Lf / Rf and a =
La / (Ra + RL) FORMULAE USED: Transfer function of DC generator, On
no load condition: VL(s) / Ef (s) = Kg / [Rf + sLf] where Kg is
gain constant Rf is field resistance in Ohms Lf is field inductance
in Henry On loaded condition: VL(s) / Ef (s) = Kg RL / [Rf (Ra +
RL) (1+sf) (1 + sa)] where Kg is gain constant Field time constant
f = Lf / Rf Rf is field resistance in Ohms Lf is field inductance
in Henry Armature time constant a = La / (Ra + RL) Ra is armature
resistance in Ohms La is armature inductance in Henry Prepared by
V.Arivumani, AP/EEE, Vels University, Chennai
(6)
(7) (8) (9)
(10) (11)
(12)
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Control Systems Laboratory Manual / II EEE, IV SEM
PROCEDURE: 1. To determine the gain constant Kg : No load or
open circuit characteristics: 1. Connections are made as shown in
the circuit diagram 2. The motor field rheostat should be in
minimum resistance position and the generator field rheostat should
be in maximum resistance position or minimum potential position
while switching ON and switching OFF the supply side DPST switch.
3. Ensure that the DPST switch on the load side is open. 4. Switch
ON the supply DPST switch. 5. Using the 3- point starter the DC
motor is started and it is brought to rated speed by adjusting the
motor field rheostat. 6. Keeping the DPST switch on the load side
open, the generated voltage Eg and field current If of generator is
noted down by varying the generator field rheostat. 7. The above
step is repeated till 125 % of rated voltage is reached. 8. A graph
is plotted between Eg and If taking If along x- axis. A tangent to
the linear portion of the curve is drawn from the origin and slope
of this line gives Kg. OBSERVATIONS: S. No. Field current, If (A)
Induced Voltage, Eg (V)
MODEL GRAPH:
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Control Systems Laboratory Manual / II EEE, IV SEM
CIRCUIT DIAGRAM: To determine gain constant, Kg:
CALCULATIONS:
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Control Systems Laboratory Manual / II EEE, IV SEM
Load characteristics: 1. Connections are made as shown in the
circuit diagram 2. The motor field rheostat should be in minimum
resistance position and the generator field rheostat should be in
maximum resistance position or minimum potential position while
switching ON and switching OFF the supply side DPST switch. 3.
Ensure that the DPST switch on the load side is open. 4. Switch ON
the supply DPST switch 5. The generator is brought to its rated
voltage by varying the generator field rheostat. 6. The DPST switch
on the load side is closed, and the load is varied for convenient
steps of load current up to 120 % of its rated capacity and the
voltmeter VL and ammeter Ia readings are observed. On each loading
the speed should be maintained at rated speed. 7. A graph is
plotted between VL and IL taking IL on x- axis. The slope of the
graph gives Kg. OBSERVATIONS: S. No. Terminal Voltage, VL (V) Load
Current, IL (A)
MODEL GRAPH:
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Control Systems Laboratory Manual / II EEE, IV SEM PROCEDURE: 2.
To determine field Inductance Lf : 1. Connections are made as per
the circuit diagram. 2. Auto transformer is varied in steps for
different voltages and corresponding voltmeter and ammeter readings
are noted down. 3. Field impedance Zf is calculated as V/I and the
average value of Zf is obtained. 4. Field resistance (Rf) is
measured using multimeter. 5. Field inductance (Lf) can be
calculated using formula Lf = (Zf2 Rf2) / 2f CIRCUIT DIAGRAM:
OBSERVATIONS: S. No Field Voltage, V (V) Field Current, I (A)
Field Impedence, Zf (Ohms)
CALCULATIONS:
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Control Systems Laboratory Manual / II EEE, IV SEM PROCEDURE: 3.
Determination of armature inductance La : 1. Connections are made
as per the circuit diagram. 2. Auto transformer is varied in steps
for different voltages and corresponding voltmeter and ammeter
readings are noted down. 3. Armature impedance Za is calculated as
V/I and the average value of Za is obtained. 4. Armature resistance
Ra is measured using multimeter. 5. Armature inductance La can be
calculated using formula, La = (Za2 Ra2) / 2f CIRCUIT DIAGRAM:
OBSERVATIONS: S. No Armature Voltage, V (V) Armature Current, I
(A) Armature Impedence, Za (Ohms)
CALCULATIONS:
CALCULATIONS: Prepared by V.Arivumani, AP/EEE, Vels University,
Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM
RESULT: The transfer function of separately excited DC generator
is determined as
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Control Systems Laboratory Manual / II EEE, IV SEM Expt. No:
Date: DETERMINATION OF TRANSFER FUNCTION OF DC MOTOR AIM: To obtain
the transfer function of field controlled DC motor. APPARATUS /
INSTRUMENTS REQUIRED: S. No Description Range Type Quantity
THEORY:
FIELD CONTROLLED MOTOR:
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Control Systems Laboratory Manual / II EEE, IV SEM
FORMULAE USED: Transfer function of field controlled DC motor,
(s) / Vf (s) = Km / [s (1+sf) (1 + sm)] where Motor gain constant,
Km = Ktf / (BRf) Ktf is motor torque constant Torque, T is 9.81 X R
(S1 S2) R is radius of the brake drum in m R = circumference of the
brake drum/ (2 ) B is viscous co-efficient of friction Rf is field
resistance in Ohms Field time constant f = Lf / Rf Rf is field
resistance in Ohms Lf is field inductance in Henry Lf = (Zf2 Rf2) /
2f Zf is field impedence in Ohms Rf is field resistance in Ohms
Mechanical time constant m = J/B Moment of inertia J = Pav /
[22(N12 N22 )((1/t1)-(1/t2))] Average power delivered to the load,
Pav= (V1I1 + I12 Ra + V2I2 + I22 Ra) / 2 Ra is armature resistance
in Ohms La is armature inductance in Henry t2 is time taken on load
in secs t1 is time taken on no load in secs Viscous Co-efficient of
friction, B = Pstray / (N1 + N2)2 Stray loss, Pstray = [22(N12 N22
)] J / t1 PROCEDURE:
Prepared by V.Arivumani, AP/EEE, Vels University, Chennai
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Control Systems Laboratory Manual / II EEE, IV SEM 1. To
determine motor torque constant, Ktf : 1. Connections are made as
shown in the circuit diagram 2. The armature current Ia of the
motor is set to some value by adjusting the armature circuit
resistance. This value of Ia is maintained constant throughout the
experiment. 3. The field current If is varied in steps by adjusting
the field rheostat and for each value of If the brake drum is
adjusted such that it just fails to rotate. The corresponding
readings of ammeter and spring balances are noted. 4. The value of
torque for each value of If is calculated 5. A graph is plotted
between torque T and field current IF taking IF along x-axis. The
slope of the graph gives the value of Ktf OBSERVATIONS: S. No.
Armature current Ia (A) Field current If (A) Spring balance
readings S1 S2 (kg) (kg) Torque T (Nm)
MODEL GRAPH:
CIRCUIT DIAGRAM: Prepared by V.Arivumani, AP/EEE, Vels
University, Chennai
57
Control Systems Laboratory Manual / II EEE, IV SEM
CALCULATIONS:
PROCEDURE 2. To determine field Inductance Lf : Prepared by
V.Arivumani, AP/EEE, Vels University, Chennai
58
Control Systems Laboratory Manual / II EEE, IV SEM
1. Connections are made as per the circuit diagram. 2. Auto
transformer is varied in steps for different voltages and
corresponding voltmeter and ammeter readings are noted down. 3.
Field impedance Zf is calculated as V/I and the average value of Zf
is obtained. 4. Field resistance (Rf) is measured using multimeter.
5. Field inductance (Lf) can be calculated using formula Lf = (Zf2
Rf2) / 2f CIRCUIT DIAGRAM:
OBSERVATIONS: S. No. Field Voltage, V (V) Field Current, I (A)
Field Impedence, Zf ()
CALCULATIONS:
PROCEDURE:
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Control Systems Laboratory Manual / II EEE, IV SEM 3. To
determine moment of inertia J and Viscous friction Co-efficient B:
1. Connections are made as shown in the circuit diagram 2. The
field current of the motor is set to some value by adjusting the
field resistance. 3. DPDT switch is thrown to position (1,11) and
the motor is made to run at a speed N1 (1700 rpm) by adjusting the
armature rheostat. 4. DPDT switch is opened from position (1,11)
and the stop watch is started simultaneously. The time taken t1 for
the speed to drop from N1(1700 rpm) to N2 ( 1300 rpm) is noted. 5.
Again the DPDT switch is thrown to position (1,11) and the motor is
made to run at a speed greater than N1 (1700 rpm) by adjusting the
armature rheostat. 6. DPDT switch is thrown to position (2,21) and
the stop watch is started when the motor speed reaches N1 (1700
rpm). The time taken t2 for the speed to drop from N1 (1700 rpm) to
N2( 1300 rpm) is noted. Simultaneously the readings of the ammeter
and voltmeter corresponding to N1 and N2 are noted. OBSERVATIONS:
S. No. N1 (rpm) t1 (Sec) V1 (V) I1 (A) N2 (rpm) T2 (Sec) V2 (V) I2
(A)
CALCULATIONS:
CIRCUIT DIAGRAM:
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Control Systems Laboratory Manual / II EEE, IV SEM
CALCULATIONS:
CALCULATIONS:
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Control Systems Laboratory Manual / II EEE, IV SEM
RESULT: The transfer function of field controlled DC motor is
determined as
Expt. No: DC POSITION CONTROL SYSTEM
Date:
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Control Systems Laboratory Manual / II EEE, IV SEM
AIM: To study the characteristics of a DC position control
system. APPARATUS / INSTRUMENTS REQUIRED:i)
DC position control kit and Motor unit Multimeter
THEORY: A DC position control system is a closed loop control
system in which the position of the mechanical load is controlled
with the position of the reference shaft. A pair of potentiometers
acts as error-measuring device. They convert the input and output
positions into proportional electric signals. The desired position
is set on the input potentiometer and the actual position is fed to
feedback potentiometer. The difference between the two angular
positions generates an error signal, which is amplified and fed to
armature circuit of the DC motor. The tachogenerator attached to
the motor shaft produces a voltage proportional to the speed which
is used for feedback. If an error exists, the motor develops a
torque to rotate the output in such a way as to reduce the error to
zero. The rotation of the motor stops when the error signal is
zero, i.e., when the desired position is reached. PROCEDURE: 1. The
input or reference potentiometer is adjusted nearer to zero
initially( R). 2. The command switch is kept in continuous mode and
some value of forward gain K A is selected. 3. For various
positions of input potentiometer ( R) the positions of the response
potentiometer ( 0) is noted. Simultaneously the reference voltage
(VR) measured between the terminals VR & E and the output
voltage (VO) measured between the terminals VO & E are noted.
4. A graph is plotted with 0 along y-axis and R along x-axis.
OBSERVATIONS:
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Control Systems Laboratory Manual / II EEE, IV SEM Reference
angular position, R (degrees) KA = KA = Output angular position, O
(degrees) KA = KA = Reference Voltage, Vr (V) KA = KA = Output
VoltageVO (V) KA = KA =
S. No
MODEL GRAPH:
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Control Systems Laboratory Manual / II EEE, IV SEM
DC POSITION CONTROL SYSTEM
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Control Systems Laboratory Manual / II EEE, IV SEM
RESULT: The DC position control system characteristics are
studied and corresponding graphs are drawn.
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Control Systems Laboratory Manual / II EEE, IV SEM Expt. No.
Date: ANALOG SIMULATION OF TYPE 0 and TYPE 1 SYSTEMS AIM: To study
the time response of first and second order type 0 and type- 1
systems. APPARATUS / INSTRUMENTS REQUIRED: 1. Linear system
simulator kit 2. CRO 3. Patch cords FORMULAE USED: Damping ratio, =
(ln MP)2 / (2 +(ln MP)2) Where MP is peak percent overshoot
obtained from the time response graph Undamped natural frequency, n
= / [tp (1 - 2)] where tp is the peak time obtained from the time
response graph Closed loop transfer function of the type 0 second
order system is C(s)/R(s) = G(s) / [1 + G(s) H(s)] where H(s) = 1
G(s) = K K2 K3 / (1+sT1) (1 + sT2) where K is the gain K2 is the
gain of the time constant 1 block =10 K3 is the gain of the time
constant 2 block =10 T1 is the time constant of time constant 1
block = 1 ms T2 is the time constant of time constant 2 block = 1
ms Closed loop transfer function of the type 1-second order system
is C(s)/R(s) = G(s) / [1 + G(s) H(s)] where H(s) = 1 G(s) = K K1 K2
/ s (1 + sT1) where K is the gain K1 is the gain of Integrator =
9.6 K2 is the gain of the time constant 1 block =10 T1 is the time
constant of time constant 1 block = 1 ms THEORY: The type number of
the system is obtained from the number of poles located at origin
in a given system. Type 0 system means there is no pole at origin.
Type 1 system means there is one pole located at the origin. The
order of the system is obtained from the highest power of s in the
denominator of closed loop transfer function of the system. The
first order system is characterized Prepared by V.Arivumani,
AP/EEE, Vels University, Chennai 67
Control Systems Laboratory Manual / II EEE, IV SEM by one pole
or a zero. Examples of first order systems are a pure integrator
and a single time constant having transfer function of the form K/s
and K/(sT+1). The second order system is characterized by two poles
and up to two zeros. The standard form of a second order system is
G(s) = n2 / (s2 + 2ns + n2) where is damping ratio and n is
undamped natural frequency. PROCEDURE: 1. To find the steady state
error of type 0 first order system 1. Connections are made in the
simulator kit as shown in the block diagram. 2. The input square
wave is set to 2 Vpp in the CRO and this is applied to the REF
terminal of error detector block. The input is also connected to
the X- channel of CRO. 3. The output from the simulator kit is
connected to the Y- channel of CRO. 4. The CRO is kept in X-Y mode
and the steady state error is obtained as the vertical displacement
between the two curves. 5. The gain K is varied and different
values of steady state errors are noted. Block diagram of Type-0
first order system
OBSERVATIONS: S. No. 1 2 3 Gain, K Steady state error, ess
TRACES FROM CRO: Prepared by V.Arivumani, AP/EEE, Vels
University, Chennai 68
Control Systems Laboratory Manual / II EEE, IV SEM For Gain, K
=
For Gain, K =
For Gain, K=
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69
Control Systems Laboratory Manual / II EEE, IV SEM
LINEAR SYSTEM SIMULATOR PATCHING DIAGRAM TO OBTAIN THE STEADY
STATE ERROR OF TYPE 0 FIRST ORDER SYSTEM
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Control Systems Laboratory Manual / II EEE, IV SEM
2. To find the steady state error of type 1 first order system
1. The blocks are Connected using the patch chords in the simulator
kit. 2. The input triangular wave is set to 2 Vpp in the CRO and
this applied o the REF terminal of error detector block. The input
is also connected to the X- channel of CRO. 3. The output from the
system is connected to the Y- channel of CRO. 4. The experiment
should be conducted at the lowest frequency to allow enough time
for the step response to reach near steady state. 5. The CRO is
kept in X-Y mode and the steady state error is obtained as the
vertical displacement between the two curves. 6. The gain K is
varied and different values of steady state errors are noted. 7.
The steady state error is also calculated theoretically and the two
values are compared. Block diagram of Type- 1 First order
system
OBSERVATIONS: S. No. 1 2 3 Gain, K Steady state error, ess
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Control Systems Laboratory Manual / II EEE, IV SEM
TRACES FROM CRO: For Gain, K =
For Gain, K =
For Gain, K =
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Control Systems Laboratory Manual / II EEE, IV SEM
LINEAR SYSTEM SIMULATOR PATCHING DIAGRAM TO OBTAIN THE STEADY
STATE ERROR OF TYPE 1 FIRST ORDER SYSTEM
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Control Systems Laboratory Manual / II EEE, IV SEM 3. To find
the closed loop response of type 0 and type- 1 second order system
1. The blocks are connected using the patch chords in the simulator
kit. 2. The input square wave is set to 2 Vpp in the CRO and this
applied to the REF terminal of error detector block. The input is
also connected to the X- channel of CRO. 3. The output from the
system is connected to the Y- channel of CRO. 4. The output
waveform is obtained in the CRO and it is traced on a graph sheet.
From the waveform the peak percent overshoot, settling time,rise
time, peak time are measured. Using these values n and are
calculated. 5. The above procedure is repeated for different values
of gain K and the values are compared with the theoretical values.
Block diagram to obtain closed loop response of Type-0 second order
system
OBSERVATIONS: Peak percent Overshoot %MP 1 2 Rise time tr (sec)
Peak Time tp (sec) Settling time ts (sec) Undamped Natural
frequency n (rad/sec)
S. No.
Gain K
Damping ratio
TRACES FROM CRO: For Gain, K = For Gain, K =
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Control Systems Laboratory Manual / II EEE, IV SEM Block diagram
to obtain closed loop response of Type-1 second order system
OBSERVATIONS: Peak percent Overshoot %MP 1 2 Rise time tr (sec)
Peak Time tp (sec) Settling time ts (sec) Undamped Natural
frequency n (rad/sec)
S. No.
Gain K
Damping ratio
TRACES FROM CRO: For Gain, K = For Gain, K =
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Control Systems Laboratory Manual / II EEE, IV SEM
LINEAR SYSTEM SIMULATOR PATCHING DIAGRAM TO OBTAIN THE CLOSED
LOOP RESPONSE OF TYPE 0 SECOND ORDER SYSTEM
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76
Control Systems Laboratory Manual / II EEE, IV SEM
LINEAR SYSTEM SIMULATOR PATCHING DIAGRAM TO OBTAIN THE CLOSED
LOOP RESPONSE OF TYPE 1 SECOND ORDER SYSTEM
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Control Systems Laboratory Manual / II EEE, IV SEM
CALCULATIONS:
RESULT: The time response of first and second order type-0 and
type-1 systems are studied.
VIVA-VOCE QUESTIONS: 1. 2. 3. 4. 5. 6. Define order and type
number. What are dominant poles? What is a closed loop system? What
is the effect of negative feedback? What are poles and zeros of a
system? Define transfer function.
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AIM: To digitally simulate the time response characteristics of a
linear system without non- linearities and to verify it manually.
APPARATUS REQUIRED: A PC with MATLAB package THEORY: The time
response characteristics of control systems are specified in terms
of time domain specifications. Systems with energy storage elements
cannot respond instantaneously and will exhibit transient
responses, whenever they are subjected to inputs or disturbances.
The desired performance characteristics of a system of any order
may be specified in terms of transient response to a unit step
input signal. The transient response characteristics of a control
system to a unit step input is specified in terms of the following
time domain specifications Delay time td Rise time tr Peak time tp
Maximum peak overshoot Mp Settling time ts STUDY OF BASIC MATLAB
COMMANDS: The name MATLAB stands for MATRIX LABORATORY. MATLAB was
originally written to provide easy access to matrix software
developed by the LINPACK and EISPACK projects. Today, MATLAB
engines incorporate the LAPACK and BLAS libraries, embedding the
state of the art in software for matrix computation. It has evolved
over a period of years with input from many users. In university
environments, it is the standard instructional tool for
introductory and advanced courses in MATHEMATICS, ENGINEERING, AND
SCIENCE. In industry, MATLAB is the tool of choice for
high-productivity research, development, and analysis. MATLAB is a
high-performance language for technical computing. It integrates
computation, visualization, and programming in an easy-to-use
environment where problems and solutions are expressed in familiar
mathematical notation. Typical uses include, Math and computation
Algorithm development Data acquisition Modeling, simulation, and
prototyping Data analysis, exploration, and visualization
Scientific and engineering graphics 79 Date: DIGITAL SIMULATION OF
FIRST ORDER SYSTEMS
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development, including graphical user interface building
It is an interactive system whose basic data element is an array
that does not require dimensioning. This allows you to solve many
technical computing problems, especially those with matrix and
vector formulations, in a fraction of the time it would take to
write a program in a scalar non-interactive language such as C or
Fortran. It also features a family of add-on application-specific
solutions called toolboxes. Very important to most users of MATLAB,
toolboxes allow you to learn and apply specialized technology.
Toolboxes are comprehensive collections of MATLAB functions
(M-files) that extend the MATLAB environment to solve particular
classes of problems. Areas in which toolboxes are available include
SIGNAL PROCESSING, CONTROL SYSTEMS, NEURAL NETWORKS, FUZZY LOGIC,
WAVELETS, SIMULATION, AND MANY OTHERS. Some practical examples of
first order systems are RL and RC circuits. PROCEDURE: 1. Derive
the transfer function of a RL series circuit. 2. Assume R= 1 Ohms L
= 0. 1 H. Find the step response theoretically and plot it on a
graph sheet. 3. To build a SIMULINK model to obtain step response /
sine response of a first order system, the following procedure is
followed: 1. In MATLAB software open a new model in SIMULINK
library browser. 2. From the continuous block in the library drag
the transfer function block. 3. From the source block in the
library drag the step input/ sine input. 4. From the sink block in
the library drag the scope. 5. From the math operations block in
the library drag the summing point. 6. Connect all to form a system
and give unity feedback to the system. 7. For changing the
parameters of the blocks connected double click the respective
block. 8. Start simulation and observe the results in scope. (Use a
mux from the signal routing block to view more than one graph in
the scope) 9. Compare the simulated and theoretical results. BLOCK
DIAGRAM: Step response of a first order system:
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Sine response of a first order system:
2. MATLAB (m-file) program to obtain the step response and
impulse response % MATLAB program to find the step response num=[
]; den=[ ]; sys = tf (num,den); step (sys); grid OUTPUT: (Paste the
graph obtained from PC)
% MATLAB program to find the impulse response num=[ ]; den=[ ];
sys = tf (num,den); impulse (sys); grid
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Control Systems Laboratory Manual / II EEE, IV SEM OUTPUT:
(Paste the graph obtained from PC)
CALCULATIONS: Unit step response of the given RL series
circuit:
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Unit Impulse response of the given RLC series circuit:
RESULT: The time response characteristics of a first order
system is simulated digitally and verified manually. VIVA-VOCE
QUESTIONS: 1. 2. 3. 4. 5. 6. 7. 8. What is MATLAB? What is the use
of MATLAB Package? What are the toolboxes available in MATLAB? What
is the use of a simulation? Differentiate real time systems and
simulated systems. Give two examples for first order system. Name
the standard test signals used in control system. What is time
response?
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Expt. No: DIGITAL SIMULATION OF SECOND ORDER SYSTEMS AIM:
Date:
To digitally simulate the time response characteristics of a
second order system and verify manually. APPARATUS REQUIRED A PC
with MATLAB Software THEORY The time characteristics of control
systems are specified in terms of time domain specifications.
Systems with energy storage elements cannot respond instantaneously
and will exhibit transient responses, whenever they are subjected
to inputs or disturbances. The desired performance characteristics
of a system of any order may be specified in terms of transient
response to a unit step input signal. The transient response
characteristics of a control system to a unit step input is
specified in terms of the following time domain specifications:
Delay time td Rise time tr Peak time tp Maximum overshoot Mp
Settling time ts PROCEDURE: 1. Derive the transfer function of a
RLC series circuit. 2. Assume R= 1 Ohms, L = 0. 1 H and C = 1 micro
Farad. Find the step response theoretically and plot it on a graph
sheet. 3. To build a SIMULINK model to obtain step response / sine
response of a second order system, the following procedure is
followed: 1. In MATLAB software open a new model in SIMULINK
library browser. 2. From the continuous block in the library drag
the transfer function block. 3. From the source block in the
library drag the step input/ sine input. 4. From the sink block in
the library drag the scope. 5. From the math operations block in
the library drag the summing point. 6. Connect all to form a system
and give unity feedback to the system. 7. For changing the
parameters of the blocks connected double click the respective
block. 8. Start simulation and observe the results in scope. (Use a
mux from the signal routing block to view more than one graph in
the scope) 9. From the step response obtained note down the rise
time, peak time, peak overshoot and settling time. 10. Compare the
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BLOCK DIAGRAM: Step response of a second order system:
Sine response of a second order system:
2. MATLAB program to obtain the step response and impulse
response of second order system. % MATLAB program to find the step
response num=[ ]; den=[ ]; sys = tf (num,den); step (sys); OUTPUT:
(Paste the graph obtained from PC)
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% MATLAB program to find the impulse response num=[ ]; den=[ ];
sys = tf (num,den); impulse (sys); OUTPUT: (Paste the graph
obtained from PC)
CALCULATIONS: Unit step response of the given RLC series
circuit:
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Unit impulse response of the given RLC series circuit:
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RESULT: The time response characteristics of the given second
order system is simulated digitally and verified manually.
VIVA-VOCE QUESTIONS: 1. 2. 3. 4. 5. 6. 7. 8. What is MATLAB? What
is the use of MATLAB Package? What are the toolboxes available in
MATLAB? What is the use of a simulation? Differentiate real time
systems and simulated systems. Give two examples for second order
system. Name the standard test signals used in control system. What
is time response?
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Control Systems Laboratory Manual / II EEE, IV SEM Expt. No:
STABILITY ANALYSIS OF LINEAR SYSTEMS a. USING BODE PLOTAIM:
Date:
To obtain the bode plot and check for stability of the system
with open loop transfer function, G(S) = APPARATUS REQUIRED: A PC
with MATLAB Software THEORY: A Linear Time-Invariant Systems is
stable if the following two notions of system stability are
satisfied When the system is excited by Bounded input, the output
is also a Bounded output. In the absence of the input, the output
tends towards zero, irrespective of the initial conditions. The
following observations are general considerations regarding system
stability, If all the roots of the characteristic equation have
negative real parts, then the impulse response is bounded and
eventually decreases to zero, then system is stable. If any root of
the characteristic equation has a positive real part, then system
is unstable. If the characteristic equation has repeated roots on
the j-axis, then system is unstable. If one are more non-repeated
roots of the characteristic equation on the j-axis, then system is
unstable. BODE PLOT : Consider a Single-Input Single-Output system
with transfer function C(s) = R(s) Where m < n. a0 sn + a1sn-1 +
+an b0 sm + b1 sm-1 + + bm
Rule 1 A system is stable if the phase lag is less than 180 at
the frequency for which the gain is unity (one). Prepared by
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Control Systems Laboratory Manual / II EEE, IV SEM Rule 2 A
system is stable if the gain is less than one (unity) at the
frequency for which the phase lag is 180. The application of these
rules to an actual process requires evaluation of the gain and
phase shift of the system for all frequencies to see if rules 1 and
2 are satisfied. This is obtained by plotting the gain and phase
versus frequency. This plot is called BODE PLOT. The gain obtained
here is open loop gain. The exact terminology is in terms of a Gain
Margin and Phase Margin from the limiting values quoted. If the
phase lag is less than 140 at the unity gain frequency, the system
is stable. This then, is a 40 Phase Margin from the limiting values
of 180. If the gain is 5dB below unity (or a gain of about 0.56)
when the phase lag is 180, the system is stable. This is 5dB Gain
Margin.
PROCEDURE: Step 1: Write a program to obtain the Bode plot for
the given system. Step 2: Assess the stability of given system
using the plot obtained. PROGRAM %BODE PLOT OF THE SYSTEM %Enter
the numerator and denominator of the transfer function num=[ den=[
sys=tf(num,den) %Specify the frequency range and enter the command
w=logspace(-2,4,1000); bode(sys,w) xlabel('Frequency') ylabel( '
Phase angle in degrees Magnitude of G(s) in decibels') title('Bode
Plot of the system %Phase cross over frequency margin(sys) [ Gm,
Pm, Wpc, Wgc ]= margin (sys) ') %To determine the Gain Margin,
Phase Margin, Gain crossover frequency and ]; ];
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MANUAL CALCULATIONS:
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OUTPUT (from manual calculation):
OUTPUT (from program):
RESULT: The Bode plot is drawn for the given transfer function
using MATLAB and verified manually. From the plot obtained, the
system is found to be ______________. VIVA-VOCE QUESTIONS: 1. 2. 3.
4.5.
6. 7. 8. 9.
Define stability of Linear Time Invariant System. Give the
stability conditions of system using Pole-Zero plot. Define Bode
Plot. What is the use of Bode Plot? What the conditions of
stability are in Bode plot? Define Stability criteria. Define
Limits of stability. Define safe regions in stability criteria.
Define Phase margin and Gain margin.
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Control Systems Laboratory Manual / II EEE, IV SEM b. Using Root
Locus AIM: To obtain the Root locus plot and to verify the
stability of the system with transfer function, G(s) = APPARATUS
REQUIRED: A PC with MATLAB Software THEORY: ROOT LOCUS PLOT: The
characteristic of the transient response of a closed-loop system is
related to the location of the closed loop poles. If the system has
a variable loop gain, then the location of the closedloop poles
depend on the value of the loop gain chosen. A simple technique
known as Root Locus Technique used for studying linear control
systems in the investigation of the trajectories of the roots of
the characteristic equation. This technique provides a graphical
method of plotting the locus of the roots in the s-plane as a given
system parameter is varied over the complete range of values (may
be from zero to infinity). The roots corresponding to a particular
value of the system parameter can then be located on the locus or
the value of the parameter for a desired root location can be
determined form the locus. The root locus is a powerful technique
as it brings into focus the complete dynamic response of the
system. The root locus also provides a measure of sensitivity of
roots to the variation in the parameter being considered. This
technique is applicable to both single as well as multiple-loop
systems. PROCEDURE: 1. Write a program to obtain the root locus
plot for the given system. 2. Assess the stability of given system
using the plot obtained. PROGRAM: %ROOT LOCUS OF THE SYSTEM% num=[
den=[ sys=tf(num,den) rlocus(sys) v=[-10,10,-8,8]; axis(v) Prepared
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Axis') ylabel('Imaginary Axis') title('Root Locus of the system')
title('Root Locus Plot of the system MANUAL CALCULATIONS: ')
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Control Systems Laboratory Manual / II EEE, IV SEM OUTPUT (from
manual calculation)
OUTPUT (from program):
RESULT: The Root locus plot is drawn for the given transfer
function, G(s)= ___________________ using MATLAB and the range of
gain K for stability is______________. VIVA-VOCE QUESTIONS: 1.
Define root locus technique. 2. What are the conditions of
stability in root locus criteria? 3. What is the advantage of root
locus technique? 4. Which method of stability analysis is more
advantageous? 5. How the stability of unstable is improved? 6. What
are the methods to improve the stability? 7. What is the use of
compensators? 8. What do you mean by Root-Loci? 9. What is
complementary Root Loci? 10. What are contours? 11. State the basic
properties of Root Locus. 12. How would you find the number of
branches of Root Loci? 13. How are the break away points of the
root locus determined? 14. How is the point of intersection of the
asymptotes with real axis found out.
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Control Systems Laboratory Manual / II EEE, IV SEM c. USING
NYQUIST PLOT AIM: To obtain the Nyquist plot and check the
stability of the system using Nyquist Stability Criterion for the
given unity feedback system with transfer function G(s)H(s) =
APPARATUS REQUIRED A PC with MATLAB Software THEORY: NYQUIST
STABILITY CRITERION:
POLAR PLOTS / NYQUIST PLOTS: The sinusoidal transfer function
G(j) is a complex function is given by G(j) = Re[ G(j)] + j
Im[G(j)] or G(j) = G(j) G(j) = M -----------(1) From equation (1),
it is seen that G(j) may be represented as a phasor of magnitude M
and phase angle . As the input frequency varies from 0 to , the
magnitude M and phase angle changes and hence the tip of the phasor
G(j) traces a locus in the complex plane. The locus thus obtained
is known as POLAR PLOT. The major advantage of the polar plot lies
in stability study of systems. Nyquist related the stability of a
system to the form of these plots. Polar plots are referred as
NYQUIST PLOTS. PROCEDURE: 1. Write a program to obtain the Nyquist
plot for the given system. 2. Assess the stability of given system
using the plot obtained.
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%NYQUIST PLOT %Enter the numerator and denominator of the transfer
function num=[ ] den=[ ] sys=tf(num,den) %Specify the frequency
range and enter the command nyquist(sys) v=[ ] axis(v) xlabel('Real
Axis'); ylabel('Imaginary Axis'); title('Nyquist Plot of the system
MANUAL CALCULATIONS:
)
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OUTPUT ( from Manual calculation)
OUTPUT (from program)
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Control Systems Laboratory Manual / II EEE, IV SEM RESULT: The
Nyquist plot is drawn for the given transfer function, G(s) =
______________________ using MATLAB and the system is found to be
______________________.
VIVA-VOCE QUESTIONS: 1. 2. 3. 4. 5. What is polar plot? What is
Nyquist plot? Define the conditions of stability in polar plot.
What is the use and advantage of polar plot? State Nyquist
stability criterion.
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STEPPER MOTOR CONTROL SYSTEM Date:
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