AKSYA 3

Control Systems and Simulation Lab

Electrical & Electronics Engineering Department-BVRIT 1

CONTROL SYSTEMS AND SIMULATION LAB

DEPARTMENT OF

ELECTRICAL AND ELECTRONICS ENGINEERING

ACADEMIC YEAR 2012-2013 III B.Tech EEE I-SEMESTER

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PREFACE

The significance of the Control Systems and Simulation Lab is renowned in the various

fields of engineering applications. For an Electrical Engineer, it is obligatory to have the

practical ideas about the Control Systems and Simulation. By this perspective we have

introduced a Laboratory manual cum Observation for Control Systems and Simulation Lab.

The manual uses the plan, cogent and simple language to explain the fundamental

aspects of Control Systems and Simulation in practical. The manual prepared very carefully

with our level best. It gives all the steps in executing an experiment.

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ACKNOWLEDGEMENT

It is one of life’s simple pleasures to say thank you for all the help that one has extended

their support. I wish to acknowledge and appreciate Assoc Prof K. Raudu, Assist. Prof.

R.Munishwar, Foreman. P Prabhu Dass, and A Ramesh for their sincere efforts made towards

developing the Control Systems and Simulation Lab manual. I wish to thank students for their

suggestions which are considered while preparing the lab manual.

I am extremely indebted to Sri.Col Dr. T. S. Surendra, Principal and Professor,

Department of Electrical and Electronics Engineering, BVRIT for his valuable inputs and

sincere support to complete the work.

Specifically, I am grateful to the Management for their constant advocacy and

incitement.

Finally, I would again like to thank the entire faculty in the Department and those people

who directly or indirectly helped in successful completion of this work.

(Prof. N. BHOOPAL)

HOD - EEE

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GUIDELINES TO WRITE YOUR OBSERVATION BOOK

1. Experiment Title, Aim, Apparatus, Procedure should be on right side.

2. Circuit diagrams, Model graphs, Observations table, Calculations table should be left side.

3. Theoretical and model calculations can be any side as per your convenience.

4. Result should always be in the ending.

5. You all are advised to leave sufficient no of pages between experiments for theoretical or

model calculations purpose.

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DO’S AND DON’TS IN THE LAB

DO’S:-

1. Proper dress has to be maintained while entering in the Lab. (Boys Tuck in and shoes, girls

with apron)

2. All students should come to the Lab with necessary tools. (Cutting Pliers 6”, Insulation

remover and phase tester)

3. Students should carry observation notes and record completed in all aspects.

4. Correct specifications of the equipment have to be mentioned in the circuit diagram.

5. Student should be aware of operating equipment.

6. Students should be at their concerned experiment table, unnecessary moment is restricted.

7. Student should follow the indent procedure to receive and deposit the equipment from the Lab

Store Room.

8. After completing the connections Students should verify the circuits by the Lab Instructor.

9. The reading must be shown to the Lecturer In-Charge for verification.

10. Students must ensure that all switches are in the OFF position, all the connections are

removed.

11. All patch cords and stools should be placed at their original positions.

DON’Ts:-

1. Don’t come late to the Lab.

2. Don’t enter into the Lab with Golden rings, bracelets and bangles.

3. Don’t make or remove the connections with power ON.

4. Don’t switch ON the supply without verifying by the Staff Member.

5. Don’t switch OFF the machine with load.

6. Don’t leave the lab without the permission of the Lecturer In-Charge.

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JAWAHARLAL NEHRU TECHNOLOGICAL

UNIVERSITY HYDERABAD

III Year B.Tech. EEE I-Semester L T/P/D C

0 -/3/- 2

(55603)CONTROL SYSTEMS AND SIMULASTION LAB

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.

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III Year B.Tech EEE I-Sem Academic year 2012-2013

S.no Name of the experiment

1 Time response of Second order System

2 Characteristics of Synchros

3 Effect of P,PD,PI,PID controller on a

second order system

4 Temperature controller using PID

5 Characteristics of Magnetic Amplifier

6 DC Position control system

7 Characteristics of AC servo motor

8 Transfer function of DC generator

9 Root locus plot, bode plot from MATLAB

10 Characteristics of DC servo motor

11 Transfer function of DC shunt motor

12 Simulation of State space models using

MAT LAB

Add on Experiments

1 Simulation of Transfer function using Operational

Amplifier

2 Lag lead compensator

3 P L C

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1. TIME RESPONSE OF SECOND ORDER SYSTEM

AIM: To study the time response of second order system with step input and square input.

Equipment required:

1. RLC components

2. Signal generator

3. Multimeter

4. C.R.O

5. BNC adaptors

6. Patch cords

b) signal source:

This signal source consists of a square wave generator of 15Hz approximately and a step

signal generator. A switch is provided to select square are step (DC) source. Amplitude of signal

source can be varied from 0v to 15v approximately for square wave and 0v to 15v

approximately for step (DC) source.

c) Second order system:

This part consists of second order system built using op-amp and an RLC circuit.

Definition:

We can define second order system by using closed transfer function

C(S)/R(S)= Wn2/S

2+2 W+Wn

2

Where is called damping ratio.

SECOND ORDER SYSTEM USING RLC :-

Calculation:

Wn= 1/ LC = 1/ 2X.32X10.6=1250

R=2 L/C

FOR =0.3, R=1500 =1, R=5000

=0.7, R= 3500 =2, R=10000

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PROCEDURE:

1. Connections are made as per the circuit diagram.

2. Switch on the main supply to the unit. Observe the source o/p by selecting square wave

and by varying amplitude using function generator.

3. First select square wave signal with a required time constant. Draw input square wave.

4. Connect signal output to second order system input using RLC.

5. Draw the graph for the respective output.

Result: Hence the steady state response for the square wave input is verified.

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2. CHARACTERSTICS OF SYNCHROS AND TRANSMITTER

Circuit Diagram:

Study of synchro transmitter:

Circuit Diagram :

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2. CHARACTERSTICS OF SYNCHROS AND TRANSMITTER

Aim: To study the characteristics of synchros as transmitter and synchro

transmitter- receiver pair.

Apparatus:

Synchros pair unit

Voltmeter (0-50v) MI-3No.s

1-Ph variac

patch cords.

Definition: A synchros on electromagnetic transducer commonly used convert an angular

position of a shaft into an electric signal.

Study of Synchro Transmitter and receiver:-

In this part or experiment we can see that because or the transformer action the angular

position of rotor is transformed into a unique set of stator voltages.

PROCEDURE:

1) Make the connections as per CKT diagram.

2) Apply 50v AC supply to the transmitter.

3) Adjust the pointer on the rotor of the transmitters to zero position

4) Observe the position across to rotate of the receiver. If it is not zero

the rotor, so as to obtain zero voltage and this value is referred to as

electrical zero position of the receiver.

5) Holding firm by position of rotor shaft at transmitters slightly. Note

down the voltage across the rotor of the receiver.

6) Now continue the readings up to 360 , in steps of 30 by increasing

the angular positions of the transmitter in steps.

7) Take rotor shaft position of transmitters on X- axis and voltage on Y

axis and draw a graph.

8) Draw graph by taking transmitter angular position on X- axis and

receiver angular position on Y axis.

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Table:

S.No

Rotor angle of

ΘTransmitter

Rotor

angle of

θ receiver

Receiver rotor

voltage

Study of synchro transmitter:

Procedure:- 1) Apply 50V,AC to the rotor of synchro transmitter.

2) Measure the voltage between s1, s2,s3 for various shaft positions from 0-3600.There voltage

which have to be –ve sign has to be desired form the knowledge of voltage between wave forms.

3) Similarly measure the voltage between S2 and S3, S3 and S1 various shaft positions.

4) Plot the graph of rotor position in degrees Vs (S1, S2),(S2,S3) and (S3,S1) respectively.

Result: Hence the characteristics of Synchros are verified

Questions:

1) Define synchros?

2) What do you understood by this experiment?

3) Write principal how angular position is converted to voltage?

4) Write the applications of synchro transmitter?

5) Write the applications of synschro receiver?

S.NO Voltage ROTOR

POSITION

SHAFT

V(S1-S3) V(S2-S3) V(S3-S4)

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3. Effect of P, PD, PI, PID Controller on a second order system

b) Integral Controller-Open loop :

Diagram of the system:

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3. Effect of P, PD, PI, PID Controller on a second order system

AIM :To study the effect of P,PD,PI,PID controller on a second order system.

APPARATUS:- PID controller unit, patch cords and CRO.

PID controller unit:-

Front panel details:-

1) Main : Main on/off switch

2) Square : Variable square wave out 0-2v.

3) Level : Potentio meter to vary the amplitude of square wave

and triangular wave

4) Frequency : Potentio meter to vary the frequency of square wave

and triangular wave

5) Triangle : Triangle wave O/P for triggering purpose in x-y

mode

6) Amplitude : Potentio meter to vary the D.C voltage from 0-12v

7) Dc : Variable Dc O/P 0-12v

8) GND : Ground terminal

9) DPM : 31/2 digit DC volt meter to measure DC voltage at

different points

10) Vin : +ve I/P of error detector feedback voltage

11) Vf : -ve I/P of error detector feedback voltage

12)Ve : Error voltage

13) P : 10 turn potentio meter to vary potential gain from 0-

20 with indicating dial

14) I : 10 turn potentio meter to vary the integral gain from

10-1000

15) D : 10 turn potentio meter to vary the derivative gain

from 1-0.01

16) Controller : PID controller with variable PID parameters.

17) ON/OFF : On/off switch for P,I,D individually

18) + : Adder

19) INV AMP : Units gain inverting amplifier to find the effect of

Positive feed back

20) Process:

A) First order system : First order system with time constant of – 3m

sec.

B) Second order system: Second order system with time constant of 5

sec.

C) Time constant : 1m sec – Suitable for square wave I/P

D) Integrator : 2m sec. Time with 1800 phase shift

A) Proportional controller – open loop:

Procedure:

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1) Make the connections as given in to the figure.

2) Connect DC voltage o f 0.5 volts to PID input.

3) Connect feed back to ground

4) Vary the proportional gain pot

5) Switch on P controller and keep I and D controller at off position

6) Vary the proportional gain pot and note down the O/P voltage

S.NO Vin Gain (Kc) VOLT

b) Integral Controller-Open loop :

Procedure:

1. Make the connections as given in the circuit diagram.

2. Connections a small voltage of .2 volts to input.

3. Connect feed back to ground.

4. Switch off P and I. Switch on D controller.

5.

d) Derivative controller – open loop

Procedure:

1.Make the connections as per circuit diagram

2.Connect a small DC voltage of .2 volts to I/P

3.Connect feed back to ground

4.Switch off P and I . Switch on D controller

D) Proportional controller –closed loop

Procedure:

1.Make the connections as shown in the figure.

2.Keep I and D controllers at off positions

3.Connect DC supply to vin

4.Connect first order plant in the loop.

5.Note down Vm, Vf,V error to direct P- gained and enter in the tabulars column.

6.Error voltage =Vs/1+G

Table :

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S.NO P-GAIN

-CS

Feedback voltage –vs Error

voltage

-Ve

Cal error

(e) Integral + Proportional + Derivate controller ( PID):

Procedure:

1. Make the connections as given in the circuit diagram

2. Connect square wave to vin

3. Connect the constant block only the loop

4. Connect X- input to triangle wave form and Y- input to feed

back input -Vf

Graph :

Result :

Questions :

1. Define proportional ?

2. Define integral controller ?

3. Why should we do not connect first order& second order in the loop of

PID controller ?

4. Define second order system ?

5. Where shall we apply PID controller ?

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TEMPERATURE CONTROLLER USING PID

CIRCUIT DIAGRAM:-

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TEMPERATURE CONTROLLER USING PID

AIM: To study the on/off Temperature controller.

APPARATUS:- 1) On/off temperature module.

2) Heater system.

3) PT-100 RTD Sensor.

4) Water Controller.

PROCEDURE:- 1) Connect the RTD sensors PT-100 to the binding post provided. Connect

the heater table to the plug provided.

2) Keep the rotary switch in zero degree position. Set the meter reading it should

be show zero degree.

3) Keep the rotary switch in RTD position; The meter reading indicates the

temperature.

4) Set the temperature value to required temperature setting.

5) Keep the RTD in water container.

6) Note the temperature at which Heater turns off.

7) Repeat the steps 3 to 6 to various temperatures.

RESULT:

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6. CHARACTERISTICS OF MAGNETIC AMPLIFIER Circuit Diagram:

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6. CHARACTERISTICS OF MAGNETIC AMPLIFIER

AIM: To study the characteristics of magnetic amplifier.

APPARATUS: magnetic amplifier kit,

patch cords,

load (100wbulb),

external dc supply

Ammeters – (0-100mA, MC)-1 No

Ammeter- (0-1A, MI)-1No

Procedure for series connected magnetic amplifier parallel connected

magnetic amplifier

1) Connections are made as per the CKT diagram

2) Switch on the main supply and give the DC power to the magnetic

amplifier through RPS.

3) Now vary the DC power in steps and note down the readings of IC and IL

and Observe the load at variable DC voltage.

4) plot the graph between IC and IL at variable position for both series

connection and parallel connection

Tabular form:

Series Magnetic amplifier:

50V

Voltage(v) IC(mA) IL(mA)

Parallel Magnetic Amplifier:

100V


100V


50V


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MODEL GRAHPH:

Result:

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7. DC POSITOIN CONTROL SYSTEM

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7. 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.

3. Now take the pot P1 to 1800

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.

3. Now take the pot P1 to 1800 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.

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Table: 1

DEGENERATIVE:

S.No I/P angular position

degrees

Output angular

position degrees

With stabilizing Remarks

Table: 2

REGENERATIVE:

Table: 3

Result:


degrees

Output angular

position degrees

With

stabilizing

Remarks


degrees

Output angular

position

degrees

With out

stabilizing

Remarks

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8.CHARACTERISTICS OF AC SERVO MOTOR

AIM: To study the characteristics of AC servo motor.

Front panel details:

1. Power : main ON/OFF switch to the unit with built in indicator.

2. RPM : tachometer to display to RPM

3. Ammeter : Ammeter to measure the DC motor armature current

4. Servomotor

ON/OFF : AC supply ON/OFF switch to the servo motor.

5. Load ON/OFF : ON/OFF switch to load the motor.

6. R : Potentio meter to vary the load 500 ohms/25watts.

7. Vdc : 12V unregulated DC supply to DC motor

8. Eb Terminals to measure the back EMF

9. Control winding: Control winding terminals of AC servo motor

10 Reference winding: Reference winding of AC servo motor.

11. Control voltage : Auto transformer to vary the AC supply to control winding.

TABLE TO PLOT SPEED Vs BACK EMF:

Sl no Speed –rpm Backemf- volts

PROCEDURE:

1. Study all the controls on the front panel.

2. Initially keep load control switch at OFF position, indicating the armature circuit of dc

machine is not connected to auxiliary dc supply – 12V keep servo motor supply switch also at

off position.

3. Ensure that load potentiometer and control voltage auto transformer at minimum position.

4. Now switch on mains supply to the unit and also AC servo motor supply switch vary the

control voltage transformer. You can observe that the AC servo motor will stars rotating and

the speed will be indicated by the tachometer in the front panel.

5. With load switch at OFF position switch ON AC servomotor and keep the speed in the

minimum position. You can observe that the AC servomotor starts moving with speed being

indicated by the tachometer and set the speed for maximum speed. Now switch on the load

switch and start loading AC servo motor by varying the laod potentiometer slowly, Note down

the corresponding values of Ia and speed and enter these readings in the table. And also note

down the control panel.

S.No Ia(mA) N(rpm) P(watts) Torque(Gm-cm)

Repeat for Vc=3/4th 230V

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Draw the graph of torque Vs speed.

K2=DT/DN

Determine the motor constant K1:

1. Apply rated voltage 230V to control winding.

2. Apply load on the motor gradually till the motor wil run in the RPM.

3. Note down I and calculate torque

4. Decrease the load on the motor slightly the motor will run at certain rpm.

5. Reduce Vc slightly till the speed the motor comes to – N rpm

6. repeat different loads.

7. Repeat for N2 rpm.

Draw the graph of Torque V/S VC

K1= DT/DVc

Ia measured by ammeter which is connected in series with the power supply & variable resistance

(load control). This method does not take in to the account the no load torque developed by the ac

servo motor. To measure torque developed at no load (i.e torque just required to rotate rotor of ac

servomotor, rotor of dc motor) the ac servomotor is switched off. Now the dc machine run as the

help of dc power supply, speed will be controlled by variable resistance again we have to effect

the measurement of Ia for a given speed. From the product of Eb( back emf developed by the

motor) and the armature current taken, we can find the mechanical power developed at the shaft.

Again we must use the formula.

P= 2pi*NT/60

Torque = P*1.019*104 *60/2pi*N

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

This torque is negligible & may not be taken in to account for normal testing.

Torque calculation for a sample data:

Ia =0.17A

Speed N= 850 rpm

For speed 850rpm- Eb = 0.96V

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Therefore power P = Eb*Ia = 0.96*0.17 = 0.1632 watts.

T= P*1.019 * 104 *60/2piN

T = 0.1632*1.019*104 *

60/2*3.142*850

T = 18.68 Gm-cm

GRAPHS: Respective graphs are drawn separately

RESULT:

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9. TRANSFER FUNCTION OF DC GENERATOR

Circuit Diagram:-

Circuit diagrams to find Rf and Lf:

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9. TRANSFER FUNCTION OF DC GENERATOR

AIM: To find out the transfer function of a DC generation, after determining the various

Constants

.APPARATUS:

S.NO NAME RANGE TYPE Qty

1 Motor generator set ______ ______ 1

2 Rheostat 290ohm/2.4A --------- 1

3 Ammeter (0-2.5)A MC 1

4 Voltmeter (0-250)V MC 1

5 Tachometer 0-5000 rpm Digital 1

6 Multimeter ------------- Digital 1.

PROCEDURE:

1.Make all the connections as per the circuit diagram

2. Keep the rheostat of motor with starter and adjust the speed to rated value.

3.Start the DC motor with starter and adjust the speed to rated value.

4.To determine the kg. the magnetization characteristics of separately excited DC generation is to

be drawn. Use the straight line position of the curve to determine Kg= EG/IF.

5. Field resistance of generation R1 is determined by volumes and ammeter method.

Tabular form:

1) Magnetization characteristics:

S.No If(A) Eg(V)

2) Field Resistance:

S.No V I Rf=V/I

3) Field Impedance:

S.No I(A) V(V) Zf(ohms)

Model Graph:

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Model Calculations:

Xf = √(Zf2 – Rf

2)

Lf = XL/2∏f

Transfer function, T(s) = Kg/1+sΤg

Where Kg = ∆Eg/∆If

Τg = Lf/Rf

RESULT:

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10. ROOT LOCUS PLOT, BODEPLOT FROM MATLAB

AIM: To plot root locus and bode plot by using MATLAB.

SIMULATION TOOLS:

1. IBM PC Compatible with MATLAB Software

2. MATLAB Simulator

PROGRAMME:

a) /* root locus */

num = [1,3];

den = [1, 2, 3, 4];

rlocus (num, den)

Grid

b) / * Bode plot * /

num = [1, 3];

den = [1,2, 3, 4];

bode (num, den)

grid

RESULT:

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11. CHRACTERISTICS OF DC SERVO MOTOR

BLOCK DIAGRAM:

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11. CHRACTERISTICS OF DC SERVO MOTOR

AIM: To study the characteristics of DC servo motor

i) Speed Vs Va ii) Speed Vs torque iii) Torque Vs Ia

APPARATUS:

DC Servo motor controller

Voltmeter - 0-30V

THEORY:

The motors that are used in automatic control systems are called servomotrs. The

servomotors are used to convert an electrical signal applied them into an angular displacement

of shaft. Depending on the supply required to run the motor, they are broadly classified as DC

servo motor and AC servomotors. But, the DC servomotrs are expensive than AC servomotors.

But, the DC servo motors have linear characteristics and so it is easier to control DC motors are

capable of delivering over 3 times their rated torque for a short time but AC motors will short at

2 to 2.5 times their rated torque. In DC servomotors mainly 2 types of motors are classified 1.

Permanent magnetic motors and electromagnetic field motors.

The DC servo motors are generally used for large power applications such as in machine

tools and robotics.

PROCEDURE:

1. Connections are made as per the circuit diagram the motor is operated on open loop.

2. Connect the motor to he o/p power amplifier in the servo controller through ammeter.

Connect a Voltmeter across the motor armature.

3. Set the controller to the proportional by connecting the I controller i/p to ground.

4. Set the proportional gain to minimum.

5. Switch on the supply to motor controller and the pulse release.

6. Set Vref =1V, slowly increase the gain Kp voltage by means of proportional gain

adjustment and find the voltage at which the motor just running.

7. vary reference voltage in speeds and for each step, note down the motor speed & Va. It

gives T Vs Va characteristics.

8. Run the motor at 1500rpm by suitably adjusting the Vref & Kp note down Va, Ia &

speed.

9. Apply load by moving brake magnet close to the disc.Apply load in steps of 0.1A. Note

down Ia, Va& speed for each step.

10. Ammeter current reaches a value above which it may not increase when the speed is low,

the eddy current induced in the disc becomes, lag which reduces the load torque.

11. Draw the graph between W Vs Va, T Vs Ia, W Vs Ia.

Tabular form: To plot w Vs Va and w Vs Eb.

S.No Vref Eb Va Ia N W=2∏N/60

Tabular form: to plot w Vs Ia and τ Vs Ia

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To find Kf from the graph Eb Vs w:

Eb = Ea – IaRa

Eb = Kb * w

Kf = ∆Eb /∆w

MODEL GRAPHS:

RESULT: Hence the characteristics of DC servomotor are drawn.

S.No Va Ia N w Τ = Kf * Ia

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12. TRANSFER FUNCTION OF D.C SHUNT MOTOR

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12. TRANSFER FUNCTION OF D.C SHUNT MOTOR

AIM: To Determine the transfer function of DC motor by conducting

Retardation test.

APPARATUS:

S. No. Description Range Type Qty

1 Ammeter (0-2) A M.C 1

2 Voltmeter (0-5) A

(0-300) V

M.C

1

2

3 Rheostat 300Ω / 2A

45 Ω / 2A

Wire

wound

1

4 SPST Switch ------ ----- 1

5 Connecting wires ---------- ----- -----

Name plate details:

Specification Shunt motor

Voltage 220v

Current 19A

Capacity 5 Hp

Speed 1500rpm

Excitation

Current 1A

Voltage 220v

THEORY:

We perform armature control of d.c motor in the system shown

Ra = resistance of armature (Ω)

La = inductance of armature wdg(h)

Ia = Armature current (A)

Ea = applied armature voltage(V)

Ed = back e.m.f (V)

Tm = torque developed by motor (N-M)

Ө = angular displacement of motor shaft

J = moment of intertia of motor and load ref motor shaft (kg-M2)

F = equivalent viscous friction coefficient of motor end load ref to motor shaft (N-M /

rad / sec)

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In servo applications the D.C motors are generally used in linear range of magnetization curve.

Therefore the air gap flux is prop to IF

Ф= kf If

The torque Im developed by motor is prop to the product of Ia and air gap flux i.e

Tm = Ki Kf If Ia , K1 is constant

In the armature controlled D.C motor the field current is sept constant so that

Tm = Kt ia ------------(1)

Where Kt is known as motor torque constant the motor back emf being prop to speed given as

Ed = Kb dӨ / dt -------------(2)

Where Kb is back emf constant . the deff eqn of armature ckt is

La dia / dt + Ra Ia + eb = va ----------(3)

The torque eqn is

J d2Ө / dt

2 + f dӨ / dt

= Tm = Kt Ia -------(4)

Taking l.t to 1,2,3 and 4

Ed(s) = skb Ө(s) --------(5)

Las Ia(s) + Ra Ia(s) + Eb(s) = Va(s) ----------(6)

Js2 Ө(s) + fs Ө(s) = Tm(s) -------(7)

Tm(s) = kf Ia(s) ------(8)

From 7&8 eqn

Js2 Ө(s) + fs Ө(s) = kf Ia(s)

Ia(s) = (Js2 + fs)/ Kt Ө(s) ------(9)

From 5,6,9

Va(s) = (Las+ Ra) (Js

2+fs)/kt Ө(s) + skb Ө(s)

= (Las + Ra) (J2s + fs) + skbkt/ kt Ө(s)

Ө(s)/Va(s) = kt / s[(Las + Ra) (Js+f) + kbkt]

The T.F is given as

G(s) = kt / s [(Las+Ra) (Js+f) + kbkt]

At constant speed kb = kt

PROCEDURE:

1. connect the circuit as per ckt diagram

2. check the rated speed of motor

3. start the motor with armature on no-load

4. Switch on the supply from armature motors and take the taken to reach different speed

from rated speed.

5. load the armature of motor with resistance load

6. switch off the supply and take time taken for different times from rated speed

7. note down the values of voltmeter and ammeter

8. draw the graph b/w N&t and draw tangent from the rated speed on y- axis on to the curve

which cuts the x- axis i.e total time taken to reach zero speed known as time constant

9. determine the different constants of the motor

10. determine the T.F of D.C motor i.e.G(s) = kt / s[kbkt+ (LaRas)(ts+f)]

OBSERVATIONS:

With out load

With load

N T (Sec) N T(sec)

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V

I

Eb

V

I

Ra

Model calculations:

Wintial = 2∏ N/60

Wfinal = 2∏ N1/60

dw/dt =( Wintial - Wfinal )/( Tintial - Tfinal)

Kb = Eb/(dw/dt)

W1 = V* I

W= J* (2∏ N1/60) * dw /dt

W+ W1 = (J * (2∏ N2/60)* 2∏ (Ninitial- N2)/60) / (Tintial - Tfinal)

W1

= (W+W1) – W

1 = VI

from the graph find Time constant τ

But τ = J/f and hence find friction coefficient f.

Therefore transfer function,

T(s) = kt / s [(Las+Ra) (Js+f) + kbkt]

Circuit Diagram:-

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RESULT:-

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13. SIMULATION OF STATE SPACE MODELS USING MATLAB

AIM: To find the transfer function of the given system, controllability,

Obeservability and System stability.

X= AX + BU

Y= CX + DU

-1 1 0

A= 0 -4 2

0 0 -10

1

B =

0 C = 1 0 1 D=(0)

1

SIMULATION TOOLS:

1. IBM PC Compatible with MATLAB Software

2. MATLAB SIMULATOR

THEORY:

State: Minimum amount of information required to estimate the future of the system.

State variable: The minimal set of these variables which describe the state of the system.

Suppose n state variables are represented as ‘n’ components of a state then the vector

is known as state vector.

x1(t)

x2(t)

X(t) =

xn n X 1

State – Space model representation

State – eq

n is X(t) = AX(t) + BU(t)

o/p eqn Y(t) = Cx(t) + DU(t)

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Transfer function matrix, T.F = C(SI – A)-1

B+D.

A system is said to be completely state controllable if it is possible to find an input u(t)

that will transfer a system from any initial state to any final state over a specified time interval.

Controllable matrix S= [ B AB A2 B ……..A

n-1B]

If rank of the matrix n, then the system is state controllable.

Rank (S) = n. [|B| ≠ 0]

A system is said to be state observability the state of the system can be determined from

the knowledge of input U(t) & o/p y(t) over a finite interval of time. The representation is W =

[CT A

T C

T (A

T)

2 C

T…….(A

T)

n-1 C

T ]

Rank (W) = n [observable]

Program-1

A= [-1 1 0 ; 0 -4 2 ; 0 0 -10]

B= [1 0 -1];

C= [1 0 1];

D= [0]

[num, den]=ss2tf [A, B, C, D];

disp(num);

disp(den);

Program-2

A= [-1 0 0, 0 -4 2, 0 0 -10];

B= [1 0 -1];

C= [1 0 1];

D= [0]

S=ctrb(A, B);

n=det(s);

if abs(n)<eps

disp(‘system is not controllable’);

else

disp(‘system is controllable’);

end

Program-3

A= [-1 0 0, 0 -4 2, 0 0 -10];

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B= [1 0 -1];

C= [1 0 1];

D= [0]

W=obsv(A,C);

n=det(W);

if abs(n)<eps

disp(‘system is not observabilety’);

else

disp(‘system is observability’);

end.

RESULT: Hence the transfer function of the given system, controllability,

observability and system stability are found.

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Add On Experiments:-

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1.SIMULATON OF TRANSFER FUNCTION USING OPERATIONAL

AMPLIFIER

Circuit Diagram:-

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1. SIMULATON OF TRANSFER FUNCTION USING OPERATIONAL

AMPLIFIER

AIM:- To simulate transfer function using operational amplifier. APPARATUS:- Bread board,

Resistors 1k and 100k,

Capacitors-4.7uf,

CRO,

Function generator.

THEORY:-The operational amplifier is a direct coupled high gain amplifier consisting of two

or more differential amplifier followed by a level shifter and output stage. The feedback is added

to control its overall response characteristics. It is used to perform a wide variety of linear and

non-linear operations.

ELECTRICAL PARAMTERS OF PO-OMP:-

INPUT OFFSET VOLTAGE:-

It is the voltage which must be supplied between the input terminal of an operational

amplifier to balance it.

OUTPUT OFFSET VOLTAGE:

It is the difference between the dc voltages present at the two output terminals.

COMMON MODE REJECTION RATIO (CMRR):-

It is defined as the ratio of the differential voltage gain (Adm) and common mode voltage

gain (Acm)

CMRR=Adm/Acm.

INPUT RESISTANCE:-

It is the equivalent resistance that can be measured at either the inverting input terminal with the

other terminal connected to ground.

SLEW RATE:-

It is the time rate of change of the closed loop amplifier output voltage under large signal

conditions.

S.R=dVo/dt\max. v/us

POWER SUPPLY REJECTION RATIO:-

It is the ratio of change in input offset voltage to the corresponding change in one power

supply voltage, all remaining power supply voltages held constant.

PROCEDURE:-

1. Connect as per circuit diagram of integrator.

2. Give a sequence input to integrator ckt via function generator.

3. Observe the output waveform on CRO for lower frequency output.

4. The frequency is adjusted to higher values to get a triangular output.

5. Note the time period and frequency of output waveform.

RESULT:-

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