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Control Systems and Simulation Lab

CONTROL SYSTEMS AND SIMULATION LAB

DEPARTMENT OFELECTRICAL AND ELECTRONICS ENGINEERING

ACADEMIC YEAR 2012-2013

III B.Tech EEE I-SEMESTER

ctrical & Electronics Engineering Department-KKR AND KSR INSTITUTE OF TECHNOLOGY AND SCIENCES 1



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P RE F AC E

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.

Electrical & Electronics Engineering Department-BVRIT 2


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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:-

DO ’ S AN D DON ’ T S I N T HE L AB

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 LabStore 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 HYDERABADIII 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 Posit ion 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 usingMAT LAB

Add on Experiments

1 Simulation of Transfer function using Operational

Amplif ier

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) s ig n al s o u r ce :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) S ec o n d o r d e r sy s t e m :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 function2 2 2C(S)/R(S)= Wn /S +2 W+Wn

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.s1-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 position4) 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 toas 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

Procedure:-Study of synchro transmitter:

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 voltagewhich have to be –ve sign has to be desired form the knowledge of voltage between waveforms.

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.

S.NO Voltage ROTOR

POSITION

SHAFT

V(S1-S3) V(S

2-S

3) V(S

3-S

4)

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?








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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 switch2) Square : Variable square wave out 0-2v.

3) Level : Potentio meter to vary the amplitude of squarewave and triangular wave

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

wave and triangular wave5) 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 terminal9) DPM : 31/2 digit DC volt meter to measure DC voltage at

different points10) 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 from10-1000

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

gain from 1-0.0116) 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) Pro po rt io na l co nt r o ller – o pen loo p:

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 PIDinput.

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 position6) Vary the proportional gain pot and note down the O/P voltage

S.NO Vin Gain (K c) 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 ground4.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 diagram2. Connect square wave to vin

3. Connect the constant block only the loop4. 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

CI RCUI T DI AGR AM:-








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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 thetemperature.

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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50V

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



6. CHARACTERISTICS OF MAGNETIC AMPLIFIER

AIM: To study the characteristics of magnetic amplifier.APPARATUS: magnetic amplifier kit,

patch cords,load (100wbulb),

external dc supplyAmmeters – (0-100mA, MC)-1 No

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

Procedure for series connected magnetic amplifier parallel connected

magnetic amplif ier

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:100V 50V

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

Parallel Magnetic Amplifier:

100V

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








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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., Tachoout)(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 fusio n by a 60 to 80 degrees. The O/P will beobserved

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 wisedirection.

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 180

0 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 indicatingover 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:

S.No I/P angular positiondegrees

Output angular position degrees

Withstabilizing

Remarks

Table: 3

S.No I/P angular position

degrees

Output angular

position

degrees

With out

stabilizing

Remarks

Result:








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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 RPM3. 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. E b 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, Notedown 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 rpm6. 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 & variableresistance (load control). This method does not take in to the account the no load torquedeveloped by the ac servo motor. To measure torque developed at no load (i.e torque justrequired 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 variableresistance 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 themechanical power developed at the shaft. Again we must use the formula.

P= 2pi*NT/60Torque = P*1.019*10

4*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 =0.17ASpeed 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 R f 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 variousConstants

.APPARATUS:

S.NO NAME RANGE TYPE Qty1 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 diagram2. 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 R f =V/I

3) Field Impedance:

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

Model Graph:








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f f


Model Calculations:


Xf = √(Z2 – R

2)

Lf = XL/2∏f

Transfer function, T(s) = Kg/1+sΤg

Where Kg = ∆Eg/∆If Τg = Lf /R f

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 broadlyclassified as DC servo motor and AC servomotors. But, the DC servomotrs are expensive thanAC servomotors. But, the DC servo motors have linear characteristics and so it is easier tocontrol DC motors are capable of delivering over 3 times their rated torque for a short time butAC motors will short at

2 to 2.5 times their rated torque. In DC servomotors mainly 2 types of motors are classified1. 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 o pen 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 islow, 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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S.No Va Ia N w Τ = K f * Ia

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.








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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 conductingRetardation 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 shownRa = 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-M

2

)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 I F

Ф= k f If

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

Tm = K i K f If Ia , K 1 is constant

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

Tm = K t ia ------------(1)Where K t is known as motor torque constant the motor back emf being prop to speed given as

Ed = K b dӨ / dt -------------(2)Where K b is back emf constant . the deff eq

nof armature ckt is

La dia / dt + R a Ia + e b = va ----------(3) The torque eq

nis

J d2Ө / dt

2+ f dӨ / dt = Tm = K t Ia -------

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

Ed(s) = sk b Ө(s) --------(5)

LasIa(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 eq

n

Js2

Ө(s) + fs Ө(s) = kf Ia(s)

Ia(s) = (Js2

+ fs)/ Kt Ө(s) ------(9)

From 5,6,9Va(s) = (La

s+ Ra) (Js

2+fs)/kt Ө(s) + sk b Ө(s)

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

Ө(s)/Va(s) = kt / s[(Las + Ra) (Js+f) + k bk t]The T.F is given as

G(s) = kt / s [(Las+Ra) (Js+f) + k bk t]At constant speed k b = k t

PROCEDURE:

1. connect the circuit as per ckt diagram2. check the rated speed of motor

3. start the motor with armature on no-load4. 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 speed7. 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 timeconstant

9. determine the different constants of the motor

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

OBSERVATIONS:

With out load With load

N T (Sec) N T(sec)








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V I Ra



V I Eb

Model calculations:

Wintial = 2∏ N/60

Wfinal = 2∏ N1/60

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

Tfinal) K b = E b/(dw/dt)W

1= 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) + k bk t]

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

1B =

0 C = 1 0 1 D=(0)

1

SIMULATION TOOLS:

THEORY:

1. IBM PC Compatible with MATLAB Software

2. MATLAB SIMULATOR

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)

X(t) =x2(t)

xn n X 1

State – Space model representation

State – eqn

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 ……..An-1

B]

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

AT

CT

(AT)2

CT…….(A

T)

n-1C

T]

Rank (W) = n [observable]

Program-1A= [-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 voltagegain (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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control_systems_and_simulation_lab.doc

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