c ontrol system

8/9/2019 C ontrol system

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AIM:

S. No Name of the Experiment Page No

1 Temperature Control System 1- 4

2 Transfer Function of DC Motor 5 - 8

3 Bode Plot using MATLAB 9 -10

4 PID Controller 11-14

5 State Space model for classical Transfer functionusing MATLAB-Verification

15-16

6 Characteristics of DC Servo Motor 17-18

7 Root Locus plot from MATLAB 21-22

8 Effect of feed back on given DC Motor 23-25

9 Conversion of state space model to Nyquist plotusing MATLAB

26

10 Time response of second order Control System 27-28

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1. TEMPERATURE CONTROL SYSTEM

To study the performance of various types of controller used to controlthe temperature of an oven.

APPARATUS:

Temperature control unitTechno meter - 1Stop clock - 1

CERCUIT DIAGRAM:

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PROCEDURE:

I.OPEN LOOP TESTING:

1. Keep switch S1 to WAIT, S2 to SET and open FEED BACK.

2. Connect potentiometer (p) output to driver i/p and switch on the

unit.

3. Set potentiometer P to 0.5 which gives Kp = 10 adjust reference

potentiometer to read 5 on the dmm.

4. Put switch S2 to the measure position and note down the room

temperature.

5. Put switch S1 to run position and note down the room

temperature readings every 30 seconds till the temperaturebecomes almost constant.

6. Plot temperature time curve on a graph paper calculate T1 and T2

hence write the transfer function of the oven including its driver

as

G(s) = Ke (ST2) / (1+ST1) with T in 0C.II.P CONTROLER:

Kp for P controller is a Kp = T1 / (K T2)

1. starting with cool oven, keep switch S1 to WAIT position &

connect P to output to the driver i/p keep R, D, and I o/ps

disconnected short FEED BACK terminals.

2. Set up potentiometer to the above calculated value of Kp

keeping in mind that maximum gain is 10.

3. Plot the observation on a linear graph paper and observe the rise

time, study state error and output overshoot.

III.P I CONTROLER:

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1. Starting with cool oven, keep switch S1 to WAIT position &

connect P & I output to the driver i/p and disconnect R, D. o/ps

short FEED BACK terminals.

2. Set P and I potentiometer to the above values of KP and K

respectively select and set the desired temperature to say 60

keep switch S2 to RUN position and record temperature plot

the observation on graph.

3. Starting with a cool oven, keep switch S1 to WAIT position &

connect P, I, and D o/ps to driver i/p keep R output

disconnected short feed back terminals.

4. Set P, I & D potentiometer according to calculated values.

IV.P ID CONTROLER:

1. Starting with cool oven, keep switch S1 to WAIT position &

connect P & I output to the driver i/p and disconnect R, D. o/ps

short FEED BACK terminals.

2. Set P, I, D according to the above calculated values of KP, KI (or)

KD keeping in mind that there is a maximum value are 20, 0.0245

and 23.5 respectively.

3. Select & set the desired temperature time readings.

4. Plot the response on a graph paper and observe Tr Steady state

error and percentage over shoots.

OBSERVATIONS:

P CONTROLER:

S.N

o

TIME TEMPERATURE

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P I CONTROLER:

S.No

TIME TEMPERATURE

PID CONTROLER:

S.No

TIME TEMPERATURE

EXPETED GRAPH:

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RESULT:

The performance of various types of controllers i.e., P, PI and PIDcontrollers to control the temperature of an oven are studied.

VIVA VOCE:

Define control system. Define open loop control system. Define open loop control system. Is temperature control system open loop are closed loop control

system?

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2. TRANSFER FUNCTION OF A DC MOTOR

AIM:To study the torque speed characteristics and determine the

transfer function of a Dc motor.

APPARATUS:

1. Trainer kit of a DC motor

2. DMM meters -2

3. Connecting wires

CIRCUIT DIAGRAM:

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PROCEDURE:

MOTOR AND GENERATOR CHARACTERISTICS:

1. Set Motor switch to ON set RESET switch to RESET set

LOAD switch to 0 position.

2. Vary Ea in small steps and take readings.

3. Plot N VS Ea and Eg VS N obtain the slopes and compute Km and KG.

TORQ SPEED CHARACTERISTICS:

1. Set Motor switch to OFF set RESET switch to RESET set


2. Connect Ea to the voltmeter and set Ea = 6V

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3. Shift the Motor switch to ON measure armature in put (Ea),

motor current (Ia) & motor speed in rpm record the readings.

4. Set the LOAD switch to 1, 2. . 5 and take readings as above.

5. Complete the table motor voltage Ea = 6 volts; Ra = 4.42.

6. Plot torque VS speed cures on a graph paper.

7. Complete B from the slope of torque speed curve and average

Kb from the table.

8. Repeat above for Ea = 8v, 10v, 12v and record the average

values of motor parameters B and Kb

STEP RESPONSE:

1. Set Motor switch to OFF set RESET switch to RESET set


2. Connect Ea to the volt meter and set it to 8V.

3. Switch ON the motor and measure Eg & the speed in rpm these

are the steady state generator voltage Eg and steady state

motor speed N respectively.

4. Set ES to 63.2% of Eg measure above this is the generator Vg at

which the counter will stop counting.5. Switch OFF the motor set RESET switch to READY.

6. Now switch the motor ON record the counter reading as time

constant in mille seconds.

7. Repeat above with Ea = 10V, 12V and tabulate the results.

8. Substitute the values of Km and Tm in equation

Gm(s) = Km / (STm + 1) = w(s) / Ea(s).

9. Using the average values of Tm, B, Kb and Ra calculate the motor

inertia from equation I = Tm (B+Kb2/Ra).

OBSERVATION:

MOTOR AND GENERATOR CHARACTERISTICS:

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S.No Ea(volts)

Ia(mA)

N(rpm)

Eg(volts)

TORQUE SPEED CHARACTERISTICS:

S.N

o

Load

Step

Ia

(mA)

N

(rpm)

W= 2n/60

(rad/sec)

Eb = Ea-IaRa

(volts)

Kb =

Eb / W

Tm = KbIa

(N-m)

STEP RESPONSE:

S.No

Ea(volts

)

Eg(volts

)

N(rpm

)

Es =0.632Eg(volts)

Timeconstant Tm

msec

Gain constantKm = N/ 30 Ea

EXPETED GRAPH:

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FORMULAE USED:

Motor gain constant = Km = KT / RaB+KTKb

Motor time constant = Tm = Raj / RaB+KTKb

Steady state armature current, Ia = (Ea Eb)/ Ra = (Ea/Ra) (KbW/Ra)

Steady state torque generated, Tm = KTIa

Tm = - KTKb / Ra(w) + KT / Ra (Ea)

Kb = Eb / W = (Ea - IaR) / W [volts/rad/sec]

Average Kb = 22.53x10-3 volts/rad/sec

B- Coefficient of viscous friction (N-m/rad/sec)

CALCULATIONS:

RESULT:The transfer function of a DC motor is derived.

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VIVA VOCE:

Define transfer function.

How transfer function is different from voltage gain ? Explain the advantages of transfer function.

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3. BODE PLOT USING MATLAB

OBJECTIVE:

To obtain the Bode Plot for the given transfer function and to

verify it using MATLAB.

)4)(3)(1(

)2(50)(

+++

+=

sss

ssG

APPARATUS:

PC with MATLAB software.

THEORY:

BODE PLOT USING MATLAB:

A stable linear system subjected to a sinusoidal input gives

sinusoidal output of the same frequency after steady state conditions

are reached. However, the magnitude and phase angle change. The

output magnitude and phase depends on the input frequency. Bode

plot give this relation in a graphical way. It can be proved that if s is

replaced by jw, the transfer function gives steady state response to

sinusoidal inputs where w is the angular frequency. The command

bode (num, den) produces the bode plot.

The command (mag, phase, w) =bode (num, den, w) can be used

for specified frequency points contained in w-vector. Result is stored in

magnitude and phase matrices. The command mag dB=20*log (mag)

produces magnitude in dB.

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The command log space (d1, d2) generates 50 points between

10d1 and 10d2, w=log space (1, 2) generates 50 points between 10-1 and

102i.e.,and 100 rad/sec. but if we have to generate 100 points use the

command, w=log space (-1, 2, 100).

)4)(3)(1(

)2(50)(

+++

+=

sss

ssG

THEORETICAL CALCULATIONS:

(- to be done by the student-)

PROGRAM:

NUM = INPUT(ENTER NUMERATOR OF THE TF);

DEN = INPUT(ENTER DENOMINATOR OF THE TF);

SYS=TF (NUM, DEN);

DISP(SYS);

BODE (SYS)

[GM, PM, Wgc, Wpc] =MARGIN (SYS)

GMDB=20*LOG10(GM)

IF((PM>0)& (GMDB>0))

DISP(GIVEN SYSTEM IS STABLE);

ELSE

IF((PM= =0)& (GMDB= =0))

DISP(GIVEN SYSTEM IS MARGINALLY STABLE);

ELSE

DISP(GIVEN SYSTEM IS STABLE)

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END

END

GRID

RESULT:

The Bode plot for the given transfer function has been obtained

and verified it by using MATLAB.

VIVA VOCE:

Explain bode plot.

Give the advantages of bode plot over Nyquist plot. Define gain cross over frequency. Define phase cross over frequency.

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4. PID CONTROLLER

AIM:To study the performance characteristics of an analog PID

controller using simulated system.

APPARATUS:

1. PID Controller

2. Connecting wires

3. C R O

4. Digital voltmeter.

CIRCUIT DIAGRAM:

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PROCEDURE:

Controller Response:

1. Apply a square wave signal of 100 mv, P-P at the in put of the

error detector connect P I and D o/p s to the summer and

display controller O/P on the CRO.

2. With P-potentiometer set to zero obtain maximum value of

P-P Square wave O/P P-P Square waveo/p

Kc = --------------------------------- =

-----------------------------

P-P square wave I/P 0.1

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3. with I - potentiometer set to maximum and P, D

potentiometer to zero , a ramp will be seen on C R O .maximum

value of K is then given by

4 x f x (P-P) triangular curve O/P ramp in

KI (max) = -------------------------------------------------------

P-P square wave amplitude in volts

Where f is the frequency of I/P

4. Set D - potentiometer to maximum and P and I potentiometers to

zero. A series of sharp pulses will be seen on C R O. this is

obviously not suitable for calibrating the D -potentiometer

applying a triangular wave at the I/P of the error detector a

square wave is seen on the C R O

P-P Square wave O/P

Kd(max) = -------------------------------------

4 x f x (P-P) Triangular wave I/P

5. Set all the three potentiometers = P, I and D to maximum values

and apply a square wave I/P of 100 mv (P-P). Observe and

trace the stop response of P I D controller, identify the effects of

P, I and D controls individually on the shape of this response.

II. Proportional control:

1) Make connections as shown in the fig, with process made up of

time delay and time constant blocks. Notice that the C R O

operations in the X - Y mode ensures stable display even at low

frequencies.

2) Set input amplitude to 1v (P-P) and frequency to low value..

3) For various values of Kc = 2-2, 2-4 . . . . . measure from screen

the value if peak over shoot and steady state error and tabulate

graph.

EXPETED GRAPH:

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CALCULATIONS:

(a) P- control:

I/P = Square wave amp ----0.1v (p-p)

O/p = square amps --amp 2.0 (p-p)

O/p voltage (p-p)Kc (max) 2.0/0.1 =20 = ---------------------------

I/p voltage (p-p)

(b) I - control:

I/p = square wave amplitude of 0.1v (p-p)

T=?

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F = 1/T

O/P=Triangular wave of amplitude v (P-P)

Ki (max) = 4 x f x o/p voltage (p-p)--------------------------------I/P Voltage [P-P]

(c). D - Control:

Input Triangular wave of amplitude V (p-p)

Time =?F =1/t

O/P Square wave of amplitude V(P-P)

O/P voltage (P-P)K d (max) = ----------------------

4 x f x I/P voltage (P-P)

RESULTS:The performance characteristics of analog controller using

simulated system

VIVA VOCE:

1. What is the need to add proportional control scheme in the

system?

2. Explain the advantages of integral control over proportional

control

3. Explain the advantages of derivative control scheme.

4. What is need include PID controller in the system?

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5. STATE SPACE MODEL FOR CLASSICALTRANSFER FUNCTION USING MATLAB

VERIFICATION

(I) CONVERSION OF TRANSFER FUNCTIONS TO STATE SPACE

MODEL:

OBJECTIVE:

To obtain the state space model for the given transfer function

and verifying it using MATLAB.

13233)( 23

2

+++

++=

sss

sssT


(-to be done by the student-)

PROGRAM:

NUM = [1 3 3]

DEN = [1 2 3 1]

[A, B, C, D] = TF2SS(NUM, DEN)

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RESULT:

The state space model of the given transfer function has been

verified using

MATLAB.

-2 -3 -1 1

A = 1 0 0 B = 0 C = 1 3 3 D =

0

0 1 0 0

(II) CONVERSION OF STATE SPACE MODEL TO TRANSFER

FUNCTION

OBJECTIVE:

To obtain the transfer function for the given state space model

and Verifying it using MATLAB.

-2 1 0 1

A = -3 0 1 B = 3 C = 1 0 0 D = 0

-1 0 0 3


( - to be done by the student - )

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PROGRAM:

A = [-2 1 0; -3 0 1; -1 0 0]

B = [1; 3; 3]

C = [1 0 0]

D = [0]

[NUM, DEN] = SS2TF (A, B, C, D)

RESULT:

The Transfer Function of the given state space model has been

verified using

MATLAB.

132

33)(

23

2

+++

++=

sss

sssT

VIVA VOCE:

1. What do you understand by state space model?

2. Explain the advantages of state space model over transferfunction approach.

3. Give the formula for transfer function in state space model.

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6. DC SERVO MOTOR SPEED TORQUECHARACTERISTCS

AIM:To study dc servo motor speed torque characteristics

APPARATUS:

DMM 2 no s

Connecting wires

DC Servo Motor

THEORY:

PROCEDURE:

FOR PLOTTING SPEED TORQUE CHARACTERISTICS OF DC SERVOMOTOR

1) Adjust spring balance so that there is minimum load on the servo

motor. Note that you have to pull the knob K in up ward direction

to apply load on the servo motor. You may make use of holes to

apply a fixed load in the system by using screw.

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2) Ensure the pot P (speed control) is in maximum and

anticlockwise position.

3) Switch on the supply and slightly press the control knob in anti

clock wise direction so that self start relay is turned ON and

armature voltage is applied to the armature from zero onwards.

4) Connect the digital or analog millimeter across the terminal

marked armature voltage in the range o to 35 volts

5) Adjust P so that Va = 10v and P2 so that Vf= 20v

6) Note down T1 ,T2 and speed and enter the result in the table

1

7) Keeping Va= 10v, adjust T1 up to 500 gm in suitable steps to get

a set of readings.

8) Now for Va= 15, 20v repeat step 6.

9) Plot speed torque characteristics.

10) You may repeat above steps for various values of field Vg

by controlling pot P2.

OBSERVATION:

Table 1 ; Radius of pulley ; R=3.54 cms/cm , VF=20 volts

Armature voltage constant Va =10, 15, 20, 25 etc

S.No

T1gm

T2gm

T1-T2

Torque [T1-T2] Rgm-cm

N[RPM]

Ia[amps]

TYPICAL READINGS: A

Pulley R=3.5cms

FIED VOLTAGE ARMATURE VOLTAGE VA=10V

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VF=20V

S.No

T1gm

T2gm

T1-T2

Torque =T3.5 cms

Speed[RPM]

Ia[amps

]

B: VF= 20V and VA =15V

FIED VOLTAGEVF=20V

ARMATURE VOLTAGE VA=15V

S.No

T1gm

T2gm

T1-T2

Torque =T3.5 cms

Speed[RPM]

Ia[amps

]

C: VF= 20V and VA =20V

FIED VOLTAGEVF=20V

ARMATURE VOLTAGE VA=20V

S.No

T1gm

T2gm

T1-T2

Torque =T3.5 cms

Speed[RPM]

Ia[amps

]

D: VF= 20V and VA =25V

FIED VOLTAGE ARMATURE VOLTAGE VA=25V

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VF=20V

S.No

T1gm

T2gm

T1-T2

Torque =T3.5 cms

Speed[RPM]

Ia[amps

]

EXPECTED GRAPH:

PRECAUTIONS:

1) The speed control knob should be always in the most anti clock

wise position before switching ON the equipment

2) In order to increase Va, rotate the knob in the clock wise

direction in a gentle fashion.

3) In order to increase the load on servo motor adjust the spring

balance in a care full fashion.

RESULT:The speed torque characteristics of DC servo motor are verified.

VIVA VOCE:

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1. What is meant by servo motor?

2. How it is different from DC motor?

3. Explain the advantages of servo motor.

4. Draw the characteristics of servo motor

7. ROOT LOCUS USING MATLAB

OBJECTIVE:

To plot the Root locus for the given transfer function and to


)52)(1(

)1()(

2+++

+=

ssss

sksG

APPARATUS:

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PC with MATLAB software.

THEORY:

ROOT LOCUS:

Roots of the transfer function move on the s-plane tracing a

particular path when gain is changed from 0 to . This path is called

root locus.

Open loop transfer function = )(sG

Closed loop transfer function =))()(1(

)(

sHsG

sG

+

The characteristic equation is )()(1 sHsG+ = 0

1)()( =sHsG

To make above equation true, )12(180)()( 0 += ksHsG ------(1)

1|)()(| =sHsG ------(2)A plot satisfying (1) and (2) is the root locus. The constant part in

)()( sHsG is called the Gain.

ROOT LOCUS PLOT USING MATLAB:

The characteristic equation can be written as 01 =+ den

num

k .

The command rlocus (num, den) gives the root locus plot.

If the system is defined in state space, root locus is obtained by the

command rlocus (A, B, C, D).

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(-to be done by the student-)

PROGRAM:

NUM = INPUT(ENTER NUMERATOR OF THE TF);

DEN = INPUT(ENTER DENOMINATOR OF THE TF);

SYS=TF (NUM, DEN)

RLOCUS (SYS)

[R,K]=RLOCUS(SYS);

[M,N]=SIZE(R);

I=1:N;

J=1:M;

IF REAL(R(J,I))>0

STR1=STRCAT(SYSTEM IS UNSTABLE FOR K= );

NUM2STR(K(I));

DISP(STR1);

BREAK;

END

END

GRID

RESULT:

The Root locus for the given transfer function has been obtained

and verified by using MATLAB.

VIVA VOCE:

1. Define root locus plot.

2. Give the advantages of root locus over bode plot.

3. Is root locus plot drawn on open loop or closed loop system?

4. What are the different types of feed backs and explain?

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8. EFFECT OF FEED BACK ON A GIVEN DCMOTOR

AIM:To study the effect of feed back on given DC motor.

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APPARATUS:

Trainer kit

Tachometer generator

Connecting wires

THEORY:

CIRCUIT DIAGRAM:

PROCEDURE:

CLOSED LOOP PERFORMANCE:

1. Set VR = 1V and KA = 5

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2. Record the speed N in rpm and the techo generator voltage VT

and steady state error ESS = VR - VT.

3. Repeat the above procedure for different values of KA.

4. Compare in each case, the steady state error computed using

the formula.

TRANSFER FUNCTION OF MOTOR TACHO GENERATOR:

1. Set VR = 1V and KA = 3.

2. Record the speed N in rpm and the tacho generator output VT.

3. Repeat the same with VR = 1V and KA = 4, 5, 6, 7 . . . 10 &

tabulate the measured motor voltage (VM = VRKA) steady state

motor speed N in rpm and tacho generator out put VT.

4. Plot N VS VM and VTVSN obtain KM from the linear regain of the

speed in rad/sec. WSS/motor voltage tacho generator gain

KT = VT, volt sec / Wss rad

5. Apply square wave signal and find the time constant using

formula given below.

6. Obtain the motor transfer using,

G(s) = Km / STm+1

OBSERVATION:

MOTOR TACHO GENERATOR CHARACTERISTICS:

S.No

KAsetting

N(rpm)

VT(volts)

Vm = VRKA(volts)

ExperimentalKa = Vm /VR

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CLOSED LOOP PERFORMANCE:

S.No

KAsetting

N(rpm)

VT(volts)

Ess = VR-VT(volts)

EXPECTED GRAPH:

THEORETICAL FORMULAE:

Keff= (KAKMKT) / (1+ KAKMKT)

Teff = 1 / (2f in [1-VT (p-p) / Vm (p-p)KMKT] )

Km = shaft speed (N) / motor voltage (Vm)

Where Km motor gain constant

And KT = VT / Wss voltage/rad

Where KT tacho generator gain

RESULT:

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Effect of feed back on a given control system is verified.

VIVA VOCE:

1. What is meant by feed back?

2. Explain the advantages of negative feed back over the positive

feed back.

3. What happen when positive feedback is given a motor?

9. CONVERSION OF STATE SPACE MODEL TO NYQUIST

PLOT

OBJECTIVE:

To obtain the Nyquist plot from the given state model and to


0 1 0

A = -3 -4 B = 1 C = 10 0 D = 0


( - to be done by the student - )

PROGRAM:

A = [0 1;-3 -4]

B = [0;1]

C = [10 0]

D = [0]

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[NUM, DEN] = SS2TF (A, B, C, D)

NYQUIST (TF (NUM, DEN))

TITLE (NYQUIST PLOT);

GRID

RESULT:

Nyquist plot for the given state model has been obtained and

verified it using MATLAB.

VIVA VOCE:

1. Define the term state.

2. Define the term state variable.

3. Is state space model unique, explain?

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10. TIME RESPONSE OF SECOND ORDERSYSTEM

OBJECTIVE:To determine the time response specifications of a second order

system using MATLAB.

814

81)(

2++

=

sssG

APPARATUS:PC with MATLAB software

THEORY:

When the resistance, inductance and capacitance are connected

in series to the voltage source e and the voltage across the capacitor

is taken as output.

The mathematical equations are

e(t) = R i(t) +L di/dt+(1/C) i dt and eo =(1/C) i dt

Ei(s)/Eo(s) = (s2+(R/L) s+(1/LC))LC

Eo(s)/Ei(s) =1/(s2+(R/L) s+(1/LC))LC

Compare with characteristic equation s2

+2 wns+wn2

=0

wn = 1/LC, = (R/2)* C/L, = cos-1( )

Damping frequency = wd = wn1- 2

TIME RESPONSE SPECIFICATIONS:

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(i) Delay Time: It is the time taken to reach 50% of its final value.

td = (1+0.7 )/ wn

(ii) Rise Time: It is the time taken to rise from 10% to 90% for over

damped system.

It is the time taken for the system response to rise from

0 to 100% for under

damped system.

It is the time taken for the system response to rise from

5% to 95% for the

critically damped system.

td = [( -tan-1(1- 2/ )]/wd

(iii) Peak Time: It is the time taken for the response to reach peakvalue for the first attempt.

tp = /wd

(iv) Settling Time: It is the time taken to reach and stay within thetolerable limit (2-5%).

ts = 4/( wn)

(v) Peak Overshoot: It is the ratio of maximum peak valuemeasured to the final value.

Mp = e- /(1- 2)


(- to be done by the student-)

PROGRAM:

NUM=[0 0 81];

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DEN=[1 4 81];STEP(NUM,DEN)

TITLE(STEP RESPONSE);

OBSERVATION TABLE:

Time Theoretical values Practical Values

td(msec)trmsec)tp(msec)ts(msec)

Mp (%)

RESULT:

The time response specifications of second order system are

determined and verified using MATLAB.

VIVA VOCE:

1. What is the need to analyze the time response?

2. Define transient response.

3. Define steady state response.

4. Define steady state error.

c ontrol system

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