control theory material

B. E. Semester III

Year: 2013

LABORATORY/PROJECT WORK

IN

CONTROL THEORY

[141701]

ELECTRICAL ENGINEERING DEPARTMENT

CERTIFICATE

This is to certify that Shri / Kum. __________________________________

Roll No. __________ of _________________________

class has satisfactorily completed the course in Control Theory

within the four walls of Government Engineering College,

Palanpur.

Date of Submission:-

______________ ________________________

Staff In-Charge Head of Electrical Engg. Dept.

Government Engineering College, Palanpur

Electrical Engineering Department

Subject: - Control Theory Student Name: - Enrollment No:-

INDEX

Sr. No.

Title Page Date Sign Remark

1. Study the principle and operation of a basic open loop and closed loop control system.

2. Derive the reduced form of block diagram of control system using block diagram reduction technique.

3. Derive the mathematical model of the physical systems and its transfer function.

4. Derive the reduced form of block diagram of control system using Masons gain formula.

5. Study the steady state behavior of Type-1 control system, on standard test signals.

6. Analyze the stability of control system using Routh stability criterion.

7. Analyze the stability of control system using root locus technique.

8. Analyze the stability of control system in frequency domain using Bode plot.

9. Analyze stability of control system in frequency domain using Nyquist stability criterion.

EXPERIMENT NO: - 1 DATE:-

AIM: Study the principle and operation of a basic open loop and closed loop Control Systems.

Apparatus:- (1) Trainer Kit for Open Loop Control system (2) Trainer kit for Close Loop Control System (3) Multimeter (4) Test Signal Generator

Theory:-

Open loop control system:-

Open loop control system is a non-feedback type control system wherein output is

neither measured nor compared with the reference input. For each reference input a fixed

operating condition exists. As there is no feedback taken, the open loop control system is

unable to overcome any variation in desired output due to internal or external disturbances.

Simple block diagram represents an Open Loop Control System in fig (1). In the trainer kit for study of open loop control system, the process is of charging of

capacitor using a constant current source. The reference input is the value of voltage to which

the capacitor has to charge. This reference input (value of voltage) can be adjusted by input command adjustment potentiometer. The output of the system is the value of voltage up to, which the capacitor is charged. Disturbance is generated by variation of constant current. The

block diagram for the system is shown in fig (2).

Close loop control system:-

Close loop Control system is a feedback type of control system wherein the

information about instantaneous state of the output is fed back to input and is continuously

compared with the reference input. Depending on the difference between the actual output and

desired output (which is indicated by reference input signal) an error signal is generated that is fed to the control element so as to bring the output of the system to desired value. If because

of internal or external disturbance, the output of the system deviates from its desired value

because of feedback mechanism, the system can self correct and hence works more efficiently

and accurately as compared to the Open loop Control System. The basic block diagram of

Close loop Control system is shown in fig (3). In the trainer kit for the study of Close Loop Control System the process remains same

i.e. charging of Capacitor using constant current source. The reference input is again variable

voltage which indicates voltage to which capacitor has to charge. Disturbance is provided by

the variation of current source. However, because of presence of feedback in this system

compared to trainer for Open loop Control System, the capacitor would charge to desired

value set by reference input in spite of change in value of current source.

Procedure:-

(A) Open Loop:-

1. Keep the Input Command Adj potentiometer on first mark on dial. 2. Keep the disturbance Adj potentiometer fully anticlockwise position for minimum

disturbance current.

3. Connect 0-100 A at position marked MA. 4. Connect 0-50V DVM across the control output terminal.

5. Switch on the power supply.

6. Press the Start Process push button. Process LED will glow.

7. Measure disturbance current and record its value. (Imin = ..) 8. As soon as the process LED is OFF, measure and record the controlled output voltage.

Controlled voltage = . (Min disturbance) 9. Now keep the disturbance Adj potentiometer in max position. That is max disturbance. 10. Press the discharge push button the controlled output voltage will be zero.

11. Now press start process push button. Process LED will be ON.

12. Repeat 7 for the Imax..

13. Repeat the above steps for the other settings of Input Command Adj potentiometer.

(B) Closed Loop:-

1. Connect 0-50 mA meter and DVM at appropriate terminals.

2. Keep the disturbance Adj potentiometer fully anticlockwise position for minimum disturbance current.

3. Switch on the power supply.

4. Keep the switch in discharge mode.

5. Set the switch in RESTART mode.

6. Connect the digital voltmeter at the output terminals. The output voltage will increase but

the error signal will decrease, measure error voltage at Error signal Terminal.

7. As soon as Error signal becomes zero output will be 1 VDC. The process LED will be

ON/OFF. As it will try to maintain output voltage constant at 1 VDC.

8. Take Observation at different setting of input command signals.

Block Diagram:-

Draw the block diagram of each system on the blank side of the paper.

Observation Table:-

For Open Loop Control System:-

Sr. No.

Input Command Setting Disturbance Current Controlled O/P Voltage

1 Mark 1 Imin

=

Imax =

2 Mark 2 Imin

=

Imax =

3 Mark 3 Imin

=

Imax =

For Closed Loop Control System:-

Sr. No Disturbance Current Input Voltage Output Voltage 1.

2.

3.

4.

5.

6.

7.

Conclusion:-

EXPERIMENT NO: -2 DATE:-

AIM: Derive the reduced form of block diagram of control system using Block diagram reduction technique.

Reduce the block diagram and find the transfer function for the following problems: 1.

2.

3.

G

HH

G G-

+

-

+

+ + R(s C(s)

+

G

H

H

G

G

-

+

-

+ + + R(s C(s)

+

-

+ G

H

H

G G+

-

+ + + R(s C(s)

G

+


AIM: - Derive the mathematical model of the physical systems and its transfer function.

(A) Analogous Systems:-

Draw Force/TorqueVoltage and Force/Torque-Current analogy for the given physical

systems:

1. 2.

(C) Electrical Mechanical Systems:-

Find the transfer functions for the following systems:

1. Find VL(s)/V(s). 2. Find 2(s)/T1(s).

R2

1 ohm

R1

1 ohm

V(t) L21 H

L31 H

L1

1 H

4. Find X(s)/E1(s). 5. Find X2(s)/X1(s).

+

-

VL(t)

EXPERIMENT NO:- 4 DATE:-

AIM: - Derive the reduced form of block diagram of control system using Masons gain formula.

Obtain the transfer function for the following systems using Masons gain formula:

1.

2.

3.

4. Construct the signal flow graph for the following set of simultaneous

equations. Find the transfer function X4(s)/X1(s) by Masons gain formula. X2 = A21X1+A23X3

X3 = A31X1+A32X2+A33X3

X4 = A42X2+A43X3


AIM: Study the steady state behavior of type 1 control system, on standard test signals.

Apparatus:- (1) Trainer kit (2) Standard test signal source (3) Digital Multimeter

Theory:-

Type 1 Control System:- The block of type 1 of control system is engraved on the front panel.

Here, Gs = 1/ Ts, Hs = 1

Hence open loop transfer function is

Gs.Hs = 1/Ts1

= 1/Ts As index of s term in denominator is one, we can say, this is a type 1 control system.

Note: steady state error ess of the control system is defined as follows:-

)(lim teet

ss

= or in Laplace form

)(lim0

ssEes

ss

=

Where e(t) or e(s) are error signals. Procedure:- Connect mains cord to 230V a.c. supply. Switch on the unit & see that the supply L.E.D.

glows on.

(A) Step Signal Analysis:- (1) Connect test signal generator output to the input terminals of the trainer. (2) Connect digital multimeter each at the input and the output terminals. (3) Switch on the test signal generator and select STEP signal for the o/p. (4) Adjust Step signal by STEP Adj potentiometer for 1V, 2V, 3V .and for each

reading, observe and record the output voltage in observation table-1.

(5) Repeat the above procedures for different settings of k.(gain control)

(6) From the readings calculate steady state error per unit step input and plot input, output graphs.

(B) Ramp Signal Analysis:- (1) Select ramp signal from Test signal generator. Keep toggle switch in discharge

position.

(2) Keep digital multimeter at the i/p & o/p terminals for 0-200mV Range, or 0-2v range. (3) Make toggle switch in restart position and the ramp signal will be available at the input

terminals of the trainer.

(4) Input voltage will go on increasing at a predefined rate. Observe input and output meters simultaneously and record the output voltage for different input voltage at

10mV, 20mV, 30mV,.250mV. Record your observations in table-2.

(5) From the readings analyze steady state error and plot input output graphs.

(C) Parabolic Signal Analysis:- (1) Select parabolic signal from Test signal generator. Keep toggle switch in discharge

position.

(2) Keep digital multimeter at the i/p & o/p terminals for 0-200mV Range, or 0-2v range. (3) Make toggle switch in restart position and the parabolic signal will be available at the

input terminals of the trainer.

(4) Input voltage will go on increasing at a predefined rate. Observe input and output meters simultaneously and record the output voltage for different input voltage at

100mV, 125mV, 150mV, 175mV.200mV. Record your observations in table-3.

(5) From the readings analyze steady state error and plot input, output graphs.

Observation Table:-

(A) For Step Input:-

Sr. No. Time (Sec) Input R(s) Output C (s)

Error R(s) C(s)

Error/Step R(s) C(s)

R(S) 1. 2. 3. 4. 5.

6. 7. 8. 9.

10.

(B) For Ramp Input:-


Error R(s) C(s)


R(S) 1. 2. 3. 4. 5. 6. 7. 8. 9.

10.

(C) For Parabolic Input:-


Error R(s) C(s)


R(S) 1. 2. 3. 4. 5. 6. 7. 8. 9.

10.

Graph: - Draw the graph of time vs. output and time vs. input on same paper for unit, ramp, and parabolic input, respectively.

Conclusion:-


AIM: Analyze the stability of control system using Routh stability criterion.

(1) Determine the stability of a control system, for given characteristic equation, using Routh Criterion:

(i) s4+10s3+35s2+50s+24=0 (ii) s5+s4+2s3+2s2+3s+15=0 (iii) s6+4s5+3s4-16s2-64s-48=0

(2) Find the range of values of K for which system will be stable: (i) s(s2+s+1)(s+4)+K=0 (ii) s3+(4+K)s2+6s+12=0 (iii) s3+3(K+1)s2+(7K+5)s+(4K+7)=0

(3) Find the range of values of K for which the system is stable. Find the positive value of K that yields pure oscillations in the system and find the frequency of the oscillations.

(4) Determine the values of K and a so that the system given below oscillates at a frequency of 2 rad / sec.

s3+as2+ (k+2) s+ (k+1) =0

K 1/s 1/s 2/s

(s+1)/(s+4)

+

-

+

-

+

-

R(s) C(s)


AIM: Analyze the stability of control system using root locus technique.

(1) For unity gain feedback control system, draw root locus for the following system: (i) G(s) = K/s(s+4)(s+2) (ii) G(s) = K(s+4)/s(s2+2s+2) (iii) G(s) = K/s(s+1)(s+2)(s+3) (iv) G(s) = K(s2 +6s+25)/s(s+1)(s+2)

(2) Consider the third order position control system with velocity feedback shown in the fig.

Determine the values of open-loop gain K so that the dominant poles of the transfer

function of the closed loop system have a damping ratio of 0.56

R(s) K/s(s+2)(s+4)

0.1

+ +

- -

C(s)


AIM: Analyze the stability of control system in frequency domain using bode plot.

(1) For unity gain feedback control system, sketch the bode plot for the following transfer functions and also find the values of Gain Margin and Phase Margin:

(i) G(s) = 80/s(s+2)(s+20) (ii) G(s) = 80(s+2)/s2(s+10)(s+40) (iii) G(s) = 242(s+5)/s(s+1)(s2+5s+121) (iv) G(s) = s2/(1+0.2s)(1+0.02s)

(2) A system has G(s) H(s) = K(s+2)/s(s+4) (s+10). Find K to get P.M. = +30o.

(3) A system has G(s) H(s) = K/s (1+s) (1+0.1s) (1+0.01s). Find the value of K for G.M. = +10 dB, P.M. = +25o.


AIM: Analyze stability of control system in frequency domain using Nyquist stability criterion.

(1) For the unity gain feedback control system, find the stability of the system using Nyquist Stability criterion:

(i) G(s) = 40/(s+4)(s2+2s+2) (ii) G(s) = 10(s+1)/(1+2s)(1+0.1s) (1+0.02s) (iii) G(s) = (1+0.5s)/s2 (1+0.1s) (1+0.02s) (iv) G(s) = 10(s+3) /s (s-1)

(2) For the control system, G(s) H(s) = K/s (s+2) (s+10). Sketch the Nyquist plot and hence calculate the range of value of K for stability.

control theory material

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