Download GTU BE/B.Tech 2019 Winter 4th Sem New 2141004 Control System Engineering Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 4th Sem New 2141004 Control System Engineering Previous Question Paper

1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? IV (New) EXAMINATION ? WINTER 2019
Subject Code: 2141004 Date: 13/12/2019

Subject Name: Control System Engineering

Time: 10:30 AM TO 01:00 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.


Q.1 (a) Explain Masson?s gain formula. 03
(b) State and explain Open loop and Closed loop control systems. Also, compare
their merits and demerits.
04
(c) For the system shown in figure-1, determine the system transfer function
?? (?? ) ?? (?? ) ? using block diagram reduction technique.

Figure ? 1
07
Q.2 (a) Derive sensitivity ?? ?? ?? for closed loop control system. 03
(b) Define: State variable, Sate trajectory, Delay time, Rise time 04
(c) Define transfer function. Obtain the transfer of the system defined by
u
x
x
x
x
x
x
?
?
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1
0
0
2 0 0
1 1 0
0 1 1
3
2
1
3
2
1
?
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?

? ?
?
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?
?
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?
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3
2
1
0 0 1
x
x
x
y
07
OR
(c) Determine the value of ?K ? and ? a? such that the system has a damping ratio of
0.8 and an undamped natural frequency of 3 rad/sec for the close loop system
with ?? (?? ) = ?? ?? (?? + 2) ? and ?? (?? ) = 1 + ???? .
07
Q.3 (a) Derive the expression for peak overshoot for a second order control system
subjected to a unit step input.
03
(b) What is analogous system? Explain Force-Voltage with suitable example. 04
(c)
Obtain the values of delay time
d
t , rise time
r
t , peak time
p
t , settling time
s
t
and peak overshoot
p
M

for the given open loop transfer function of a unity
feedback control system ?? (?? ) = 25 ?? (?? + 5) ? .
07
OR
Q.3 (a) Derive the expression for peak time for a second order control system subjected
to a unit step input.
03
(b) Derive Correlation Between Transfer Functions and State-Space Equations. 04
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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? IV (New) EXAMINATION ? WINTER 2019
Subject Code: 2141004 Date: 13/12/2019

Subject Name: Control System Engineering

Time: 10:30 AM TO 01:00 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.


Q.1 (a) Explain Masson?s gain formula. 03
(b) State and explain Open loop and Closed loop control systems. Also, compare
their merits and demerits.
04
(c) For the system shown in figure-1, determine the system transfer function
?? (?? ) ?? (?? ) ? using block diagram reduction technique.

Figure ? 1
07
Q.2 (a) Derive sensitivity ?? ?? ?? for closed loop control system. 03
(b) Define: State variable, Sate trajectory, Delay time, Rise time 04
(c) Define transfer function. Obtain the transfer of the system defined by
u
x
x
x
x
x
x
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
1
0
0
2 0 0
1 1 0
0 1 1
3
2
1
3
2
1
?
?
?

? ?
?
?
?
?
?
?
?
?
?
?
?
3
2
1
0 0 1
x
x
x
y
07
OR
(c) Determine the value of ?K ? and ? a? such that the system has a damping ratio of
0.8 and an undamped natural frequency of 3 rad/sec for the close loop system
with ?? (?? ) = ?? ?? (?? + 2) ? and ?? (?? ) = 1 + ???? .
07
Q.3 (a) Derive the expression for peak overshoot for a second order control system
subjected to a unit step input.
03
(b) What is analogous system? Explain Force-Voltage with suitable example. 04
(c)
Obtain the values of delay time
d
t , rise time
r
t , peak time
p
t , settling time
s
t
and peak overshoot
p
M

for the given open loop transfer function of a unity
feedback control system ?? (?? ) = 25 ?? (?? + 5) ? .
07
OR
Q.3 (a) Derive the expression for peak time for a second order control system subjected
to a unit step input.
03
(b) Derive Correlation Between Transfer Functions and State-Space Equations. 04
2
(c) Derive the expression for ?? (?? ) for a unity feedback system having forward
transfer function ? ?
) 2 (
2
n
n
s s
s G
??
?
?
? .
07
Q.4 (a) Define: Frequency response, Gain margin, Phase margin 03
(b) Discuss: Relative stability 04
(c) Sketch the Root locus plot for the unity feedback system having transfer function
?? (?? ) =
?? ?? (?? +1)(?? +3)(?? +5)

07
OR
Q.4 (a) Define: Root locus, Polar plot, Break-in point 03
(b) Explain, how to obtain Gain margin and Phase margin using Polar plots? 04
(c) Determine gain margin and phase margin using bode plot for the system having
transfer function ?? (?? )?? (?? ) = 10 ?? (1 + 0.5?? )(1 + 0.01?? ) ? and comment on
stability.
07
Q.5 (a) The characteristic equation of Feedback control system is
?? 4
+ 2?? 3
+ (4 + ?? )?? 2
+ 9?? + 25 = 0
Determine range of K for system stability.
03
(b) Discuss in brief about PID controller. 04
(c) What is compensator? Explain Phase-Lag compensator in detail. 07
OR

Q.5 (a) By means of Routh criterion, determine the range of K for stability of the system
described by characteristic equation, ?? 3
+ 8?? 2
+ 2?? + 4?? = 0.
03
(b)
Draw the polar plot for the given transfer function ?? (?? )?? (?? ) =
10
?? (?? +2)(?? +5)

04
(c)
A unity feedback system with open loop transfer function ?? (?? ) =
?? ?? (?? +2)
is to be
compensated to meet the following specifications:
? Damping ration ?? = 0.5
? Damped natural frequency ?? ?? = 4 ?????? ?????? ?
Design the lead compensator to meet the given specifications.
07

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