Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 4th Sem New 2141708 Control System Previous Question Paper
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV (NEW) EXAMINATION ? WINTER 2018
Subject Code:2141708 Date:28/11/2018
Subject Name:Control System
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
MARKS
Q.1 (a) Explain Initial value theorem and Final Theorem in Laplace
Transformation.
03
(b) Find the inverse Laplace Transform of the following function:
?? (?? ) =
5?? +3
(?? +1)(?? +2)(?? +3)
04
(c) Explain in detail open loop and closed loop control system along
with example, advantages and disadvantages.
07
Q.2 (a) Write advantages and disadvantages of polar plot. 03
(b) Explain constant-M circle. 04
(c) Sketch the bode plot and determine the gain cross-over and phase
cross over frequencies for the following transfer function.
?? (?? ) =
10
?? (1 + 0.5?? )(1 + 0.1?? )
07
OR
(c) Draw the Bode plot for a system having
?? (?? )?? (?? ) =
100
?? (?? + 1)(?? + 2)
Find gain margin, phase margin.
07
Q.3 (a)
Obtain the transfer function of following electrical system.
03
(b)
Derive force-voltage and force-current analogy.
04
(c)
Obtain the transfer function from the given signal flow graph.
07
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV (NEW) EXAMINATION ? WINTER 2018
Subject Code:2141708 Date:28/11/2018
Subject Name:Control System
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
MARKS
Q.1 (a) Explain Initial value theorem and Final Theorem in Laplace
Transformation.
03
(b) Find the inverse Laplace Transform of the following function:
?? (?? ) =
5?? +3
(?? +1)(?? +2)(?? +3)
04
(c) Explain in detail open loop and closed loop control system along
with example, advantages and disadvantages.
07
Q.2 (a) Write advantages and disadvantages of polar plot. 03
(b) Explain constant-M circle. 04
(c) Sketch the bode plot and determine the gain cross-over and phase
cross over frequencies for the following transfer function.
?? (?? ) =
10
?? (1 + 0.5?? )(1 + 0.1?? )
07
OR
(c) Draw the Bode plot for a system having
?? (?? )?? (?? ) =
100
?? (?? + 1)(?? + 2)
Find gain margin, phase margin.
07
Q.3 (a)
Obtain the transfer function of following electrical system.
03
(b)
Derive force-voltage and force-current analogy.
04
(c)
Obtain the transfer function from the given signal flow graph.
07
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2
OR
Q.3 (a) Explain absolute stability, relative stability and BIBO stability. 03
(b)
Determine the transfer function of a system whose block diagram is given
below.
04
(c) Derive the transfer function of armature-controlled DC motor. 07
Q.4 (a) A unity feedback system has transfer function
?? (?? ) =
?? (2?? + 1)
?? (4?? + 1)(?? + 1)
2
Determine the value of K, if the steady state value of error to be less
than 0.1 when an input r(t) = 1 + 5t is applied.
03
(b) State the rules for construction of root locus. 04
(c) Draw the root-locus for open-loop transfer function
?? (?? )?? (?? ) =
?? ?? (?? + 3)(?? 2
+ 2?? + 2)
when K is varied from 0 to infinity.
07
OR
Q.4 (a) Derive steady state errors for unit step, unit ramp and unit parabolic
input.
03
(b) A unity feedback system is given by open loop transfer function
?? (?? ) =
?? ?? (?? + 10)
Determine the gain K with damping factor of 0.5. Also determine
settling time, peak overshoot and peak time for a unit step input with
the obtained K.
04
(c) The open loop transfer function of a feedback control system is
?? (?? )?? (?? ) =
?? ?? (?? + 4)(?? 2
+ 4?? + 20)
Find the root locus as K is varied from 0 to infinity.
07
Q.5 (a) Consider the characteristic equation
s
4
+ 8s
3
+ 18s
2
+ 16s + 5 = 0
Find out the stability using Hurwitz?s criterion.
03
(b) Compute e
-At
if 04
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?IV (NEW) EXAMINATION ? WINTER 2018
Subject Code:2141708 Date:28/11/2018
Subject Name:Control System
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
MARKS
Q.1 (a) Explain Initial value theorem and Final Theorem in Laplace
Transformation.
03
(b) Find the inverse Laplace Transform of the following function:
?? (?? ) =
5?? +3
(?? +1)(?? +2)(?? +3)
04
(c) Explain in detail open loop and closed loop control system along
with example, advantages and disadvantages.
07
Q.2 (a) Write advantages and disadvantages of polar plot. 03
(b) Explain constant-M circle. 04
(c) Sketch the bode plot and determine the gain cross-over and phase
cross over frequencies for the following transfer function.
?? (?? ) =
10
?? (1 + 0.5?? )(1 + 0.1?? )
07
OR
(c) Draw the Bode plot for a system having
?? (?? )?? (?? ) =
100
?? (?? + 1)(?? + 2)
Find gain margin, phase margin.
07
Q.3 (a)
Obtain the transfer function of following electrical system.
03
(b)
Derive force-voltage and force-current analogy.
04
(c)
Obtain the transfer function from the given signal flow graph.
07
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2
OR
Q.3 (a) Explain absolute stability, relative stability and BIBO stability. 03
(b)
Determine the transfer function of a system whose block diagram is given
below.
04
(c) Derive the transfer function of armature-controlled DC motor. 07
Q.4 (a) A unity feedback system has transfer function
?? (?? ) =
?? (2?? + 1)
?? (4?? + 1)(?? + 1)
2
Determine the value of K, if the steady state value of error to be less
than 0.1 when an input r(t) = 1 + 5t is applied.
03
(b) State the rules for construction of root locus. 04
(c) Draw the root-locus for open-loop transfer function
?? (?? )?? (?? ) =
?? ?? (?? + 3)(?? 2
+ 2?? + 2)
when K is varied from 0 to infinity.
07
OR
Q.4 (a) Derive steady state errors for unit step, unit ramp and unit parabolic
input.
03
(b) A unity feedback system is given by open loop transfer function
?? (?? ) =
?? ?? (?? + 10)
Determine the gain K with damping factor of 0.5. Also determine
settling time, peak overshoot and peak time for a unit step input with
the obtained K.
04
(c) The open loop transfer function of a feedback control system is
?? (?? )?? (?? ) =
?? ?? (?? + 4)(?? 2
+ 4?? + 20)
Find the root locus as K is varied from 0 to infinity.
07
Q.5 (a) Consider the characteristic equation
s
4
+ 8s
3
+ 18s
2
+ 16s + 5 = 0
Find out the stability using Hurwitz?s criterion.
03
(b) Compute e
-At
if 04
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3
?? = [
1 0
1 1
]
using laplace transform method.
(c) Obtain the transfer function of the system having following state
transition equations.
[
?? 1
? ?? 2
? ?? 3
? ] = [
0 1 0
0 0 1
?5 ?25 ?5
] [
?? 1
?? 2
?? 3
] + [
0
25
?120
] ??
?? = [
1 0 0
] [
?? 1
?? 2
?? 3
]
07
OR
Q.5 (a) What are the advantages of state variable analysis over classical
methods?
03
(b) Using Routh?s test determine the stability of a system whose
characteristic equation is given by
s
6
+ 2s
5
+ 8s
4
+ 12s
3
+ 20s
2
+ 16s + 16 = 0
04
(c)
Obtain the state equations for the following system.
07
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This post was last modified on 20 February 2020