Download GTU BE/B.Tech 2019 Winter 3rd Sem New 3131101 Control Systems Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 3rd Sem New 3131101 Control Systems Previous Question Paper

1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? III (New) EXAMINATION ? WINTER 2019
Subject Code: 3131101 Date: 28/11/2019

Subject Name: Control Systems
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 Open loop and Closed loop control system with example. 03
(b) Define: Transfer function, Self loop, Steady-state error, 04
(c) Obtain the overall transfer function C/R of the system whose signal flow
graph shown in following figure.

07

Q.2 (a) Explain the conditions for Stable, Marginally stable and Unstable systems. 03
(b) Derive the expressions for error constants
p
K ,
v
K and
a
K corresponding
to step, ramp and parabolic input respectively.
04
(c) Consider the feedback system with
?? (?? ) = 4 ?? (?? + 0.2) ? and ?? (?? ) = 1 + ???? . Determine the value of ??? ? such
that the damping ratio is 0.5. Also obtain the values of rise time ?? ?? and
peak overshoot ?? ??
for its step response.
07
OR
(c) Derive expressions of (i) Rise time, ?? ?? (ii) Peak time, ?? ?? and (ii) Peak
overshoot, ?? ?? for a second order control system subjected to a unit step
input.
07
Q.3 (a) Explain: Frequency response, Root locus, Centroid 03
(b) The characteristic equation of the system is:
4?? 4
+ 2?? 3
+ ????
2
+ 2?? + 1 = 0.
Find ?? ??????
and ?? ??????
.
04
(c) Using Routh?s criterion check the stability of a system whose characteristic
equation is given by
?? 6
+ 3?? 5
+ 5?? 4
+ 9?? 3
+ 8?? 2
+ 6?? + 4 = 0
07
OR
Q.3 (a) Explain concept of Relative stability. 03
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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? III (New) EXAMINATION ? WINTER 2019
Subject Code: 3131101 Date: 28/11/2019

Subject Name: Control Systems
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 Open loop and Closed loop control system with example. 03
(b) Define: Transfer function, Self loop, Steady-state error, 04
(c) Obtain the overall transfer function C/R of the system whose signal flow
graph shown in following figure.

07

Q.2 (a) Explain the conditions for Stable, Marginally stable and Unstable systems. 03
(b) Derive the expressions for error constants
p
K ,
v
K and
a
K corresponding
to step, ramp and parabolic input respectively.
04
(c) Consider the feedback system with
?? (?? ) = 4 ?? (?? + 0.2) ? and ?? (?? ) = 1 + ???? . Determine the value of ??? ? such
that the damping ratio is 0.5. Also obtain the values of rise time ?? ?? and
peak overshoot ?? ??
for its step response.
07
OR
(c) Derive expressions of (i) Rise time, ?? ?? (ii) Peak time, ?? ?? and (ii) Peak
overshoot, ?? ?? for a second order control system subjected to a unit step
input.
07
Q.3 (a) Explain: Frequency response, Root locus, Centroid 03
(b) The characteristic equation of the system is:
4?? 4
+ 2?? 3
+ ????
2
+ 2?? + 1 = 0.
Find ?? ??????
and ?? ??????
.
04
(c) Using Routh?s criterion check the stability of a system whose characteristic
equation is given by
?? 6
+ 3?? 5
+ 5?? 4
+ 9?? 3
+ 8?? 2
+ 6?? + 4 = 0
07
OR
Q.3 (a) Explain concept of Relative stability. 03
2
(b) Write short note on PID controller. 04
(c) Using Routh array determine the range of K for a unity feedback system
whose open loop transfer function is given by
?? (?? ) =
?? ?? (?? + 1)(?? + 3)(?? + 5)

07
Q.4 (a) Explain: State, State variable, state trajectory 03
(b) Draw the polar plot considering a unity feedback system with open loop
transfer function
?? (?? ) =
10
?? (?? + 2)(?? + 5)

04
(c) A unity feedback system has the loop transfer function
G(s) =
K
(s + 1)(s + 3)(s + 5)

a) Find Centroid and Breakaway point.
b) Sketch the Root Locus.
07
OR
Q.4 (a) Explain: Gain margin, Phase margin, Polar plot 03
(b) Write short note on Lag compensator. 04
(c)
A unity feedback system with open loop transfer function G(s) =
K
s(s+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
Q.5 (a) Derive Correlation Between Transfer Functions and State-Space
Equations.
03
(b) Determine the transfer function for the following system.
[
?? 1
? ?? 2
? ] = [
0 3
?2 ?5
] [
?? 1
?? 2
] + [
1 1
1 1
] ??
and ?? = [
2 1
1 0
] [
?? 1
?? 2
]
04
(c) The feed forward transfer function of a close loop system is ?? (?? ) =
1 ?? (?? + 1) ? and feedback transfer function is ?? (?? ) = 1 (?? + 2) ? .
(i) Draw the polar plot of ?? (?? )?? (?? ).
(ii) Find ?? corresponding to ??? (???? )?? (???? ) = 180
?
.
(iii)Find |?? (???? )?? (???? )| corresponding to frequency obtain in (ii).
07
OR

Q.5 (a) Explain standard test signals. 03
(b) Discuss Nyquist stability criterion. 04
(c) Draw the Nyquit plot for unity feedback system having ?? (?? ) = 10 ?
(?? + 1)(?? + 2) . Also, comment on system stability.
07

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