Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 6th Sem New 2161707 Control System Design Previous Question Paper
1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI (NEW) EXAMINATION ? WINTER 2018
Subject Code:2161707 Date:16/11/2018
Subject Name:Control System Design
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) Consider a linear system described by differential equation
?? ? + 2?? ? + ?? = ?? ? + ??
Test the controllability of the system by Kalman?s test.
03
(b) Explain basic electrical lead-lag compensator. 04
(c) With suitable example, explain the robust PID Controller. 07
Q.2 (a) Discuss about the advantages of state space method over conventional
method.
03
(b)
Write steps to design a lag compensator for a given system in frequency domain.
04
(c)
Obtain state model of field-controlled DC servomotor. Choose ?, ?? ? and if as
state variables.
07
OR
(c) Design a lag compensator using root-locus method for a system whose open-
loop transfer function is given by
?? (?? ) =
?? ?? (?? + 1)(?? + 4)
The system is to be compensated for following specifications:
Damping ratio = 0.5, settling time = 10 sec, velocity error constant ? 5 sec
-1
07
Q.3 (a) Give the properties of state transition matrix. 03
(b) Give the design steps of lead compensator in frequency domain. 04
(c) Design a phase lead compensation network in frequency domain for a system
having open-loop transfer function
?? (?? )?? (?? ) =
?? ?? 2
( 1 + 0.05?? )
The system have acceleration error co-efficient=100 sec
-2
for the phase
margin of 20
o
07
OR
Q.3 (a) Obtain the state-space equation and output equation for the system described
by differential equation given by
??? + 4?? ? + 5?? ? + 2?? = 2??? + ?? ? + ?? ? + 2??
03
(b)
Explain dead beat response with suitable example.
04
(c)
Explain robustness of the system with reference to system sensitivity.
07
Q.4 (a) Explain Internal Model Design. 03
(b) Explain the following terms for robust control system.
(i) sensitivity function
(ii) complementary sensitivity function
(iii) additive perturbation
(iv) multiplicative perturbation
04
(c)
Explain the control of uncertain parameter in robust control system.
07
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI (NEW) EXAMINATION ? WINTER 2018
Subject Code:2161707 Date:16/11/2018
Subject Name:Control System Design
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) Consider a linear system described by differential equation
?? ? + 2?? ? + ?? = ?? ? + ??
Test the controllability of the system by Kalman?s test.
03
(b) Explain basic electrical lead-lag compensator. 04
(c) With suitable example, explain the robust PID Controller. 07
Q.2 (a) Discuss about the advantages of state space method over conventional
method.
03
(b)
Write steps to design a lag compensator for a given system in frequency domain.
04
(c)
Obtain state model of field-controlled DC servomotor. Choose ?, ?? ? and if as
state variables.
07
OR
(c) Design a lag compensator using root-locus method for a system whose open-
loop transfer function is given by
?? (?? ) =
?? ?? (?? + 1)(?? + 4)
The system is to be compensated for following specifications:
Damping ratio = 0.5, settling time = 10 sec, velocity error constant ? 5 sec
-1
07
Q.3 (a) Give the properties of state transition matrix. 03
(b) Give the design steps of lead compensator in frequency domain. 04
(c) Design a phase lead compensation network in frequency domain for a system
having open-loop transfer function
?? (?? )?? (?? ) =
?? ?? 2
( 1 + 0.05?? )
The system have acceleration error co-efficient=100 sec
-2
for the phase
margin of 20
o
07
OR
Q.3 (a) Obtain the state-space equation and output equation for the system described
by differential equation given by
??? + 4?? ? + 5?? ? + 2?? = 2??? + ?? ? + ?? ? + 2??
03
(b)
Explain dead beat response with suitable example.
04
(c)
Explain robustness of the system with reference to system sensitivity.
07
Q.4 (a) Explain Internal Model Design. 03
(b) Explain the following terms for robust control system.
(i) sensitivity function
(ii) complementary sensitivity function
(iii) additive perturbation
(iv) multiplicative perturbation
04
(c)
Explain the control of uncertain parameter in robust control system.
07
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2
OR
Q.4 (a) Determine the transfer function from the following data.
?? = [
?3 1
0 ?1
], ?? = [
1
1
], ?? = [
1 1
], D = 0
03
(b)
Discuss the Full state Controller and Observer with associated block diagram.
04
(c) State and derive Ackermann?s formula for determination of the state feedback
gain matrix K.
07
Q.5 (a) Explain Ricatti Equation. 03
(b) Explain Liapnov?s stability criterion theorem. 04
(c) Determine the state transition matrix and solution of the system described by
the vector-differential equation
[
?? 1
? ?? 2
? ] = [
1 2
?3 ?4
] [
?? 1
?? 2
] + [
0
1
] ?? (?? )
Where u(t) = 1, t ? 0
= 0, t < 0
Assume the system to be initially relaxed.
07
OR
Q.5 (a) Explain performance index of optimal control system. 03
(b) Explain positive definite and positive semidefinite function. 04
(c) Explain Linear Quadratic Regulator. 07
*************
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This post was last modified on 20 February 2020