Download GTU BE/B.Tech 2019 Summer 6th Sem New 2161707 Control System Design Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 6th Sem New 2161707 Control System Design Previous Question Paper

1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI(NEW) ? EXAMINATION ? SUMMER 2019
Subject Code:2161707 Date:10/05/2019
Subject Name:Control System Design
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.

MARKS

Q.1 (a) Derive state space model of series RLC circuit. 03
(b) Check for observability of a system having following coefficient matrices
using Kalmann?s test.
?? = [
0 1 0
0 0 1
?24 ?26 ?9
] , ?? = [
0
0
1
] ?????? ?? = [
2 1 0
]
04
(c) Perform diagonalization of a given matrix A
?? = [
0 1 0
3 0 2
?12 ?7 ?6
]
07

Q.2 (a) Discuss about the advantages of state space method over conventional
method.
03
(b) Give the design steps of lag compensator in frequency domain. 04
(c) Obtain the time response of the following system
[
?? 1
? ?? 2
? ] = [
1 0
1 1
] [
?? 1
?? 2
] + [
1
1
] ??
where u(t) is a unit step occurring at t = 0 and ?? ?? (0) = [1 0].
07
OR
(c) State and derive Ackermann?s formula for determination of the state
feedback gain matrix K.
07
Q.3 (a) What is state transition matrix? Give its properties. 03
(b) Obtain the transfer function for the control system having state space model
as
[
?? 1
? ?? 2
? ] = [
?4 ?1
2 ?1
] [
?? 1
?? 2
] + [
3
2
] ??
?? = [
2 3
] [
?? 1
?? 2
]
04
(c) Describe the parameters that are used to analyze the robustness of control
systems.
07
OR
Q.3 (a) Discuss the various Uncertainties in Parameter variation for robust control
system design.

03
(b)
Write steps to design a lead-lag compensator for a given system in frequency domain.
04
(c) The open-loop transfer function of a unity feedback control system is given
by
?? (?? ) =
?? ?? (1 + 0.2?? )

Design a suitable compensator in frequency domain for Kv = 10 and PM
= 50
o
.



07
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1
Seat No.: ________ Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER ?VI(NEW) ? EXAMINATION ? SUMMER 2019
Subject Code:2161707 Date:10/05/2019
Subject Name:Control System Design
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.

MARKS

Q.1 (a) Derive state space model of series RLC circuit. 03
(b) Check for observability of a system having following coefficient matrices
using Kalmann?s test.
?? = [
0 1 0
0 0 1
?24 ?26 ?9
] , ?? = [
0
0
1
] ?????? ?? = [
2 1 0
]
04
(c) Perform diagonalization of a given matrix A
?? = [
0 1 0
3 0 2
?12 ?7 ?6
]
07

Q.2 (a) Discuss about the advantages of state space method over conventional
method.
03
(b) Give the design steps of lag compensator in frequency domain. 04
(c) Obtain the time response of the following system
[
?? 1
? ?? 2
? ] = [
1 0
1 1
] [
?? 1
?? 2
] + [
1
1
] ??
where u(t) is a unit step occurring at t = 0 and ?? ?? (0) = [1 0].
07
OR
(c) State and derive Ackermann?s formula for determination of the state
feedback gain matrix K.
07
Q.3 (a) What is state transition matrix? Give its properties. 03
(b) Obtain the transfer function for the control system having state space model
as
[
?? 1
? ?? 2
? ] = [
?4 ?1
2 ?1
] [
?? 1
?? 2
] + [
3
2
] ??
?? = [
2 3
] [
?? 1
?? 2
]
04
(c) Describe the parameters that are used to analyze the robustness of control
systems.
07
OR
Q.3 (a) Discuss the various Uncertainties in Parameter variation for robust control
system design.

03
(b)
Write steps to design a lead-lag compensator for a given system in frequency domain.
04
(c) The open-loop transfer function of a unity feedback control system is given
by
?? (?? ) =
?? ?? (1 + 0.2?? )

Design a suitable compensator in frequency domain for Kv = 10 and PM
= 50
o
.



07
2


Q.4 (a) Find ?? (?? ) = ?? ????
for given matrix A using Cayley-Hamilton technique.
?? = [
0 ?1
2 3
]
03
(b) Derive the transfer function of lead compensator using electrical network. 04
(c) Write a short note on the design of robust PID controlled system. 07
OR
Q.4 (a) Write a short note on Internal Model design. 03
(b) Discuss about systems with prefilter. 04
(c) The open loop transfer function of a unity feedback system is
?? (?? )?? (?? ) =
?? ?? (?? + 4)(?? + 5)

Design a suitable lag compensator using root locus technique for velocity
constant ? 5 and damping ratio = 0.707.
07
Q.5 (a) Explain positive definite and negative semi definite function. 03
(b) Discuss about Lyapunov?s stability criteria. 04
(c) Explain LQR and Riccatti equation. 07
OR

Q.5 (a) Describe the design of dead beat response with example. 03
(b) Discuss about the considerations to be kept in mind while designing the robust
control system

04
(c) Explain Optimal Control Design. 07

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