Download GTU BE/B.Tech 2018 Winter 8th Sem New 2181705 Advance Control Theory Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2018 Winter 8th Sem New 2181705 Advance Control Theory Previous Question Paper

1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ?VIII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2181705 Date: 29/11/2018

Subject Name: Advance Control Theory

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.


Q.1 (a) Introduce terms positive definite, negative definite and indefinite function. 03
(b) Discuss about mapping between s and z domain. 04
(c) Describe fuzzification and defuzzification in detail. 07

Q.2 (a) Discuss about zero-order hold. 03
(b) Discuss error dynamics of full order state observer. 04
(c)
Consider the system ( 1) ( ) ( ) x k Gx k Hu k ? ? ? where
01
0.16 1
G
??
?
??
??
??
and
0
1
H
??
?
??
??
. Determine a suitable state feedback gain matrix K such that the
system will have the closed loop poles at 0.5 0.5 zj ?? .
07
OR
(c) Discuss stability in the sense of Lyapunov and state Lyapunov theorem on
stability.
07
Q.3 (a) Give difference between full order observer and minimum order observer. 03
(b) Obtain discrete time pulse transfer function by taking z transform when the
sampling period T=1 of the following continuous time system

1
()
( 2)
Gs
ss
?
?

04
(c) Describe about digital implementation of PID controller. 07
OR
Q.3 (a) State and briefly explain sampling theorem. 03
(b) Write about interaction and decoupling in multivariable systems. 04
(c) Obtain discrete time state and ouput equations when the sampling period T=1
of the following continuous time system

1
()
( 2)
Gs
ss
?
?

07
Q.4 (a) Comment on describing function analysis for nonlinear systems. 03
(b) Brief about phase plane analysis. 04
(c) Explain any for type of common nonlinearities in instruments. 07
OR
Q.4 (a) Comment on stability of nonlinear systems. 03
(b) Write a note on phase trajectories. 04
(c) Discuss two degree of freedom controller design with example. 07
Q.5 (a) Give introduction about relative gain array for multivariable systems. 03
(b) Explain jump resonance in non-linear system. 04
(c) With sketch explain terms stability, asymptotic stability and Instability. 07
OR

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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ?VIII (NEW) EXAMINATION ? WINTER 2018
Subject Code: 2181705 Date: 29/11/2018

Subject Name: Advance Control Theory

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.


Q.1 (a) Introduce terms positive definite, negative definite and indefinite function. 03
(b) Discuss about mapping between s and z domain. 04
(c) Describe fuzzification and defuzzification in detail. 07

Q.2 (a) Discuss about zero-order hold. 03
(b) Discuss error dynamics of full order state observer. 04
(c)
Consider the system ( 1) ( ) ( ) x k Gx k Hu k ? ? ? where
01
0.16 1
G
??
?
??
??
??
and
0
1
H
??
?
??
??
. Determine a suitable state feedback gain matrix K such that the
system will have the closed loop poles at 0.5 0.5 zj ?? .
07
OR
(c) Discuss stability in the sense of Lyapunov and state Lyapunov theorem on
stability.
07
Q.3 (a) Give difference between full order observer and minimum order observer. 03
(b) Obtain discrete time pulse transfer function by taking z transform when the
sampling period T=1 of the following continuous time system

1
()
( 2)
Gs
ss
?
?

04
(c) Describe about digital implementation of PID controller. 07
OR
Q.3 (a) State and briefly explain sampling theorem. 03
(b) Write about interaction and decoupling in multivariable systems. 04
(c) Obtain discrete time state and ouput equations when the sampling period T=1
of the following continuous time system

1
()
( 2)
Gs
ss
?
?

07
Q.4 (a) Comment on describing function analysis for nonlinear systems. 03
(b) Brief about phase plane analysis. 04
(c) Explain any for type of common nonlinearities in instruments. 07
OR
Q.4 (a) Comment on stability of nonlinear systems. 03
(b) Write a note on phase trajectories. 04
(c) Discuss two degree of freedom controller design with example. 07
Q.5 (a) Give introduction about relative gain array for multivariable systems. 03
(b) Explain jump resonance in non-linear system. 04
(c) With sketch explain terms stability, asymptotic stability and Instability. 07
OR

2
Q.5 (a) Introduce membership functions for fuzzy logic based systems. 03
(b) Discuss fuzzy logic applications in control systems. 04
(c) Draw root locus diagrams in the z plane for the system shown in Fig. for
the sampling period T=2 sec and
*
( ) ( ( ))
1
DD
z
G z G s K
z
??
?
Z .



07

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