Download GTU BE/B.Tech 2019 Summer 8th Sem New 2181705 Advance Control Theory Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Summer 8th Sem New 2181705 Advance Control Theory Previous Question Paper

1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ?VIII(NEW) EXAMINATION ? SUMMER 2019
Subject Code:2181705 Date:17/05/2019

Subject Name:Advance Control Theory

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) State effect of sample time on stability of LTI system. 03
(b) Comment on stability of nonlinear system and limit cycles. 04









(c) Derive the transfer function of Zero order hold. 07
Q.2 (a) Explain the block diagram of the digital control system. 03
(b) Explain phase plane, phase trajectory, phase portrait. 04
(c) Explain Singular points in detail 07
OR
(c) Describe the digital implementation of PID controller. 07
Q.3 (a) State sampling theorem. 03
(b) Obtain the z-transform of Unit -Step function 04
(c) Consider the system described by
y(k)-0.6y(k-1)-0.81y(k-2)+0.67y(k-3)-0.12y(k-4)=x(k)
Where x(k) is the input and y(k) is the output of the system. Determine
the stability of the system.
07
OR
Q.3 (a) List the methods of inverse Z-transform. 03
(b) Find the z-domain transfer function of the following s domain transfer
functions i.)
22
()
a
s b a ??
ii.)
2
()
s
sa ?

04
(c) For the sampled-data control system shown in figure. Find the output c(k)
for r(t)=unit step.

07
Q.4 (a) Derive the relationship between z and s-domain. Also explain the mapping
of s-domain in to z-domain.
03
(b) Explain the describing function analysis? 04
(c) Obtain the describing function of relay with hysteresis type of non-
linearity. Comment on the memory type non-linearity and memory less
non-linearity.
07
OR
Q.4 (a) Give the application of fuzzy logic in control system. 03
(b) What is RGA analysis? 04
(c) Design the state feedback controller for the system 07
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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ?VIII(NEW) EXAMINATION ? SUMMER 2019
Subject Code:2181705 Date:17/05/2019

Subject Name:Advance Control Theory

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) State effect of sample time on stability of LTI system. 03
(b) Comment on stability of nonlinear system and limit cycles. 04









(c) Derive the transfer function of Zero order hold. 07
Q.2 (a) Explain the block diagram of the digital control system. 03
(b) Explain phase plane, phase trajectory, phase portrait. 04
(c) Explain Singular points in detail 07
OR
(c) Describe the digital implementation of PID controller. 07
Q.3 (a) State sampling theorem. 03
(b) Obtain the z-transform of Unit -Step function 04
(c) Consider the system described by
y(k)-0.6y(k-1)-0.81y(k-2)+0.67y(k-3)-0.12y(k-4)=x(k)
Where x(k) is the input and y(k) is the output of the system. Determine
the stability of the system.
07
OR
Q.3 (a) List the methods of inverse Z-transform. 03
(b) Find the z-domain transfer function of the following s domain transfer
functions i.)
22
()
a
s b a ??
ii.)
2
()
s
sa ?

04
(c) For the sampled-data control system shown in figure. Find the output c(k)
for r(t)=unit step.

07
Q.4 (a) Derive the relationship between z and s-domain. Also explain the mapping
of s-domain in to z-domain.
03
(b) Explain the describing function analysis? 04
(c) Obtain the describing function of relay with hysteresis type of non-
linearity. Comment on the memory type non-linearity and memory less
non-linearity.
07
OR
Q.4 (a) Give the application of fuzzy logic in control system. 03
(b) What is RGA analysis? 04
(c) Design the state feedback controller for the system 07
2
0 1 0
( 1) ( ) ( )
0.16 1 1
x k x k u k
? ? ? ?
? ? ?
? ? ? ?
??
? ? ? ?

Such that the systems will have closed loop poles are z=0.5?j0.5
Q.5 (a) Examine the stability of the following characteristic equation:

32
( ) 1.1 0.1 0.2 0 P z z z z ? ? ? ? ?
03
b) What are fuzzy membership function and its types 04
(c) Explain fuzzification and defuzzification briefly. Also write the features of
membership function
07
OR

Q.5 (a) What is two degrees of freedom control? 03
(b)
Explain the graphical method of drawing the phase plane with suitable
example.
04
(c) Explain multivariable systems with example. What is interacting and non-
interacting systems?
07

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