# Download GTU B.Tech 2020 Summer 4th Sem 3141708 Control Theory Question Paper

Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Summer 4th Sem 3141708 Control Theory Previous Question Paper

Seat No.: ________
Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER? IV EXAMINATION ? SUMMER 2020
Subject Code: 3141708 Date:27/10/2020
Subject Name: 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) Differentiate between open loop and close loop system
03

(b) For mechanical translational system. Write the analogous
04
electrical elements in force voltage and force-current analogy.

(c) Explain standard Test signals & derive equation of steady state
07

e
rror.
Q.2 (a) Define transfer function and Explain importance of Laplace
03
transform in control system.

(b) Explain following terms with necessary diagrams. (1) Delay Time
04
(2) Rise Time (3) Peak Time (4) Steady state error

(c) For the given mechanical system Write down differential
07
equations, mechanical circuit diagram and obtain force-current
analogy.

OR

(c) What is force voltage analogous system? Which are the analogues
07
quantities according to this method?
Q.3 (a) State the limitation of Routh criterion and how these limitations
03
are overcome by Root Locus.

(b) Explain the mathematical model of thermal system.
04

(c) A linear feedback control system has the block diagram shown in
07
Figure. Using block diagram reduction rules, obtain overall
transfer function C(S)/R (S).

1

OR
Q.3 (a) Derive unit step response of a first order system.
03

(b) By means of Routh criterion, determine the stability of the system
04
described by characteristic equations.
S4+8S3+18S2+16S+5=0
Comment on location of the roots.

(c) For the signal flow graph shown in Figure, using Masson's gain
07
formula determine the overall transfer function C/ R.
Q.4 (a) Define pole, zero and order of a system.
03

(b) Explain Performance Indices.
04

(c) List all the rules to construct a root locus and explain.
07

OR

Q.4 (a) Derive expression of KP, KV, KA for Type `0' control system
03

(b) Define and explain following terms with respect to frequency
04
response (i) Gain Margin (ii) Phase Margin

(c) Explain Sensitivity of Control Systems to Parameter Variations.
07
Q.5 (a) Define : 1) state variable, 2) state vector, 3) state space
03

(b) With example explain the location of the roots of characteristics
04
equation for the stable control system.

(c) Sketch the root locus for the given open loop transfer function
07
()()= K /s (s + 2)(s + 3)

OR
Q.5 (a) Explain the Nyquist stability criterion.
03
(b) Sketch polar plot for the system with open loop transfer function
04
is ()(
)= 1/(s + 4)(s + 2)
(c) Sketch the Bode plot and determine the gain margin and phase
07
margin for the given unity feedback control system.
()()= k / s (1+0.02s)(1 + 0.04s).

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