GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- IV (New) EXAMINATION - WINTER 2019
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Subject Code: 2141004 Date: 13/12/2019
Subject Name: Control System Engineering
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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Q1 (a) Explain Masson’s gain formula. 03
(b) State and explain Open loop and Closed loop control systems. Also, compare their merits and demerits. 04
(c) For the system shown in figure-1, determine the system transfer function C(s)/R(s) using block diagram reduction technique. 07
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R(s) C(s)
H1
OR
Q1 (a) Derive sensitivity SK for closed loop control system. 03
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(b) Define: State variable, State trajectory, Delay time, Rise time 04
(c) Define transfer function. Obtain the transfer of the system defined by 07
X1 = -1 1 0 | 0 X1
X2 = 0 -1 1|X2|+|0|u y=[1 0 0]|X1
X3 = 0 0 -2|X3 1 X2
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Q2 (a) Determine the value of ‘K’ and ‘a’ such that the system has a damping ratio of 03
0.8 and an undamped natural frequency of 3 rad/sec for the close loop system
with G(s) = K/s(s + 2) and H(s) = 1 + as.
(b) Derive the expression for peak overshoot for a second order control system 04
subjected to a unit step input.
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(c) What is analogous system? Explain Force-Voltage with suitable example. 07
OR
Q2 (a) Obtain the values of delay time td, rise time tr, peak time Tp, settling time ts 03
and peak overshoot Mp for the given open loop transfer function of a unity
feedback control system G (s) = 25/s(s + 5).
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(b) Derive the expression for peak time for a second order control system subjected 04
to a unit step input.
(c) Derive Correlation Between Transfer Functions and State-Space Equations. 07
transfer function G(s)= K/s(s+2?)
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Q.4 (a) Define: Frequency response, Gain margin, Phase margin 03
(b) Discuss: Relative stability 04
(c) Sketch the Root locus plot for the unity feedback system having transfer function 07
G(s) = K/s(s+2)
OR
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Q.4 (a) Define: Root locus, Polar plot, Break-in point 03
(b) Explain, how to obtain Gain margin and Phase margin using Polar plots? 04
(c) Determine gain margin and phase margin using bode plot for the system having 07
transfer function G(s)H(s) = 10/s(1+ 0.5s)(1+ 0.01s) and comment on stability.
Q.5 (a) The characteristic equation of Feedback control system is 03
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s4+2s³+ (4+K)s²+9s+25=0
Determine range of K for system stability.
(b) Discuss in brief about PID controller. 04
(c) What is compensator? Explain Phase-Lag compensator in detail. 07
OR
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Q.5 (a) By means of Routh criterion, determine the range of K for stability of the system 03
described by characteristic equation, s³ + 8s² + 2s + 4K = 0.
(b) Draw the polar plot for the given transfer function G(s)H(s) = 1/s(s+1) 04
(c) A unity feedback system with open loop transfer function G(s) = K/s(s+2) is to be 07
compensated to meet the following specifications:
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- Damping ration ? = 0.5
- Damped natural frequency ? = 4 rad/sec
Design the lead compensator to meet the given specifications.
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