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Seat No.:
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Enrolment No.
GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER-IV (NEW) EXAMINATION - WINTER 2020
Subject Code:3141708 Date:11/02/2021
Subject Name:Control Theory
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Time:02:30 PM TO 04:30 PM Total Marks:56
Instructions:
- Attempt any FOUR questions out of EIGHT questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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MARKS
Q.1 (a) Differentiate between open loop system and closed loop systems 03
(b) Define Transfer function. Find the impulse response of a system whose 04 transfer function is G=1/(s+4)
(c) Find the overall transfer function of RLC circuit with output across 07 capacitor.
Q.2 (a) Write mason’s gain formula. 03
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(b) Difference between signal flow graph and block diagram 04 representation of system
(c) For the hovering systems given by 07
x= [0 6]
4=l =5
(a) Find the roots of the characteristic equation
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(b) Find the state transition matrix ®(t),
Q.3 (a) Define 1. Source node, 2. Loop, 3. Sink node 03
(b) Find the transfer function for the following system 04
X = [ 0 1 ]x + [0]u
-5 -10 0
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y=[0 10]x
(c) Find the mathematical model of the mechanical network 07
Y,
|-—+lf I [
B, B,
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]__ eK, M| Kz Ml — L
Q.4 (a) What is analogous of all variables in mechanical network in force- 03 current analogy?
(b) Explain liquid level systems in brief 04
(c) What is state space model? Define states. Derive the expression for 07 converting state model to transfer function?
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Q.5 (a) Find the polar plot of G=1/s 03
(b) What is Bode plot. What should be the input to the system to obtain 04 bode plot. What are the units of scales used for plotting bode plot
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(c) Sketch Bode plots of a unity feedback control system having open- 07 loop transfer function as given below. The magnitude plot of this function should be an exact one and not an approximation. Find the GMandPM G(s)=s(s+0.5)(s” +3.2s+64)
Q.6 (a) Find the eigen values for system represented by 4 = [0 1] 03
[3 2]
(b) Write the rules for drawing root locus 04
(c) Sketch the root locus for an open loop transfer function 07
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G(s)=k(s+2)/s(s+1)Q.7 (a) Explain standard test signals 03
(b) For the system G=25/S*+4S+25, find the natural frequency, damping 04 ratio. Depending on the damping ratio, describe the system
(c) A unity feedback control system’s open loop transfer function is 07
G(s) = k(s +13) / (s(s + 3)(s + 6))
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Using Routh criterion, calculate the range of k for the system to be stable. If the value of k=1, comment on stability.Q.8 (a) For the closed loop system G=(S+1)(S+3)/S3(S+1)(S+3), find the 03
following 1. Order, 2. Type, 3. characteristic-equation
(b) Check the system stability for system whose characteristic equation is 04 given by S*-8S3+16S+5=0
(c) Draw unit step response of a second-order control systems. Describe 07 all specification in detail.
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