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GUJARAT TECHNOLOGICAL UNIVERSITY
SEMESTER-IV(NEW) — EXAMINATION - SUMMER 2019
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Subject Code:2141708 Date:13/05/2019
Subject Name: Control System
Time:02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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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+6)
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(c) Using block diagram reduction technique, find out overall transfer 07 function C(s)/R(s) for the diagram shown in fig.1.
R(s)
Q.2 (a) Write Mason’s gain formula and define each term of the formula. 03
(b) Differentiate between signal flow graph and block diagram 04 representation of system.
(c) The open loop transfer function of a unity feedback system is 07
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G(s)H(s) = k(s + 13) / s(s+3)(s+7)
Using Routh’s criterion calculate the range of k for system to be stable. If the value of k=1, comment on stability.
OR
(c) Derive and draw the unit step response of second order 07 underdamped system.
Q.3 (a) Define the following terms: 03
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- Type of a system
- BIBO stability
- Time constant
b) Briefly explain the first order system and its response to unit step 04 input.
(c) Sketch the root locus plot of a control system whose open loop 07 transfer function is given by
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GH(s) = k / s(s+4)(s2+4s+8)
OR
Q.3 (a) Explain the concept of linearity and time invariance in the context 03 of control system.
(b) Define following terms: 04
- rise time
- peak time
- settling time
- peak overshoot
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transfer function is given by
G(s)H(s) = k / s(s + 5)
Q.4 (a) Determine the transfer function of a system described by following 03 state space model
A=[0 2; -1 -1] B=[0; 1], C=[1 0], D=0
(b) State the properties of state transition matrix. 04
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(c) Consider an open loop transfer function 07
G(s)H(s) = 50 / (s+1)(s+2)
Using Nyquist stability criterion, determine whether the system is stable when the feedback path is closed.
OR
Q.4 (a) Discuss the limitations of transfer functions and advantages of analysis 03 of control systems using state space.
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(b) Write a note on steady state error and error constants. 04
(c) Explain Nyquist stability criterion. 07
Q.5 (a) Define bandwidth, gain margin and phase margin for frequency 03 response.
(b) Draw the polar plot of G(s) =10/[s(s+2)]. 04
(c) The open loop transfer function of a unity feedback system is 07
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G(s)H(s) = 50 / (s + 1)(s + 3)
From the Bode plot, determine gain margin and phase margin.
OR
Q.5 (a) Discuss the effect of time delay on the stability of the process. 03
(b) Discuss Nichol’s chart and its application. 04
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(c) The open loop transfer function of a unity feedback system is given 07 by
G(s)H(s) = 10(1 + 0.5s) / s(s + 1)(0.25s + 1)
Draw the Bode plot and determine gain margin and phase margin.
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