GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER-V (NEW) EXAMINATION - WINTER 2018
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Subject Code:2150909 Date:27/11/2018Subject Name:Control System Engineering
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
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2. Make suitable assumptions wherever necessary.3. Figures to the right indicate full marks.
MARKS
Q.1 (a) Describe the basic three objectives of any control system. 03
(b) By applying the final-value theorem, find the final value of f(t) whose 04
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Laplace transform is given byFs)= 10 / s(s+1)
Also verify the result by taking inverse Laplace transform method.
(c) Simplify the block diagram shown in Fig. I using block diagram reduction 07
technique and obtain R(s) / C(s)
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Q.2 (a) Draw Signal flow graph for following set of equations. 03
X1 = -X2 - 3X3 + 3
X2 = 5X1 - 2X2 + X3
X3 = 4X1 + X2 - 5X3 + 5
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(b) When defining the transfer function, what happens to initial conditions of 04the system? Give suitable examples.
(c) Find the transfer function C/R shown below for the system using Mason’s 07
gain Formula shown in Figure II.
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OR
(c) Derive the Mason’s Gain formula for Signal Flow graph. 07
Q.3 (a) Obtain the unit step response of a unity feedback system whose open loop 03
transfer function is 25 / S(S+1)
(b) Draw the step response of values of damping ration (i) § > 1 (ii) =1 (iii) 04
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<1 (1v) 0<§<1.(c) Derive Overall transfer function of Field controlled DC motor. 07
OR
Q.3 (a) Find the steady state error when unit step input is applied to closed loop 03
transfer function G(s)= 9 / (s+10)
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(b) Define Magnitude and angle criteria for the Root Locus analysis. 04(c) For the figure shown in figure. III determine the value of K and k such that 07
the system has a damping ratio { of 0.7 and an undamped natural
frequency wn of 4 rad/sec.
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Q.4 (a) Define Magnitude Plot and Phase plot of bode plot. 03
(b) Define Gain Margin and Phase margin from Nyquist plot. 04
(c) Consider the following Characteristic equation 07
s4+ks3+s2+s+1=0
Determine the range of K for stability.
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OR
Q.4 (a) How stability can be ensured from Routh Table? 03
(b) How stability can be ensured from Open loop poles and closed loop poles? 04
(c) Draw the Rough sketch of the root Locus for the given transfer function. 07
G(s) = k(s+2) / (s2+2s+3)
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Q.5 (a) Determine the roots is not for the given transfer function using angle criterion. 03
G(s) = K(s+2)(s+3) / s(s+1)
(b) Define the Gain margin and phase Margin when Gain and Phase cross- 04
over frequency is zero and infinity in bode plot.
(c) Draw the Bode plot and find Gain Margin and Phase margin for the 07
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given transfer function.G(s)= k / s(1+0.1s)(1+ 0.5s)
OR
Q.5 (a) Comment on the stability using Nyquist plot with the encirclement around 03
the point -1+j0.
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(b) Explain the significance of proportional control. 04(c) Draw a Nyquist plot for the given transfer function 07
G(s)= k / s2(1+sT1)
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