GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER-IV (OLD) EXAMINATION - WINTER 2018
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Subject Code:141701 Date: 10/12/2018Subject Name: Control Theory
Time: 02:30 PM TO 05:00 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.
Q.1 (a) State and explain Open loop and Closed loop control systems. Also, compare their merits and demerits. 07
(b) Using block diagram reduction technique find the closed loop transfer function of the system whose block diagram is given in figure 1. 07
Q.2 (a) Define Following Terms: 07
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(I) Transfer Function (II) State (III) Self Loop (IV) Source Node (V) Rise Time(VI) Delay Time (VII) Peak Time
(b) A unity feedback system is characterized by open loop transfer function G(s) = K/s(s + 8). Determine gain K so that system-will have damping ration of 0.7. 07
OR
(b) A system has transfer Function C(s)/R(s) = 10 /s + 2. Determine its unit impulse, step and ramp response with zero initial conditions. Sketch the response. 07
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Q.3 (a) What is analogous system? Explain Force-Voltage and Force-Current Analogy with suitable example. 07
(b) A coupled spring-mass system is shown in the figure 2. Obtain the differential equations describing the system. 07
OR
Q.3 (a) Describe Correlation between transfer function and state-space equations with suitable example. 07
(b) Obtain a state-space representation of the system shown in figure 3. 07
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Q.4 (a) Explain Routh-Hurwitz criterion use to determine system stability with suitable example. 07
(b) Determine range of K for system stability for the characteristic equation of feedback system is S4 + 20S3 + 15S2 + 2S + K = 0. 07
OR
Q.4 (a) State and explain the Nyquist stability criterion use to determine system stability. 07
(b) Sketch the Bode plot for the transfer function G(s)= 10/s(1 + 0.5s)(1 + 0.01s). Also, determine Gain margin, Phase margin and comment on system stability. 07
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Q.5 (a) Define: Root locus, Frequency response, Gain margin, Phase margin, Polar plot, Bode plot, Break-in point. 07
(b) Draw the Nyquist plot for G(s) = 1/s(s — 1) and comment on system stability. 07
OR
Q.5 (a) State and explain the Nyquist stability criterion use to determine system stability. 07
(b) Sketch the Root locus plot for the unity feedback system having G(s)=K/s(s+2)(s+4). 07
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