GUJARAT TECHNOLOGICAL UNIVERSITY
SEMESTER-IV(NEW) — EXAMINATION - SUMMER 2019
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Subject Code:2142003 Date:15/05/2019
Subject Name: Control Theory
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) Define: 1) delay time, 2) rise time, 3) pick time. 03
(b) State the advantages of frequency response of control system. 04
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(c) Give the difference between block diagram and SFG method. 07
Q.2 (a) Derive transfer function of Field controlled D.C. Motor. 03
(b) Derive and sketch the time response of 1st order control system for the unit step input. 04
(c) Determine the transfer function of the following electric network. 07
R
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C C
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OR
(c) Find mathematical model of following system. 07
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B
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Q.3 (a) Explain initial value and final value theorem. 03
(b) Explain Force-Voltage analogous system. 04
(c) Write a short note on Gear Train and derive all the required equation. 07
OR
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Q.3 (a) Define Gain crossover frequency. 03
(b) Explain Force-Current analogous system. 04
FIG 1.
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Q.4 (a) Define : 1) state variable, 2) state vector, 3) state space 03
(b) A unity feedback system has G(s) = k(s+1) / (s(s+5)). Using Routh Hurwitz criteria find range of k for the closed loop system to be stable. 04
(c) Simplify the block diagram shown in Figure 2. Then; obtain the closed-loop transfer function C(s)/R(s). 07
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Fig 2.
OR
Q.4 (a) Derive expression of Kp, Kv, Ka for Type ‘0’ control system. 03
(b) Define thermal resistance and thermal capacitance. Also derive the transfer function of Thermometer placed in water bath as a Thermal system. 04
(c) For the system having the open loop transfer function 07
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10 / (s(s+10))
Determine the stability of the system by plotting the Bode plot of the system.
Q.5 (a) Define and explain following terms with respect to frequency response (1) Gain Margin (ii) Phase Margin (iii) Stability 03
(b) Write advantages and disadvantages of nyquist plot. 04
(c) A feedback control system has open loop transfer function 07
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k / (s(s+ 4)(s^2 + 4s + 20))
Plot the root locus for K= 0 to 8. Indicate all point on it.
OR
Q.5 (a) Explain with suitable example, one method for linearization of nonlinear mathematical model. 03
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(b) Discuss the response under damped condition and critical damping for second order system. 04
(c) Explain constant-M circles and constant-N circles by deriving related expressions. Explain how resonant peak can be obtained. 07
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