GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- IV (Old) EXAMINATION - WINTER 2019
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Subject Code: 141701 Date: 14/12/2019
Subject Name: Control Theory
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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Q.1 (a) Write short notes on open loop control systems and closed loop control systems. Discuss their advantages and disadvantages.
(b) Explain Standard Test signals & derive equation of steady state error. Discuss steady state error constants also.
Q.2 (a) Explain Rules for block diagram reduction technique.
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(b) Explain constant-M circles and constant-N circles by deriving related expressions. Explain how resonant peak can be obtained.
OR
(b) State and explain Nyquist Stability criteria. Explain about phase margin and gain margin using Nyquist plot.
Q.3 (a) Derive expressions of (1) Rise time, tr (i1) Peak time, tp and (iii) Peak overshoot, Mp
(b) Draw the approximate root-locus diagram for close loop system whose transfer function is given by G(S)H(S) = K/ S (S+2) (S+5)
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OR
Q.3 (a) Briefly explain the first order system and its time response to a unit ramp input.
(b) Derive the transfer function for armature controlled DC motor.
Q.4 (a) By means of Routh criterion, determine the stability of the system described by characteristic equations.
(1)S*+28°+832+4S+3=0
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(2) 384+ 1083 + 582 + 58 +2.=0
(b) Explain force current and.force voltage analogy with suitable example.
OR
Q.4 (a) Explain Mason’s Gain Formula for signal flow Graph with a simple example.
(b) Draw the Polar Plot for the open loop transfer function G(S) = 100/ (S+2) (S+4) (s+8).
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Q.5 (a) Define the following terms:- (1) Gain Margin (2) Phase margin (3) Gain cross over frequency (4) phase cross over frequency (5) Band Width (6) Corner frequency (7) Transfer function.
(b) Draw the Bode Plot for the system having the following transfer function G(S)= 10/ S (S+1) (S+10) and determine stability of the system.
OR
Q.5 (a) Explain the various rules for construction of root locus.
(b) Write definitions of state and state variables. Derive expression of transfer function of the system which is represented in the following standard state space form: X =AX + BU And Y =CX + DU
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