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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
PDDC SEMESTER-IV EXAMINATION WINTER 2018
Subject Code:X41102 Date: 22/11/2018
Subject Name: Control Theory
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1

Define and explain following terms in reference to control theory:
Open loop control
Closed loop control
Transfer function
Feed forward system
04

Justify "Feedback improves the time constant of a control system".
03

Determine the overall transfer function for a given block diagram also verify same with the help of Signal Flow Graph. (See Fig. 1).
07
Q.2

What do you mean by transient steady state response? Also write the significance of the same.
07

Explain force-voltage and force-current analogy.
07
OR

For the second order system with transfer function as given 4 (S2 2S Obtain Maximum percentage overshoot Mp and Peak Time Tp.
07
Q.3

Derive the expression for the time response of first order system for unit step and ramp inputs.
07

Derive expressions for the steady state errors of type 0 and type 1 system exited to unit step and unit ramp.
07
OR
Q.3

State and explain the Routh's stability criterion.
07

Determine the stability of a system having following characteristic equations: s6 s5 5s4 3s3 2s2 4s 8 0.
07
Q.4

Explain rules for construction of Root Locus.
07

Write a brief note on Nyquist Criterion.
07
OR
Q.4

Write a short note on polar plots and its significance.
07

Draw the root locus for a unity feedback control system has an open loop transfer function
07
Q.5

Define gain cross over frequency and phase cross over frequency.
07

Sketch the bode plot for the
07
OR
Q.5

Write a note on correlation between time and frequency response of 2nd order systems.
07

For a series RLC circuit draw the state diagram and derive the vector matrix form.
07
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Fig. 1