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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
PDDC SEMESTER-III EXAMINATION WINTER 2018
Subject Code:X30903 Date: 28/11/2018
Subject Name: Control Theory
Time: 10:30 AM TO 01:00 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

What is control system? State types of control systems. Explain in brief openloop and closedloop control system with suitable example. Also compare both the systems.
07

Using block diagram reduction technique find the closed loop transfer function of the system whose block diagram is shown in Figure below.
07
Q.2

Using Manson's gain formula, obtain overall transfer function of signal flow graph shown in Fig.
07
2

Obtain the transfer function of the mechanical system shown in fig
07
OR

Define the following terms:
Delay Time Rise Time Settling Time Peak Time Steady State error Mason's Gain Formula Maximum Overshoot
07
Q.3

Explain Gain Margin Phase Margin Gain crossover frequency
Phase crossover frequency
07

Draw the Bode Plot for the following Transfer Function:

07
OR
Q.3

Draw the Nyquist Plot for the following Transfer Function:
10/S2
07

State how type and order of control system is determined? Define steady state error and derive static error coefficients.
07
Q.4

Draw the root locus plot for a system having open loop transfer function
K
07

Obtain the differential equations for the system shown in fig. and also draw analogous electrical circuit based on torque voltage analogy.
07
OR
Q.4

Write short note on PID controller.
07

Write a brief note on polar plots with a sketch of a simple example.
07
Q.5

Derive the transfer function of a armature controlled D.C. motor.
07

Check the stability of the given characteristic equation S5+2S4+3S3+6S2+2S+1=0 using Routh's method.
07
OR
Q.5

Explain Standard Test Signals used in control system.
07

Derive an expression for the time response of a second-order control system subjected to a unit step input
07