# WBUT Exam Papers B Tech EE

## Control System Sem 5th Dec 3rd 2007

Full Marks : 7

GROUP – A (Multiple Choice Type Questions)

Choose the correct alternatives for any ten of the following : 10×1 = 10

1) The type of a transfer function denotes the number of

sO zeros at origin        b) poles at infinity

c) poles at origin        d) finite poles.

il) The characteristic equation of a system is s 2 + 2s + 2 = 0. The system is

a) critically damped      b) underdamped

c) overdamped             d) none of these.

Ill) Addition of a pole to the closed loop transfer function

a)      increases rise time    b) decreases rise time

c) increases overshoot    d) has no effect.

iv)             By the use of PD control to the second order system, the rise time

0 decreases              b) Increases

c)      remains same d)

has no effect.

v)               When the phase crossover frequency is equal to the galri crossover frequency, the system exhibits

a)               sustained oscillations

b)               damped oscillatory response

c)               oscillations of increasing amplitude

d)              overdamped response.

■ vl) If the gain of the open loop system is doubled, the gain margin

 a) is not affected c) becomes half
 b) gets doubled d) becomes ^ th.

vii)           The function Y+ sT ^as s^°Pe °f

viii)         “Synchros” are popularly used as transmitter of

a) digital data           b) mathematical data

c) angular data           d) all of these.

ix)             A 2nd order system exhibits 100% overshoot. Its damping coefficient is a) equal to 0          b) equal to 1 c) <1 d) >1.

x)               For the transfer function G ( s) H ( s ) = s ( s + i /( s + 0 5 ) ’

the phase crossover frequency is a) 0-5 rad/sec       b)

xi)             Transfer function with unit magnitude & antisymmetric pole-zero patterns correspond to

a) all pass system                                    b)

c) non-minimum phase systems d)

xii)           A linear time invariant system obeys

a)              the principle of superposition

b)              the principle of homogeneity

c)               both the principles in (a) & (b)

d)
none of these.

GROUP -B ( Short Answer Type Questions )

Answer any three of the following.

2. Determine the transfer function of the network shown below in Jig. 1

 E ■

Pig. 1

Use block diagram reduction technique to find out the overall transfer function of the system shown below in Jig. 2.

•——4 <*■ hHlD-p5]—*&—*•=- }    *       L5ZW—————– J

Pig. 2

Consider the following mechanical translation system. F denotes force, X denotes displacement, M denotes mass, B denotes friction coefficient & K denotes spring constant. As shown below in Jig. 3.

a)              Write down the differential equations governing the system shown below.

b)              Draw the corresponding electrical equivalent circuit using force-voltage analogy.

 777′

1. A unity feedback system Is characterized by the open loop transfer function
2. 1

G( s) = s ( 0-5 s+ 1 ) ( 0-2 s + 1 ) •

Determine the steady state errors for unit step, unit ramp & unit acceleration input. Also determine the damping ratio & natural frequency of the dominant roots.

1. The open loop transfer function of a unity feedback system is given by
2. q ( s )                 fS       where k & T are positive constants. By how much should the

s ( Ts + 1 )

amplifier gain be reduced so that the peak overshoot of unit step response of the system is reduced from 75% to 25% ?

GROUP – C ( Long Answer Type Questions )

Answer any three questions.                                      3 x 15 = 45

1. a) Draw the Bode plot of the following system. Find the relative stability of the

system. :            10 ( s + 2 ) s(s^ + s+ 1) •

b)              Derive the transfer function from the following Bode plot shown below in fg. 4­10 + 5

-dC*.

I JMzJtiSsu. I j fft 1

Sketch the root locus of a system whose open loop transfer function is given by

k_____

s(s + 2)(s + 4)‘

Evaluate the value of k at a point where the root loci crosses the imaginary axis. Determine the frequency.

Calculate the values of k so that the dominant pair of complex poles of the system has a damping ratio of 0-5.

State Routh’s stability criterion.

Using Routh’s stability criterion, determine the value of K for which the closed loop system with unity feedback system with open loop transfer function

exhibits sustained oscillation.

Why is the step function used to characterise the dynamic behaviour of a 2nd order system ? State whether the impulse function can be used for this purpose or not.                                   3 + 7 + 5

State & explain the Nyquist criterion for studying stability of a control system.

A unity feedback control system has open loop transfer function K

s(s2+s+4)

Draw the Nyquist plot & hence investigate the stability of the system for various values of k.

 c) 11. a) b> c)