**2015**

1.
The polar plot of the transfer function G(s)
= 10(s+1)/(s+10) for 0 <
ω
< ∞
will be in the

a)
first quadrant

b)
second quadrant

c)
third quadrant

d)
fourth quadrant

**
**

**Solution :**https://www.youtube.com/watch?v=-2VWgQ6uM1I

2.
A unity negative feedback system has the open loop transfer function

the value of the gain K (>0) at which the root locus crosses the imaginary axis is __________________

the value of the gain K (>0) at which the root locus crosses the imaginary axis is __________________

**
**

**Solution :**https://www.youtube.com/watch?v=taFVjNfxJ_Q

3.
A lead compensator network includes a parallel combination fo R and
C in the feed-forward path. If the transfer function of the
compensator is GC(s) =
(s+2)/(s+4) , the value of
RC is ___________

**
**

**Solution :**https://www.youtube.com/watch?v=DeKH-DPUdMo

When
the plant operates in a unity feedback configuration, the condition
for the stability of the closed loop system is

a)
K

_{P}> K_{I}/2 > 0
b)
2K

_{I}> K_{P}> 0
c)
2K

_{I}< K_{P}
d)
2K

_{I}> K_{P}**
**

**Solution :**https://www.youtube.com/watch?v=1jJORFpuY5Y

The
value of a gain K( >0 ) for which -1+j2 lies on the root locus is
_________.

**
**

**Solution :**https://www.youtube.com/watch?v=IhF_FZ9IJvI

6.
A unity negative feedback system has an open loop transfer function
G(s) = K / S(S+10), the gain K for the system to have a damping ratio
of 0.25 is _____________

**
**

**Solution :**https://www.youtube.com/watch?v=LCcmOh0C1rY

**
**

**Solution :**https://www.youtube.com/watch?v=rqTM5Z91Ihc

8.
By performing cascading and/or summing/differencing operations using
transfer function blocks G

_{1}(s) and G_{2}(s), one CANNOT realize a transfer function of the form**
**

**Solution :**https://www.youtube.com/watch?v=4HChAlhqy2E

The
unit step response of the system approaches a steady state value of
_____________

**
**

**Solution :**https://www.youtube.com/watch?v=dk2BLg2jp9U

The
response y(t) is

a)
sin (t)

b)
1 –
e

^{t}
c)
1 – cos (t)

d)
0

**
**

**Solution :**https://www.youtube.com/watch?v=Ax6VxSUUJtA

**
**

**Solution :**https://www.youtube.com/watch?v=gRlkHoZYDX4

12.
Consider the differential equation dx/dt = 10 – 0.2x with initial
condition x(0) = 1. The response x(t) for t > 0 is

a)
2 – e

^{-0.2t}
b)
2 – e

^{0.2t}
c)
50 – 49e

^{-0.2t}
d)
50 – 49e

^{0.2t}**
**

**Solution :**https://www.youtube.com/watch?v=AXJqGP3EzsE

13.
The transfer function of a first order controller is given as Gc(s) =
K(s+a)
/ (s+b),
where K, a and b are positive real numbers. The condition for this
controller to act as a phase lead compensator is

a)
a < b

b)
a > b

c)
K < ab

d)
K > ab

**
**

**Solution :**https://www.youtube.com/watch?v=uKr3VkkMkow

14.
Consider the Bode plot shown in figure.

Assume that all the poles and zeros are real valued. The value of f

Assume that all the poles and zeros are real valued. The value of f

_{H}– f_{L}(in Hertz) is ____________________**
**

**Solution :**https://www.youtube.com/watch?v=R95T4ztuNQo

15.
The phase margin (in degrees ) of the system G(s) = 10 /s(s+10)
is _____________

**
**

**Solution :**https://www.youtube.com/watch?v=WXHKVhdLeOc

16.
The characteristic equation of an LTI system is given by F(s) = s

^{5}+ 2s^{4}+ 3s^{3}+ 6s^{2 }– 4s – 8 = 0. The number of roots that lie strictly in the left half S – plane is __________.**
**

**Solution :**https://www.youtube.com/watch?v=oz77HAXHwQU

**
**

**Solution :**https://www.youtube.com/watch?v=z5t9oMUeA-U

**
**

**Solution :**https://www.youtube.com/watch?v=mhCsqV9Gd2g

19. The position control of
a DC servo-motor is given in the figure. The values of the parameters
are KT = 1 N-mA, R

_{a}= 1 ohm, L_{a}= 0.1 H, J = 5 kg-m^{2}, B = 1 N-m/(rad/sec) and Kb = 1 volt/(rad/sec). The steady state position response(in radians) due to unit impulse disturbance torque T_{d}is _______.**
**

**Solution :**https://www.youtube.com/watch?v=mbkr17M1Cng