**2009**

1.
The magnitude plot of a rational transfer function G(s) with real
coefficients is shown below. Which of the following compensator has
such a magnitude plot?

a)
Lead compensator

b)
Lag compensator

c)
PID compensator

d)
Lead – Lag compensator

**Solution :**https://www.youtube.com/watch?v=JVBUSrYEb7Q

2.
If the transfer function of the following circuit is V

_{o}(s)/V_{i}(s) = 1/(2+sCR), then the value of the load resistor R_{L}is
a)
R/4

b)
R/2

c)
R

d)
2R

**Solution :**https://www.youtube.com/watch?v=0bJX_BCy6bc

3.
consider the system,

where p and q are arbitrary
real numbers, which one of the following statements about the
controllability of the system is TRUE?
a)
the system is completely state controllable for any non zero values
of p and q

b)
only p=0 and q=0 result in controllability

c)
the system is uncontrollable for all values of p and q

d)
we cannot conclude about controllability from the given data

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

4.
the feedback configuration and the pole-zero locations of G(s) = (s

The root locus
for negative values of k, i.e. for –∞
< k < 0, has break away/break in points and angle of
departure at pole P (w.r.t. the positive real axis) equal to^{2}– 2s + 2)/(s^{2}+ 2s +2), are shown below.
a)
± √2
and 0

^{o}
b)
± √2
and 45

^{o}
c)
± √3
and 0

^{o}
d)
± √3
and 45

^{o}**Solution :**https://www.youtube.com/watch?v=uagcsFAoEB0

5.
The unit step response of an under damped second order system has
steady state value of – 2. Which of the following transfer functions
has these properties?

**Solution :**https://www.youtube.com/watch?v=FVflQ49wsF8

**Common Data Questions: (6 & 7)**

The
Nyquist plot of a stable transfer function G(s) is shown in the
figure. We are interested in the stability of the closed loop system
in the feedback configuration shown.

6.
Which of the following statements is TRUE?

a)
G(s) is an all pass filter

b)
G(s) has a zero in the right half plane

c)
G(s) is the impedance of a passive network

d)
G(s) is marginally stable

**Solution :**https://www.youtube.com/watch?v=2t0EyW64kfI

7.
The gain and phase margin of G(s) for closed loop stability are

a)
6 dB and 180

^{o}
b)
3 dB and 180

^{o}
c)
6 dB and 90

^{o}
d)
3 dB and 90

^{o}**Solution :**https://www.youtube.com/watch?v=RlFKoEWXgw8