**2014**

1. The forward path transfer
function of a unity feedback system is given by

The value of K which
will place both the poles of the closed loop system at the same
location is

_________________

2. Consider the feedback
system shown in the figure. The Nyquist plot of G(s) is also shown.
Which of the following conclusions is correct?

a) G(s) is an all pass
filter

b) G(s) is a strictly
proper transfer function

c) G(s) is a stable and
minimum phase transfer function

d) The closed loop system
is unstable for sufficiently large and positive k

3. In the circuit shown, the
value of capacitor C (in mF) needed to have critically damped
response i(t) is ______________________

4. A system is described by
the following differential equation, where u(t) is the input to the
system and y(t) is the output of the system.

When y(0) = 1 and u(t) is a
unit step function, y(t) is

5. consider the state space
model of a system, as given below.

The given system is

a) controllable and
observable

b) uncontrollable and
observable

c) uncontrollable and
unobservable

d) controllable and
unobservable

6. The phase margin in
degrees of

calculated using the
asymptotic Bode plot is ____________

7. For the following
feedback system

The 2% settling time of the
step response is required to be less than 2 seconds.

Which one of the following
compensators C(s) achieves this?

8. The natural frequency of
an undamped second order system is 40 rad/sec. If the system is
damped with a damping ratio 0.3, the damped natural frequency in
rad/sec is ______________

9. For the system shown,

when the X_{1}(s)
= 0, the transfer function Y(s)/X_{2}(s) is

10. An unforced linear time
invariant (LTI) system is represented by

If the initial
conditions are x1(0) = 1 and x2(0) = - 1, then the solution of the
state equation is

11. The Bode asymptotic
magnitude plot of a minimum phase system is shown in the figure.

If the system is
connected in a unity negative feedback configuration, the steady
state error of the closed loop system, to a unit ramp input is
_____________

12. Consider the state
space system expressed by the signal flow diagram shown in the
figure.

The corresponding
system is

a) always controllable

b) always observable

c) always stable

d) always unstable

13. Consider the following
block diagram in the figure.

The transfer
function C(s)/R(s) is

14. The input -3e^{2t}u(t),
where u(t) is the unit step function, is applied to a system with
transfer function (S-2)/(S+3). If the initial value of the output is
-2, then the value of the output at steady state is _____________

15. The steady state error
of the system shown in the figure for a unit step input is
___________

16. The state equation of a
second order linear system is given by

17. In the root locus plot
shown in the figure, the pole/zero marks and the arrows have been
removed. Which one of the following tranfer functions has this root
locus?

18. In a Bode magnitude
plot, which one of the following slopes would be exhibited at high
frequencies by a 4^{th} order all pole system?

a) – 80 dB/decade

b) – 40 dB/decade

c) + 40 dB/decade

d) + 80 dB/decade

19. For the second order
closed loop system shown in the figure,

the natural frequency (in
rad/sec) is

a) 16

b) 4

c) 2

d) 1

20. The state transition
matrix Φ(t)
of a system,

21. Consider a transfer
function

with p a positive real
parameter. The maximum value of p until which G_{p} remains
stable is ______________

22. The characteristic
equation of a unity negative feedback system is 1+KG(s) = 0. The open
loop transfer function G(s) has one pole at zero and two poles at –
1. The root locus of the system for varying K is shown in the figure.

The constant damping ratio
line, for ζ
= 0.5, intersects the root locus at point A. The distance from the
origin to point A is given as 0.5. The value of K at point A is
____________