**GATE 2007**

1.
If the closed loop transfer function of a control system is given as
T(s) = (s – 5)

**/**[(s + 2)(s + 3)], then it is
a)
an unstable system

b)
an uncontrollable system

c)
a minimum phase system

d)
a non-minimum phase system

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

2.
If the Laplace Transform of a signal y(t) is Y(s) = 1

**/**[s(s – 1)], then its final value is:
a)
– 1

b)
0

c)
1

d)
unbounded

**Solution :**https://www.youtube.com/watch?v=cvCDerivzj0

3.
A control system with a PD controller is shown in the figure.

If the
velocity error constant K_{v}= 1000 and the damping ratio ξ = 0.5, then the values of K

_{p}and K

_{D}are

a)
K

_{p}= 100, K_{D}= 0.09
b)
K

_{p}= 100, K_{D}= 0.9
c)
K

_{p}= 10, K_{D}= 0.09
d)
K

_{p}= 10, K_{D}= 0.9**Solution :**https://www.youtube.com/watch?v=vxHx4zTs5vg

4.
The transfer function of a plant is T(s) = 5

**/**[(s + 5)(s^{2}+ s + 1)]. The second order approximation of T(s) using dominant pole concept is**Solution :**https://www.youtube.com/watch?v=y1BxLLTHJOI

5.
The open loop transfer function of a plant is given as G(s) = 1

**/**(s^{2}– 1). If the plant is operated in a unity feedback configuration, then the lead compensator that can stabilize this control system is**Solution :**https://www.youtube.com/watch?v=HJ09FtxcO-I

6.
A unity feedback control system has an open loop transfer function
G(s) = – K

**/**[s(s^{2}+ 7s + 12)]. The gain k for which s = –1+j1 will lie on the root locus of this system is
a)
4

b)
5.5

c)
6.5

d)
10

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

7.
The asymptotic Bode plot of a transfer function is as shown in
figure. The transfer function G(s) corresponding to this Bode plot is

**Solution :**https://www.youtube.com/watch?v=fpM5ezwr90c

8.
The state space representation of a separately excited DC servo
motor dynamics is given as

where
ω is the speed of the motor, i

_{a}is the armature current and u is the armature voltage. The transfer function of the motor is**Solution :**https://www.youtube.com/watch?v=jTt-sWQZS0Y

**Statement for Linked Answer Questions 9 & 10:**

9.
The eigen value and eigen vector pairs (λ

_{i}, v_{i}) for the system are

**Solution :**

10.
The system matrix A is

**Solution :**