**GATE 2005**

1.
A linear system is equivalently represented by two sets of state
equations

Ẋ = AX + BU and Ẇ = CW + DU.

The eigen values of the
representations are also computed as |λ| and |μ|. Which one of the
following statements is TRUE?

**Answer :**

**Solution :**

2.
Which one of the following polar diagrams corresponds to a lag
network?

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

3.
Despite the percentage of negative feedback, control systems still
have problems of Instability because the

a)
components used have non-linearity

b)
dynamic equations of the sub-systems are not know exactly

c)
mathematical analysis involves approximations

d)
system has large negative phase angle at high frequencies

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

4.
The polar diagram of a conditionally stable system for open loop
gain K = 1 is shown in figure. The open loop transfer function of the
system is known to be stable. The closed loop system is stable for

**Solution :**https://www.youtube.com/watch?v=1mBpd1vOX78

5.
In the derivation of expression for peak percent overshoot, which
one of the following conditions is NOT required?

a)
system is linear and time invariant

b)
system transfer function has a pair of complex conjugate poles and
no zeros

c)
there is no transportation delay in the system

d)
the system has zero initial conditions

**Solution :**https://www.youtube.com/watch?v=CCM2Ygcsj1s

6.
A ramp input applied to an unity feedback system results in 5%
steady state error. The Type number and zero frequency gain of the
system are respectively

a)
1 and 20

b)
0 and 20

c)
0 and 1/20

d)
1 and 1/20

**Solution :**https://www.youtube.com/watch?v=cmSIdjxqW-s

7.
A double integrator plant, G(s) = K/S

^{2}, H(s) = 1 is to be compensated to achieve the damping ratio ξ = 0.5, and an undamped natural frequency ω_{n}= 5 rad/sec. Which one of the following compensator G_{c}(s) will be suitable?

**Solution :**https://www.youtube.com/watch?v=5FCT5oDsBf0

8.
A unity feedback system is given as G(s) = k(1 – s) / [s(s + 3)].
Indicate the correct root locus diagram.

**Solution :**https://www.youtube.com/watch?v=cCAfe9ydiU8

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

The
open loop transfer function of a unity feedback is given by G(s) =
3e

^{–2s }**/**[s(s + 2)].
9.
The Gain and Phase cross over frequencies in rad/sec are,
respectively

a)
0.932 and 1.26

b)
0.632 and 0.485

c)
0.485 and 0.632

d)
1.26 and 0.632

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

10.
based on the above results, the Gain and Phase Margins of the system
will be

a)
–7.09 dB and 87.5

^{o}
b)
7.09 dB and 87.5

^{o}
c)
7.09 dB and –87.5

^{o}
d)
–7.09 dB and –87.5

^{o}

**Solution :**https://www.youtube.com/watch?v=aHVPuRMM0q8