**GATE 2006**

1.
The open loop transfer function of a unity gain feedback control
system is given by G(s) = K

**/**[(s + 1)(s + 2)]. The gain margin of the system in dB is given by
a)
0

b)
1

c)
20

d)
∞

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

2.
In the system shown below, x(t) = (sint).u(t). In steady state, the
response y(t) will be

**Solution :**https://www.youtube.com/watch?v=QR9858_QPOg

3.
Consider two transfer functions G

_{1}(s) = 1 / (s^{2}+ as + b) and G_{2}(s) = s / (s^{2}+ as + b). The 3 dB bandwidths of their frequency responses are, respectively

**Solution :**

4.
The unit step response of a system starting from rest is given by
c(t) = 1 – e

^{–}^{2t}for t ≥ 0. The transfer function of the system is
a)
1 / (1 + 2s)

b)
2 / (2 + s)

c)
1 / (2 + s)

d)
2s / (1 + 2s)

**Solution :**https://www.youtube.com/watch?v=KvqQF5J_bgY

5.
The Nyquist plot of G(jω)H(jω) for a closed loop control system,
passes through ( –1, j0) point on the GH – plane. The gain margin
of the system in dB is equal to

a)
infinite

b)
greater than zero

c)
less than zero

d)
zero

**Solution :**https://www.youtube.com/watch?v=skWe48mXRqg

6.
The positive values of "K" and "a" so that the
system shown in the figure below oscillates at a frequency of 2
rad/sec respectively are

a)
1, 0.75

b)
2, 0.75

c)
1, 1

d)
2, 2

**Solution :**https://www.youtube.com/watch?v=VYWtxlytlC8

7.
The unit impulse response of a system is h(t) = e

^{–}^{t}, t ≥ 0. For this system, the steady state value of the output for unit step input is equal to
a)
–1

b)
0

c)
1

d)
∞

**Solution :**https://www.youtube.com/watch?v=8jfSroqXbV8

8.
The transfer function of a phase lead compensator is given by G

_{c}(s) = (1 + 3Ts)/(1 + Ts) where T ≥ 0. The maximum phase shift provided by such a compensator is
a)
π/2

b)
π/3

c)
π/4

d)
π/6

**Solution :**https://www.youtube.com/watch?v=B6_LDoAZ3-I

9.
A linear system is described by the following state equation, then
the state transition matrix of the system is

**Solution :**https://www.youtube.com/watch?v=SdKm17kCbFg

**Statement for Linked Answer questions: (10 and 11)**

Consider
a unity gain feedback control system whose open loop transfer
function is G(s) = (as + 1)

**/**s^{2}.
10.
The value of "a" so that the system has a phase margin
equal to π/4 is approximately equal to

a)
2.40

b)
1.40

c)
0.84

d)
0.74

11.
With the value of "a" set for phase margin of π/4, the
value of unit impulse response of the open loop system at t = 1
second is equal to

a)
3.40

b)
2.40

c)
1.84

d)
1.74

**Solution (10 & 11) :**https://www.youtube.com/watch?v=DlzZDVlirog

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