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 G1(s) = 1 / (s2
+ as + b) and G2(s) = s / (s2 + 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 Gc(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)/s2.
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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