GATE 2006 ECE Control Systems - Complete Video Solutions with Answers


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) ∞

Answer:D




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


Answer:A





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


Answer:C
Solution :





4. The unit step response of a system starting from rest is given by c(t) = 1 – e2t 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)

Answer:B





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

Answer:D





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

Answer:B



7. The unit impulse response of a system is h(t) = et, 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) ∞

Answer:C



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

Answer:D



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


Answer:A




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

Answer:C

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

Answer:C




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