### 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) ∞

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

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 – 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)

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

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

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) ∞

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

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

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