### GATE 2004 ECE Control Systems - Complete Video Solutions with Answers

GATE 2004

1. The gain margin for the system with open loop transfer function G(s)H(s) = 2(1 + s)/s2, is
a) ∞
b) 0
c) 1
d) - ∞

2. Given G(s)H(s) = K /[s(s + 1)(s + 3)], the point of intersection of the asymptotes of the root loci with the real axis is
a) - 4
b) 1.33
c) - 1.33
d) 4

3. Consider the Bode magnitude plot shown in figure. The transfer function H(s) is

4. The transfer function H(s) of an RLC circuit is given as 106/[s2+20s+106], then the Q – factor of this circuit is
a) 25
b) 50
c) 100
d) 5000

5. For the circuit shown in figure, the initial conditions are zero. Its transfer function Vo(t)/Vi(t) is

6. A system has poles at 0.01 Hz, 1 Hz and 80 Hz; zeros at 5 Hz, 100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is
a) - 90o
b) 0o
c) 90o
d) - 180o

7. Consider the signal flow graph shown in figure. The gain X5/X1 is

8. The open loop transfer function of a unity feedback system is G(s) = K/[s(s2 + s + 2)(s + 3)]. The range of K for which the system is stable is
a) 21/44 > K > 0
b) 13 > K > 0
c) 21/4 < K < ∞
d) - 6 < K < ∞

9. for the polynomial R(s) = s5 + s4 + 2s3 + 2s2 + 3s + 15, the number of roots which lie in the Right Half of the S-plane is
a) 4
b) 2
c) 3
d) 1

10. The state variable equations of a system are:
1 = -3x1 -x2 + u
2 = 2x1
y = x1 + u
Then the system is
a) controllable but not observable
b) observable but not controllable
c) neither controllable nor observable
d) controllable and observable

11. The state transition matrix eAt for the given matrix A, is