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) - ∞


Answer:B



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


Answer:C




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



Answer:C





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


Answer:B





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



Answer:D





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


Answer:A



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



Answer:C




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 < ∞


Answer:A





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


Answer:B




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


Answer:D



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



Answer:B




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