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

Solution :    https://www.youtube.com/watch?v=L2Y_rS_Zc9M

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

Solution :   https://www.youtube.com/watch?v=1eQ1YNdEF_4

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

Answer:C

Solution :   https://www.youtube.com/watch?v=0K0Ls-_nRDQ

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

Solution :   https://www.youtube.com/watch?v=uyZ1HtXU6Ow

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

Answer:D

Solution :   https://www.youtube.com/watch?v=JKzEzWRjN4Q

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) - 90^o

b) 0^o

c) 90^o

d) - 180^o

Answer:A

Solution :    https://www.youtube.com/watch?v=8SWwr0wlV0E

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

Answer:C

Solution :    https://www.youtube.com/watch?v=e6XPNiFMSGo

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

Solution :    https://www.youtube.com/watch?v=KmUOC_i7USs

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

Solution :   https://www.youtube.com/watch?v=P_CSEbYpX0s

10. The state variable equations of a system are:

ẋ₁ = -3x₁ -x₂ + u

ẋ₂ = 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

Solution :    https://www.youtube.com/watch?v=CVH0VsecVuQ

11. The state transition matrix e^At for the given matrix A, is

Answer:B

Solution :   https://www.youtube.com/watch?v=w9zVGFsZ3Bw