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# Control system | GATE Questions on Time domain analysis

1) For a second order system, damping ratio , 0< $\zeta$  <1 , the roots of the characteristic polynomial are

a) Real, but not equal

b) Real and equal

c) Complex conjugates

d) Imaginary

2) For a second order control system with the closed loop transfer function

T(s) = $\frac {9}{s^2+4s+9}$ , the settling time for  2 percent band is (In seconds)

a) 1.5

b)2

c) 3

d) 4

3) Consider a system with transfer function G(s)= $\frac {s+6}{Ks^2+s+6}$ . Its damping ratio will be 0.5 when the value of K is

a) 2/6

b) 3

c) 1/6

d) 6

4) A unity feedback control system has the open loop transfer function

G(s)= $\frac {4(1+2s)} {s^2(s+2)}$ . If the input to the system is a unit ramp, the steady state error will be

a) 0

b) 0.5

c) 2

d) Infinity

5) A causal system having the transfer function G(s) = $\frac {1}{s+2}$ is excited with 10 u(t). The time  at which the output reaches 99% of its steady state value is

a) 2.7 seconds

b) 2.5 seconds

c) 2.3 seconds

d) 2.1 seconds

6) A ramp input applied to an unity feedback system results in 5% steady state error. The type number and zero frequency gain of the system are

a) 1 and 20

b) 0 and 20

c) 0 and 1/20

d) 1 and 1/20 Gpbhupinder (@gpbhup… on GATE : Multiple choice questio…