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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


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