1
GATE EE 2003
+2
-0.6
The block diagram of a control system is shown in Fig. The transfer function $$G(s) = Y(s)/U(s)$$ of the system is
A
$${1 \over {18\left( {1 + {s \over {12}}} \right)\left( {1 + {s \over 3}} \right)}}$$
B
$${1 \over {27\left( {1 + {s \over 6}} \right)\left( {1 + {s \over 9}} \right)}}$$
C
$${1 \over {27\left( {1 + {s \over {12}}} \right)\left( {1 + {s \over 9}} \right)}}$$
D
$${1 \over {27\left( {1 + {s \over 9}} \right)\left( {1 + {s \over 3}} \right)}}$$
2
GATE EE 2003
+1
-0.3
A control system is defined by the following mathematical relationship $${{{d^2}x} \over {d{t^2}}} + 6{{dx} \over {dt}} + 5x = 12\left( {1 - {e^{ - 2t}}} \right)$$$The response of the system as $$\,t \to \infty$$ is A $$x=6$$ B $$x=2$$ C $$x=2.4$$ D $$x=-2$$ 3 GATE EE 2003 MCQ (Single Correct Answer) +2 -0.6 The block diagram shown in fig given is a unity feedback closed loop control system. The steady state error in the response of the above system to unit step input is A $$25\%$$ B $$0.75\%$$ C $$6\%$$ D $$33\%$$ 4 GATE EE 2003 MCQ (Single Correct Answer) +2 -0.6 A control system with certain excitation is governed by the following mathematical equation $${{{d^2}x} \over {d{t^2}}} + {1 \over 2}{{dx} \over {dt}} + {1 \over {18}}x = 10 + 5{e^{ - 4t}} + 2{e^{ - 5t}}$$$
The natural time constants of the response of the system are
A
$$2s$$ and $$5s$$
B
$$3s$$ and $$6s$$
C
$$4s$$ and $$5s$$
D
$$1/3s$$ and $$1/6s$$
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