1
GATE ECE 2005
MCQ (Single Correct Answer)
+1
-0.3
A linear system is equivalently represented by two sets of state equations. $$\mathop x\limits^ \bullet = \,\,{\rm A}X\,\, + BU$$ and $$\mathop W\limits^ \bullet = \,\,CW\,\, + DU.$$ The eigen values of the representations are also computed as $$\left[ \lambda \right]\,\,\,\,and\,\,\,\,\left[ \mu \right].$$ Which one of the following statements is true?
A
$$\left[ \lambda \right]\, = \,\left[ \mu \right]\,\,and\,X\, = W$$
B
$$\left[ \lambda \right]\, = \,\left[ \mu \right]\,\,and\,X\, \ne W$$
C
$$\left[ \lambda \right]\, \ne \,\left[ \mu \right]\,\,and\,X\, = W$$
D
$$\left[ \lambda \right]\, \ne \,\left[ \mu \right]\,\,and\,X\, \ne W$$
2
GATE ECE 2005
MCQ (Single Correct Answer)
+2
-0.6
A double integrator plant, $$G(s) = {K \over {{s^2}}},H(s) = 1$$ is to be compensated to achieve the damping ratio $$\zeta = 0.5$$ and an undamped natural frequency, $${\omega _n} = 5$$ rad/sec. Which one of the following compensator $${G_c}(s)$$ will be suitable?
A
$${{s + 3} \over {s + 9.9}}$$
B
$${{s + 9.9} \over {s + 3}}$$
C
$${{s - 6} \over {s + 8.33}}$$
D
$${{s + 6} \over s}$$
3
GATE ECE 2005
MCQ (Single Correct Answer)
+2
-0.6
The open loop transfer function of a unity feedback system is given by g(s)=$${{3{e^{ - 2s}}} \over {s\left( {s + 2} \right)}}.$$ Based on the above results, the gain and phase margins of the system will be
A
$$ - 7.09$$ dB and $${87.5^0}$$
B
$$ 7.09$$ dB and $${87.5^0}$$
C
$$ 7.09$$ dB and $${-87.5^0}$$
D
$$ - 7.09$$ dB and $${-87.5^0}$$
4
GATE ECE 2005
MCQ (Single Correct Answer)
+2
-0.6
The polar diagram of a conditionally stable system for open loop gain K=1 is shown in figure. The open loop transfer function of the system is known to be stable. The closed loop system is stable for GATE ECE 2005 Control Systems - Frequency Response Analysis Question 35 English
A
$$K < 5$$ and $${1 \over 2} < K < {1 \over 8}$$
B
$$K < {1 \over 8}and{1 \over 2} < K < 5$$
C
$$K < {1 \over 8}$$ and 5 < K
D
$$K > {1 \over 8}$$ and K < 5
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