1
GATE ECE 2009
+2
-0.6
The Nyquist plot of a stable transfer function G(s) is shown in the figure. We are interested in the stability of the closed loop system in the feedback configuration shown. The gain and phase margins of G(s) for closed loop stability are
A
6 dB and $$180^\circ$$
B
3 dB and $$180^\circ$$
C
6 dB and $$90^\circ$$
D
3 dB and $$90^\circ$$
2
GATE ECE 2009
+1
-0.3
The magnitude plot of a rational transfer function G(s), with real coefficient is shown in figure. Which of the following compensators has such a magnitude plot?
A
B
Lag compensator
C
PID controller
D
Lea-lag compensator
3
GATE ECE 2009
MCQ (More than One Correct Answer)
+1
-0.3
Consider the system $${{dx} \over {dt}} = Ax + Bu$$ with $${\rm A} = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right]\,\,\,and\,\,\,{\rm B} = \left[ {\matrix{ p \cr q \cr } } \right],$$

where p and q are arbitrary real numbers. Which of the following statesments about the controllability of the system is true?

A
The system is completely state controllable for any nonzero values of p and q.
B
Only p =0 and q=0 result in controllability.
C
The system is uncontrollable for all values of p and q.
D
We cannot conclude about controllability from the given data.
4
GATE ECE 2009
+2
-0.6
If X=1 in the logic equation $$\left[ {X + Z\left\{ {\overline Y + (\overline Z + X\overline {Y)} } \right\}} \right]$$ $$\left\{ {\overline X + \overline Z (X + Y)} \right\} = 1,$$ then
A
Y=Z
B
Y= $${\overline Z }$$
C
Z= 1
D
Z= 0
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