1
GATE ECE 2008
+2
-0.6
A certain system has transfer function $$G\left(s\right)=\frac{s+8}{s^2+\alpha s-4}$$, where $$\alpha$$ is a parameter. Consider the standard negative unity feedback configuration as shown below Which of the following statements is true?
A
The closed loop system is never stable for any value of $$\alpha$$
B
For some positive values of $$\alpha$$, the closed loop system is stable, but not for all positive values
C
For all positive values of $$\alpha$$, the closed loop system is stable
D
The closed loop system is stable for all values of $$\alpha$$, both positive and negative
2
GATE ECE 2006
+2
-0.6
The positive values of “K” and “a” so that the system shown in the figure below oscillates at a frequency of 2 rad/sec respectively are
A
1, 0.75
B
2, 0.75
C
1, 1
D
2, 2
3
GATE ECE 2004
+2
-0.6
For the polynomial
P(s) = s5 + s4 + 2s3 + 2s2 + 3s + 15 ,
the number of roots which lie in the right half of the s-plane is
A
4
B
2
C
3
D
1
4
GATE ECE 2003
+2
-0.6
The open-loop transfer function of a unity feedback system is $$G\left(s\right)=\frac k{s\left(s^2+s+2\right)\left(s+3\right)}$$\$ the range of 'k' for which the system is stable
A
$$\frac{21}4>k>0$$
B
13 > k > 0
C
$$\frac{21}4<\;k\;<\;\infty$$
D
$$-6\;<\;k\;<\;\infty$$
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