1
GATE ECE 2018
Numerical
+2
-0.67
For a unity feedback control system with the forward path transfer function

$$G(s) = {K \over {s\left( {s + 2} \right)}}$$

The peak resonant magnitude Mr of the closed-loop frequency response is 2. The corresponding value of the gain K (correct to two decimal places) is _________.
2
GATE ECE 2017 Set 2
+2
-0.6
A unity feedback control system is characterized by the open loop transfer function $$G(s) = {{10k\left( {s + 2} \right)} \over {\left( {{s^3} + 3{s^2} + 10} \right)}}$$ The Nyquist path and the corresponding Nyquist plot of g(s) are shown in the figures below. If 0 < K < 1, then number of poles of the closed loop transfer function that lie in the right half of the s-plane is
A
0
B
1
C
2
D
3
3
GATE ECE 2017 Set 1
+2
-0.6
The Nyquist plot of the transfer function $$G(s) = {k \over {\left( {{s^2} + 2s + 2} \right)\left( {s + 2} \right)}}$$ does not encircle the point (-1+j0) for K = 10 but does encircle the point (-1+j0) for K = 100. Then the closed loop system (having unity gain feedback) is
A
stable for K = 10 and stable for K = 100
B
stable for K = 10 and unstable for K = 100
C
unstable for K = 10 and stable for K =100
D
unstable for K = 10 and unstable for K = 100
4
GATE ECE 2016 Set 2
Numerical
+2
-0
The asymptotic Bode phase plot of $${\rm{G(s) = }}{k \over {\left( {s + 0.1} \right)\left( {s + 10} \right)\left( {s + {p_1}} \right)}},$$ with k and p1 both positive, is shown below. The value of p1 is ________
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