A system with transfer function $G(s)=\frac{1}{(s+1)(s+a)}, a>0$ is subjected to input $5 \cos 3 t$. The steady state output of the system is $\frac{1}{\sqrt{10}} \cos (3 t-1.892)$. The value of $a$ is
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2
GATE ECE 2018
Numerical
+2
-0
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 _________.
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3
GATE ECE 2018
Numerical
+2
-0
The figure below shows the Bode magnitude and phase plots of a stable transfer function
Consider the negative unity feedback configuration with gain k in the feedforward path.
The closed loop is stable for k < k0. The maximum value of k0 is ______.
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4
GATE ECE 2017 Set 2
MCQ (Single Correct Answer)
+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
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