1
GATE ECE 2024
+2
-1.33

Consider a unity negative feedback control system with forward path gain $G(s) = \frac{K}{(s + 1)(s + 2)(s + 3)}$ as shown.

The impulse response of the closed-loop system decays faster than $e^{-t}$ if ________.

A

$1 \leq K \leq 5$

B

$7 \leq K \leq 21$

C

$-4 \leq K \leq -1$

D

$-24 \leq K \leq -6$

2
GATE ECE 2016 Set 2
Numerical
+2
-0
In the feedback system shown below $$G\left(S\right)\;=\frac1{(s^2\;+\;2s)}$$$The step response of the closed-loop system should have minimum settling time and have no overshoot. The required value of gain k to achieve this is __________. Your input ____ 3 GATE ECE 2016 Set 1 Numerical +2 -0 The open-loop transfer function of a unity-feedback control system is $$G\left(S\right)\;=\frac K{s(s\;+\;2)}$$$ For the peak overshoot of the closed-loop system to a unit step input to be 10%, the value of K is __________.
4
GATE ECE 2015 Set 2
+2
-0.6
The output of a standard second–order system for a unit step input is given as $$y\left(t\right)=1-\frac2{\sqrt3}e^{-t}\cos\left(\sqrt3t\;-\;\frac{\mathrm\pi}6\right)$$\$ The transfer function of the system is
A
$$\frac2{\left(s+2\right)\left(s+\sqrt3\right)}$$
B
$$\frac1{s^2+2s+1}$$
C
$$\frac3{s^2+2s+3}$$
D
$$\frac4{s^2+2s+4}$$
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