1
GATE ECE 2022
+1
-0.33

Two linear time-invariant systems with transfer functions

$${G_1}(s) = {{10} \over {{s^2} + s + 1}}$$ and $${G_2}(s) = {{10} \over {{s^2} + s\sqrt {10} + 10}}$$

have unit step responses y1(t) and y2(t), respectively. Which of the following statements is/are true?

A
y1(t) and y2(t) have the same percentage peak overshoot.
B
y1(t) and y2(t) have the same steady-state value.
C
y1(t) and y2(t) have the same damped frequency of oscillation.
D
y1(t) and y2(t) have the same 2% settling time.
2
GATE ECE 2022
Numerical
+1
-0.33

The block diagram of a closed-loop control system is shown in the figure. R(s), Y(s), and D(s) are the Laplace transforms of the time-domain signals r(t), y(t), and d(t), respectively. Let the error signal be defined as e(t) = r(t) $$-$$ y(t). Assuming the reference input r(t) = 0 for all t, the steady-state error e($$\infty$$), due to a unit step disturbance d(t), is __________ (rounded off to two decimal places).

3
GATE ECE 2017 Set 1
Numerical
+1
-0
The open loop transfer function $$\mathrm G\left(\mathrm s\right)\;=\;\frac{\left(\mathrm s\;+\;1\right)}{\mathrm s^\mathrm p\left(\mathrm s\;+\;2\right)\left(\mathrm s\;+\;3\right)}$$\$ Where p is an integer, is connected in unity feedback configuration as shown in figure. Given that the steady state error is zero for unit step input and is 6 for unit ramp input, the value of the parameter p is _________.
4
GATE ECE 2016 Set 3
+1
-0.3
For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as $$G\left(s\right)\;=\;\frac2{s\left(s\;+\;1\right)}$$ .The steady state error ess due to a unit step input is
A
$$0$$
B
0.5
C
1.0
D
$$\infty$$
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