1
GATE EE 2024
+1
-0.33

Consider the standard second-order system of the form $\frac{\omega_n^2}{s^2 + 2\zeta\omega_n s + \omega_n^2}$ with the poles $p$ and $p^\ast$ having negative real parts. The pole locations are also shown in the figure. Now consider two such second-order systems as defined below:

System 1: $\omega_n = 3$ rad/sec and $\theta = 60^{\circ}$
System 2: $\omega_n = 1$ rad/sec and $\theta = 70^{\circ}$

Which one of the following statements is correct?

A

Settling time of System 1 is more than that of System 2.

B

Settling time of System 2 is more than that of System 1.

C

Settling times of both the systems are the same.

D

Settling time cannot be computed from the given information.

2
GATE EE 2024
+1
-0.33

Consider the cascaded system as shown in the figure. Neglecting the faster component of the transient response, which one of the following options is a first-order pole-only approximation such that the steady-state values of the unit step responses of the original and the approximated systems are same?

A

$\frac{1}{s + 1}$

B

$\frac{2}{s + 1}$

C

$\frac{1}{s + 20}$

D

$\frac{2}{s + 20}$

3
GATE EE 2022
+1
-0.33

The damping ratio and undamped natural frequency of a closed loop system as shown in the figure, are denoted as $$\xi$$ and $$\omega$$n are

A
$$\xi$$ = 0.5 and $$\omega$$n = 10 rad/s
B
$$\xi$$ = 0.1 and $$\omega$$n = 10 rad/s
C
$$\xi$$ = 0.707 and $$\omega$$n = 10 rad/s
D
$$\xi$$ = 0.707 and $$\omega$$n = 100 rad/s
4
GATE EE 2017 Set 2
+1
-0.3
When a unit ramp input is applied to the unity feedback system having closed loop transfer function $${{C\left( s \right)} \over {R\left( s \right)}} = {{Ks + b} \over {{s^2} + as + b}},\,\left( {a > 0,\,b > 0,\,K > 0} \right),$$ the steady state error will be
A
$$0$$
B
$${a \over b}$$
C
$${{a + K} \over b}$$
D
$${{a - K} \over b}$$
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