1
GATE EE 2024
MCQ (Single Correct Answer)
+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?

GATE EE 2024 Control Systems - Time Response Analysis Question 3 English
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
MCQ (Single Correct Answer)
+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?

GATE EE 2024 Control Systems - Time Response Analysis Question 2 English
A

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

B

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

C

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

D

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

3
GATE EE 2024
Numerical
+2
-0

Consider the closed-loop system shown in the figure with $$G(s) = \frac{K(s^2 - 2s + 2)}{(s^2 + 2s + 5)}.$$ The root locus for the closed-loop system is to be drawn for $0 \leq K < \infty$. The angle of departure (between $0^{o}$ and $360^{o})$ of the root locus branch drawn from the pole $(−1 + j2)$, in degrees, is _________________ (rounded off to the nearest integer).

GATE EE 2024 Control Systems - Root Locus Techniques Question 2 English
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4
GATE EE 2024
Numerical
+2
-0

Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude plot of $G(s)$ has a constant slope of $-20$ dB/decade at least till $100$ rad/sec with the gain crossover frequency being $10$ rad/sec. The asymptotic Bode phase plot remains constant at $-90^{o}$ at least till $\omega = 10$ rad/sec. The steady-state error of the closed-loop system for a unit ramp input is ________________ (rounded off to 2 decimal places).

GATE EE 2024 Control Systems - Polar Nyquist and Bode Plot Question 3 English
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