Test 1 - Control System | Electronics and Communication (ECE)

Question 1 Multiple Choice (Single Answer)

A PD controller is used to compensate a system. Compared to the uncompensated system, the compensated system has

a higher type number
reduced damping
higher noise amplification
larger transient overshoot

Question 2 Multiple Choice (Single Answer)

If the closed-loop transfer function of a control system is given as T(s) = ^{$$\dfrac{s-5}{(s+2)(s+3)}$$}, then it is

an unstable system
an uncontrollable system
a minimum phase system
a non-minimum phase system

Question 3 Multiple Choice (Single Answer)

The open-loop transfer function of a unity-gain feedback control system is given by

G (s) = ^{$$\dfrac{k}{(s+1)(s+2)}$$}

The gain margin of the system in dB is given by

0
1
20
$\infty$

Question 4 Multiple Choice (Single Answer)

Despite the presence of negative feedback, control systems still have problems of instability because the

used components have nonlinearities
dynamic equations of the subsystems are not known
mathematical analysis involves approximations
system has large negative phase angle at high frequencies

Question 5 Multiple Choice (Single Answer)

A system with transfer function
G (s) = $$\dfrac{(s^2+9)(s+2)}{(s+1)(s+3)(s+4)}$$
Is excited by sin($\omega$t). The steady-state output of the system is zero at

$\omega$= 1 rad/s
$\omega$= 2 rad/s
$\omega$= 3 rad/s
$\omega$= 4 rad/s

Question 6 Multiple Choice (Single Answer)

The input-output transfer function of a plant H(x) = $$\dfrac{100}{s(s+10)^2}$$. The plant is placed in a unity negative feedback configuration as shown in the figure below.

The gain margin of the system under closed loop unity negative feedback is

0dB
20dB
26 dB
46 dB

Question 7 Multiple Choice (Single Answer)

Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems?

Question 8 Multiple Choice (Single Answer)

For the asymptotic Bode magnitude plot shown below, the system transfer function can be

$$ \dfrac{10s+1}{0.1s + 1} $$
$$ \dfrac{100s+1}{0.1s + 1} $$
$$ \dfrac{100s}{10s + 1} $$
$$ \dfrac{0.1s+1}{10s + 1} $$

Question 9 Multiple Choice (Single Answer)

The number of open right half plane of
G (s) = ^{$
\dfrac{10}{s^5+2s^4+3s^3+6s^2+5s+3}
$}

0
1
2
3

Question 10 Multiple Choice (Single Answer)

The state variable description of an LTI system is given by
$
\left(
\begin{array}
x_1 \\ x_2 \\ x_3
\end{array}
\right)
$= $
\left(
\begin{array}
\ 0&a_1&0\\
0&0&a_2\\
a_3&0&0
\end{array}
\right)
$$
\left(
\begin{array}
\ x_1\\
x_2\\
x_3
\end{array}
\right)
$+ $
\left(
\begin{array}
\ 0\\
0\\
1
\end{array}
\right)
u
$
y = (1 0 0) $
\left(
\begin{array}
\ x_1\\
x_2\\
x_3
\end{array}
\right)
$
Where y is output and u is the input. The system is controllable for

a_{1 $\ne$}0, a₂ = 0, a_{3 $\ne$}0
a₁= 0, a₂ $\ne$0, a₃ $\ne$0
a₁ = 0, a₂ $\ne$0, a₃ = 0
a₁ $\ne$ 0, a₂ $\ne$0, a₃ = 0

Question 11 Multiple Choice (Single Answer)

The root locus of the system G (s) H(s) = $\dfrac{k}{s(s+2)(s+3)}$ has the break - away point located at

(- 0.5,0)
(- 2.548,0)
(- 4,0)
(- 0.784,0)

Question 12 Multiple Choice (Single Answer)

The input-output transfer function of a plant H(x) = $\dfrac{100}{s(s+10)^2}$. The plant is placed in a unity negative feedback configuration as shown in the figure below.

The signal flow graph that DOES NOT model the plant transfer function H(s) is

Question 13 Multiple Choice (Single Answer)

The feedback configuration and the pole-zero locations of are shown below. The root locus for negative values of k , i.e. for -$\infty$< k < 0, has breakaway / break-in points and angle of departure at pole P (with respect to the positive real axis) equal to

$\pm \sqrt2 $ and 0⁰
$\pm \sqrt2 $ and 45⁰
$\pm \sqrt3 $ and 0⁰
$\pm \sqrt3 $ and 45⁰

Question 14 Multiple Choice (Single Answer)

For the transfer function G (j$\omega$ ) = 5 + j$\omega$, the corresponding Nyquist plot for positive frequency has the form

Question 15 Multiple Choice (Single Answer)

A causal system having the transfer function H(s) = 1 /(s+2) is excited with 10u(t) . The time at which the output reaches 99% of its steady state value is

2.7 sec
2.5 sec
2.3 sec
2.1 sec

Question 16 Multiple Choice (Single Answer)

The transfer function of a compensator is given as

G_c(s) = ^{$\dfrac{s+a}{s+b}$}

G_c (s) is a lead compensator if

a = 1, b = 2
a = 3, b = 2
a = – 3, b = – 1
a = 3, b = 1

Question 17 Multiple Choice (Single Answer)

The gain margin for the system with open-loop transfer function
G(s) H(s) = ^{$\dfrac{2(1+s)}{s^2}, \ is$}

$\infty$
0
1
– ^_$\infty$

Question 18 Multiple Choice (Single Answer)

A double integrator plant, ^{$G(s) = \dfrac{k}{s^2} \ H(s) = 1$} is to be compensated to achieve the damping ratio ^_$\xi$ = 0.5, and an undamped natural, ^{_{$\omega_n = 5\ rad/s$}}. Which one of the following compensator G_c(S) will be suitable?

$\dfrac{s+3}{s+9.9}$
$\dfrac{s+9.9}{s+3}$
$\dfrac{s-6}{s+8.33}$
$\dfrac{s+6}{s}$

Question 19 Multiple Choice (Single Answer)

Consider the system
$\dfrac{dx}{dt}$= Ax + Bu with A = $
\left[
\begin{array}
\ 1&0\\
0&1
\end{array}
\right]
$ and B = $
\left[
\begin{array}
\ p\\
q
\end{array}
\right]
$

where p and q are arbitrary real numbers. Which of the following statements about the controllability of the system is true?

The system is completely state controllable for any non-zero values of p and q.
Only p = 0 and q = 0 result in controllability.
The system is uncontrollable for all values of p and q.
We cannot conclude about controllability from the given data.

Test 1 - Control System | Electronics and Communication (ECE)

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