Time-Domain Analysis: Master Control Systems with Step and Impulse Responses

Question 1

Which of the following is NOT a characteristic of a step response?

Accepted Answer

Damping ratio

Answer

Rise time

Answer

Settling time

Answer

Overshoot

Question 2

The impulse response of a system is defined as:

Accepted Answer

The response of the system to a unit impulse input

Answer

The time derivative of the step response

Answer

The Laplace transform of the system's transfer function

Answer

The Fourier transform of the system's output

Question 3

The settling time of a system is defined as the time it takes for the system's output to:

Accepted Answer

Reach and stay within a specified percentage of its final value

Answer

Reach its maximum value

Answer

Reach its steady-state value

Answer

Cross the zero axis

Question 4

The Nyquist stability criterion is used to determine the stability of a system based on:

Accepted Answer

The shape of the system's Nyquist plot

Answer

The location of the system's zeros in the complex plane

Answer

The location of the system's poles in the complex plane

Answer

The magnitude of the system's transfer function

Question 5

The impulse response of a system describes its output when subjected to:

Accepted Answer

A brief, intense input

Answer

A constant input

Answer

A periodic input

Answer

A random input

Question 6

In the root locus plot, a system is considered unstable if:

Accepted Answer

Any closed-loop poles are in the right-half plane

Answer

Any poles are on the imaginary axis

Answer

The system has more zeros than poles

Answer

The gain margin is less than 1

Question 7

A system characterized by a step response y(t) = 1 - e^(-2t) can be classified as:

Accepted Answer

Stable

Answer

Unstable

Answer

Marginally stable

Question 8

The impulse response of a system represents its output due to an input of:

Accepted Answer

Unit impulse function

Answer

Unit step function

Answer

Unit ramp function

Question 9

Which factor does NOT influence the stability of a control system?

Accepted Answer

Input signal amplitude

Answer

System poles

Answer

System zeros

Question 10

For a type 0 system, the steady-state error to a unit step input is:

Accepted Answer

0

Answer

Infinity

Answer

1

Question 11

The time constant of a first-order system corresponds to the time it takes for the output to reach:

Accepted Answer

Half of its final value

Answer

Double of its final value

Answer

The maximum overshoot value

Question 12

An overdamped system's step response exhibits:

Accepted Answer

Quick settling without oscillations

Answer

Slow settling with oscillations

Answer

Continuously oscillating behavior

Question 13

The primary function of a PID controller is to:

Accepted Answer

Enhance stability and performance

Answer

Increase system bandwidth

Answer

Reduce noise levels

Question 14

The Routh-Hurwitz criterion can be used to determine the:

Accepted Answer

Stability of a system

Answer

Number of poles in the right half-plane

Answer

Number of poles in the left half-plane

Answer

Damping ratio of the system

Question 15

The impulse response of a system is represented mathematically by:

Accepted Answer

h(t)

Answer

G(s)

Answer

H(jw)

Answer

f(t) * δ(t)

Question 16

The time constant of a first-order system is defined as:

Accepted Answer

τ = RC

Answer

τ = L/R

Answer

τ = L/C

Answer

τ = R/C

Question 17

The unit impulse function is defined as:

Accepted Answer

δ(t) = ∞ at t = 0, 0 otherwise

Answer

δ(t) = 1

Answer

δ(t) = 0

Answer

δ(t) = ∞

Question 18

Which of the following is NOT a consequence of instability in a control system?

Accepted Answer

Enhanced system response

Answer

Unbounded output

Answer

Loss of control

Answer

Poor performance

Question 19

The Laplace transform of the unit step function is:

Accepted Answer

1/s

Answer

s

Answer

1

Answer

0

Question 20

In time-domain analysis, the output response of a system to a unit step input is referred to as its:

Accepted Answer

Step response

Answer

Transfer function

Answer

Impulse response

Answer

Gain

Question 21

Which parameter measures the speed at which a system responds to an input signal?

Accepted Answer

Rise time

Answer

Damping ratio

Answer

Overshoot

Answer

Settling time

Question 22

A system is considered stable if its output:

Accepted Answer

Settles down to a constant value

Answer

Increases indefinitely

Answer

Oscillates indefinitely

Answer

Is unpredictable

Question 23

The Routh-Hurwitz criterion is employed to analyze the stability of a system with a transfer function expressed as a:

Accepted Answer

Rational polynomial

Answer

Trigonometric function

Answer

Exponential function

Answer

Logarithmic function

Question 24

In a stable system, the poles of the transfer function must be located in the:

Accepted Answer

Left half-plane

Answer

Right half-plane

Answer

Imaginary axis

Answer

Origin

Question 25

For a system with a resonant frequency of 10 Hz, the maximum output amplitude will occur when subjected to a sinusoidal input signal with a frequency of:

Accepted Answer

10 Hz

Answer

5 Hz

Answer

15 Hz

Answer

20 Hz

Question 26

What is the step response of a first-order system?

Accepted Answer

y(t) = 1 - e^(-t/τ)

Answer

y(t) = e^(-t/τ)

Answer

y(t) = t * e^(-t/τ)

Answer

y(t) = (1 - e^(-t/τ)) / t

Question 27

What is the impulse response of a system with a transfer function of H(s) = 1/(s + 2)?

Accepted Answer

h(t) = e^(-2t)

Answer

h(t) = 2e^(-2t)

Answer

h(t) = -e^(-2t)

Answer

h(t) = -2e^(-2t)

Question 28

According to the Routh-Hurwitz criterion, a system is stable if?

Accepted Answer

The number of sign changes in the first column of the Routh table is even

Answer

All coefficients of the characteristic equation are positive

Answer

All coefficients of the characteristic equation have the same sign

Answer

The number of sign changes in the first column of the Routh table is odd

Question 29

If the Nyquist plot of a system crosses the real axis at -0.7, what is the gain margin?

Accepted Answer

1.43

Answer

0.7

Answer

2.86

Answer

4.29

Question 30

What is the purpose of using a lead compensator?

Accepted Answer

To increase the bandwidth of the system

Answer

To decrease the bandwidth of the system

Answer

To increase the stability of the system

Answer

To decrease the stability of the system

Question 31

Which of the following is a non-linear control system?

Accepted Answer

Bang-bang controller

Answer

PID controller

Answer

Proportional controller

Answer

Integral controller

Question 32

What type of controller is a PID controller?

Accepted Answer

Proportional-integral-derivative controller

Answer

Proportional-integral controller

Answer

Proportional-derivative controller

Answer

Integral-derivative controller