Time-Domain Analysis of Control Systems: Interactive Learning Quizzes

Question 1

The impulse response of a system is a plot of the system's output to which of the following inputs?

Accepted Answer

Unit impulse

Answer

Unit step

Answer

Unit ramp

Answer

Unit sinusoid

Question 2

Which of the following is the Laplace transform of the derivative of a function f(t)?

Accepted Answer

sL{f(t)} - f(0)

Answer

sL{f(t)}

Answer

sL{f(t)} + f(0)

Answer

L{sf(t)}

Question 3

The impulse response of a time-invariant system is its output response to:

Accepted Answer

A unit impulse input

Answer

A unit step input

Answer

A sinusoidal input

Answer

A random input

Question 4

The transfer function of a linear time-invariant system is defined as the ratio of the Laplace transform of the system's:

Accepted Answer

Output to input

Answer

Input to output

Answer

Impulse response to step response

Answer

Step response to impulse response

Question 5

A Bode plot is a graphical representation of a system's:

Accepted Answer

Magnitude and phase versus frequency

Answer

Step response versus time

Answer

Impulse response versus time

Answer

Frequency response versus time

Question 6

A system with a high phase margin is considered to be:

Accepted Answer

More stable

Answer

Less stable

Answer

Marginally stable

Answer

Unstable

Question 7

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

Accepted Answer

Nyquist plot

Answer

Bode plot

Answer

Step response plot

Answer

Impulse response plot

Question 8

A properly designed control system should generally have:

Accepted Answer

Low gain and high phase margin

Answer

High gain and low phase margin

Answer

High gain and high phase margin

Answer

Low gain and low phase margin

Question 9

In a step response, the system's output is plotted against which variable?

Accepted Answer

Time

Answer

Frequency

Answer

Input amplitude

Answer

Phase shift

Question 10

Which control system category includes all the following types: open-loop, closed-loop, and adaptive?

Accepted Answer

All control systems

Answer

Linear systems

Answer

Feedback systems

Answer

Nonlinear systems

Question 11

What is the primary function of feedback in a control system?

Accepted Answer

To minimize the difference between desired and actual output

Answer

To increase the system's bandwidth

Answer

To decrease the system's gain

Answer

To improve system stability

Question 12

Which time-domain performance measure indicates how quickly the system responds?

Accepted Answer

Rise time

Answer

Settling time

Answer

Overshoot

Answer

Steady-state error

Question 13

Which of the following is the stability criterion for a system with a transfer function G(s)?

Accepted Answer

All poles of G(s) must be in the left half-plane.

Answer

All poles of G(s) must be in the right half-plane.

Answer

All poles of G(s) must be on the imaginary axis.

Answer

All poles of G(s) must be at the origin.

Question 14

To determine the transfer function of a linear time-invariant (LTI) system, what mathematical operation can be applied to its impulse response?

Accepted Answer

Apply the Laplace transform

Answer

Apply the Fourier transform

Answer

Take the inverse Laplace transform

Question 15

In control systems, which control strategy is specifically designed to address the challenges posed by time delays?

Accepted Answer

Smith predictor

Answer

Proportional-Integral-Derivative (PID) controller

Answer

Lead compensator

Answer

Kalman filter

Question 16

In a control system, what is the primary goal of a controller?

Accepted Answer

Minimize error between desired and actual outputs

Answer

Maintain output at desired value

Answer

Maximize system efficiency

Answer

Prevent system instability

Question 17

What is the Laplace transform of the unit step function?

Accepted Answer

1/s

Answer

1/s^2

Answer

s^2

Answer

s

Question 18

Which of the following is NOT a time-domain analysis technique for control systems?

Accepted Answer

Frequency response

Answer

Impulse response

Answer

Step response

Answer

Ramp response

Question 19

The impulse response of a system is defined as the output of the system to:

Accepted Answer

A unit impulse input

Answer

A unit step input

Answer

A unit ramp input

Answer

A unit sinusoidal input

Question 20

The step response of a system is:

Accepted Answer

The output of the system to a unit step input

Answer

The derivative of the impulse response

Answer

The integral of the impulse response

Answer

The Laplace transform of the impulse response

Question 21

Which of the following is NOT a characteristic of a stable control system?

Accepted Answer

Positive feedback

Answer

Bounded outputs for bounded inputs

Answer

Zero steady-state error for constant inputs

Answer

Negative feedback

Question 22

The transfer function of a system is:

Accepted Answer

The ratio of the Laplace transform of the output to the Laplace transform of the input

Answer

The inverse Laplace transform of the system's impulse response

Answer

The differential equation that describes the system

Answer

The frequency response of the system

Question 23

What is the time constant of a first-order system defined as?

Accepted Answer

The time it takes for the system to reach 63.2% of its final value

Answer

The time it takes for the system to reach 95% of its final value

Answer

The time it takes for the system to reach 50% of its final value

Answer

The time it takes for the system to reach 36.8% of its final value

Question 24

Which of the following is a measure of system stability when plotted in the s-plane?

Accepted Answer

Poles

Answer

Eigenvalues

Answer

Zeros

Answer

Transfer function

Question 25

What is the settling time of a second-order system?

Accepted Answer

The time it takes for the system to reach and stay within a specified tolerance of its final value

Answer

The time it takes for the system to reach 95% of its final value

Answer

The time it takes for the system to reach 63.2% of its final value

Answer

The time it takes for the system to reach 50% of its final value

Question 26

What is a primary purpose of a feedback system?

Accepted Answer

To reduce the effects of disturbances and improve system performance

Answer

To increase the system's gain and bandwidth without bound

Answer

To make the system more stable always

Answer

To eliminate nonlinearities in the system

Question 27

What mathematical function is defined as 1 for t greater than or equal to 0 and 0 for t less than 0?

Accepted Answer

A unit step function

Answer

A unit impulse function

Answer

An exponential function

Answer

A sinusoidal function

Question 28

What is the term for the system's output response to a unit impulse input?

Accepted Answer

Impulse response

Answer

Step response

Answer

Frequency response

Answer

Bode plot

Question 29

A negative phase margin in a control system indicates:

Accepted Answer

System instability

Answer

System stability

Answer

Marginal stability

Answer

Inconclusive stability

Question 30

Define the bandwidth of a control system.

Accepted Answer

Frequency range where the magnitude of the frequency response is greater than -3 dB

Answer

Frequency at which the phase angle of the frequency response is 180 degrees

Answer

Frequency at which the system becomes unstable

Answer

Response time of the system

Question 31

What is the purpose of the Nyquist criterion?

Accepted Answer

Determine the stability of a closed-loop system

Answer

Calculate the bandwidth of a system

Answer

Evaluate the gain margin of a system

Answer

Estimate the phase margin of a system

Question 32

What is the formula for the closed-loop transfer function of a feedback control system?

Accepted Answer

G/(1+GH)

Answer

H/(1+GH)

Answer

(G+H)/(1+GH)

Answer

(G-H)/(1-GH)

Question 33

Define the unit impulse response of a system.

Accepted Answer

The system's response to a unit impulse input

Answer

The system's response to a unit step input

Answer

The system's response to a unit ramp input

Answer

The system's response to a unit sinusoidal input

Question 34

Determine the final value of a system's response to a unit step input with a settling time of 5 seconds.

Accepted Answer

1

Answer

0

Answer

5

Answer

Cannot be determined.

Question 35

When a unit step input is applied to a first-order system, what parameter determines the time it takes for the system's output to reach approximately 63.2% of its final value?

Accepted Answer

Time constant

Answer

Steady-state gain

Answer

Damping ratio

Answer

Natural frequency

Question 36

For a second-order system represented by the differential equation `m * d^2y/dt^2 + c * dy/dt + k * y = u(t)` (where m, c, and k are constants, y is the output, and u(t) is the input), what is its characteristic equation?

Accepted Answer

ms^2 + cs + k = 0

Answer

ms + c + k = 0

Answer

1/m * s^2 + c * s + k = 0

Answer

m + c/s + k/s^2 = 0

Question 37

Which of the following statements accurately describes the impulse response of a stable system?

Accepted Answer

It approaches zero as time approaches infinity.

Answer

It is unbounded as time approaches infinity.

Answer

It oscillates with constant amplitude.

Answer

It is always a step function.

Question 38

If a system exhibits oscillations with decreasing amplitude over time when subjected to a step input, what type of damping does it possess?

Accepted Answer

Underdamped

Answer

Overdamped

Answer

Critically damped

Answer

Undamped

Question 39

Which parameters directly influence the settling time of a second-order system?

Accepted Answer

Damping ratio and natural frequency

Answer

Input amplitude and system order

Answer

Steady-state gain and time constant

Answer

Rise time and peak time

Question 40

What is the approximate percentage overshoot for a system with a damping ratio of 0.5?

Accepted Answer

16.3%

Answer

0%

Answer

100%

Answer

5%

Question 41

Which method allows us to determine the time response of a system to any arbitrary input?

Accepted Answer

Convolution integral

Answer

Routh-Hurwitz criterion

Answer

Root locus method

Answer

Laplace transform

Question 42

If a system's step response exhibits a constant steady-state error, what type of system is it classified as?

Accepted Answer

Type 0 system

Answer

Unstable system

Answer

Type 2 system

Answer

Type 1 system

Question 43

Which of the following techniques is specifically used to analyze the stability of a system in the time domain?

Accepted Answer

Routh-Hurwitz criterion

Answer

Nyquist plot

Answer

Root locus plot

Answer

Bode plot