Time-Domain Analysis of Control Systems Quizzes | Control Systems | Bachelor of Science in Electrical Engineering

Question 1

In a first-order system, the time constant (τ) is defined as:

Accepted Answer

The time it takes the system's response to reach 63.2% of its final value

Answer

The time it takes the system's response to reach 98% of its final value

Answer

The time it takes the system's response to reach 100% of its final value

Answer

The time it takes for the system to oscillate between its initial and final values

Question 2

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

Accepted Answer

Response oscillates indefinitely

Answer

Bounded output

Answer

Output decays to zero over time

Answer

Fast settling time

Question 3

The Nyquist stability criterion is primarily used for assessing the stability of:

Accepted Answer

Closed-loop systems

Answer

Open-loop systems

Answer

Nonlinear systems

Answer

Time-varying systems

Question 4

The impulse response of a system represents:

Accepted Answer

System's output due to a unit impulse input

Answer

Input that results in a unit impulse output from the system

Answer

Time system takes to reach its steady-state value

Answer

Frequency at which the system oscillates

Question 5

The time constant of a control system is best defined as the time required for the system to reach:

Accepted Answer

63.2% of its final value

Answer

95% of its final value

Answer

100% of its final value

Answer

36.8% of its final value

Question 6

Which graphical technique is utilized for evaluating the time-domain stability of a control system?

Accepted Answer

Root locus

Answer

Nyquist plot

Answer

Bode plot

Answer

Laplace transform

Question 7

The root locus plot traces the roots of the characteristic equation of a control system as a parameter varies.

Accepted Answer

Gain

Answer

Damping ratio

Answer

Time constant

Answer

Natural frequency

Question 8

A Bode plot comprises which two graphs?

Accepted Answer

Magnitude and phase

Answer

Magnitude and gain

Answer

Phase and gain

Answer

Gain and frequency

Question 9

Which compensation technique is primarily used to increase phase margin in a control system?

Accepted Answer

Lead compensation

Answer

Lag compensation

Answer

PID controller

Answer

State feedback

Question 10

A stable control system is one that exhibits:

Accepted Answer

Negative feedback

Answer

Positive feedback

Answer

High gains

Answer

Oscillatory response

Question 11

Which parameter of a second-order control system primarily affects its level of overshoot?

Accepted Answer

Damping ratio

Answer

Natural frequency

Answer

Gain

Answer

Time constant

Question 12

Which of the following is NOT a type of transient response in a control system?

Accepted Answer

Damped

Answer

Critically damped

Answer

Underdamped

Answer

Overdamped

Question 13

The steady-state error of a control system represents the difference between:

Accepted Answer

Actual and desired output

Answer

Reference input and output

Answer

Input and output

Answer

Error and predicted error

Question 14

What percentage of its final value does a first-order system reach after one time constant?

Accepted Answer

63.2%

Answer

25%

Answer

50%

Answer

90%

Question 15

Which characteristic is NOT indicative of a stable control system?

Accepted Answer

Negative damping

Answer

Bounded output for bounded input

Answer

Positive damping

Answer

Poles located in the left-half of the s-plane

Question 16

What does the root locus of a control system graphically represent?

Accepted Answer

Poles and zeros of the system

Answer

Poles of the system only

Answer

Zeros of the system only

Answer

Frequency response of the system

Question 17

Define the gain margin of a control system.

Accepted Answer

Maximum allowable gain before instability occurs

Answer

Minimum allowable gain before instability occurs

Answer

Frequency at which system gain is unity

Answer

Frequency at which system phase shift is 180 degrees

Question 18

What does the phase margin of a control system represent?

Accepted Answer

Maximum allowable phase shift before instability occurs

Answer

Minimum allowable phase shift before instability occurs

Answer

Frequency at which system gain is unity

Answer

Frequency at which system phase shift is 180 degrees

Question 19

What does the transfer function of a system mathematically represent?

Accepted Answer

Input-output relationship of the system

Answer

Frequency response of the system

Answer

Stability of the system

Answer

Time response of the system

Question 20

What is the primary purpose of the Nyquist criterion?

Accepted Answer

Determining the stability of a closed-loop control system

Answer

Obtaining the frequency response of a control system

Answer

Calculating the time response of a control system

Answer

Deriving the transfer function of a control system

Question 21

The general form of the time-domain differential equation for a second-order control system is:

Accepted Answer

ay''(t) + by'(t) + cy(t) = 0

Answer

ay'''(t) + by''(t) + cy'(t) = 0

Answer

ay''(t) + by(t) + cy'(t) = 0

Answer

ay'''(t) + by'(t) + cy(t) = 0

Question 22

The transient response of a control system represents:

Accepted Answer

The initial behavior before steady state is reached

Answer

The final behavior after steady state is reached

Answer

The overall response to an input

Answer

The time required to reach steady state

Question 23

The distinction between a type 0 and a type 1 control system is:

Accepted Answer

Type 0 systems have zero steady-state error to step inputs, unlike type 1 systems

Answer

Type 1 systems have zero steady-state error to step inputs, unlike type 0 systems

Answer

Type 0 systems respond faster than type 1 systems

Answer

There is no difference between type 0 and type 1 control systems

Question 24

To perform a stability analysis of a control system using the root locus technique, which steps are necessary?

Accepted Answer

Determine the characteristic equation, plot the root locus, and evaluate the location of the closed-loop poles.

Answer

Apply a sinusoidal input and measure the output response.

Answer

Simulate the system's response to a step input using software.

Question 25

How can nonlinearities impact the transient and steady-state behavior of a control system?

Accepted Answer

Nonlinearities can lead to system instability.

Accepted Answer

Nonlinearities can cause limit cycles in the system.

Accepted Answer

Nonlinearities can result in multiple steady-state operating points.

Answer

Nonlinearities do not affect the transient response of the system.

Question 26

Define the time constant of a first-order control system.

Accepted Answer

Time required to reach 63.2% of its final value

Answer

Time required to reach 100% of its final value

Answer

Time required to reach 50% of its final value

Answer

Time required to reach 25% of its final value

Question 27

What is the steady-state error of a control system?

Accepted Answer

Error present after a transient response

Answer

Error present before a transient response

Answer

Error present during a transient response

Answer

Error present when the input is zero

Question 28

In a Bode plot, at what frequency does the phase angle become -180 degrees?

Accepted Answer

Phase crossover frequency

Answer

Cutoff frequency

Answer

Corner frequency

Answer

Gain crossover frequency

Question 29

Define the settling time of a control system.

Accepted Answer

Time to reach within 2% of its final value

Answer

Time to reach within 5% of its final value

Answer

Time to reach within 10% of its final value

Answer

Time to reach within 20% of its final value

Question 30

What is a transfer function of a control system?

Accepted Answer

Mathematical model of the input-output relationship

Answer

Graphical representation of the system's response

Answer

Table of input-output values

Answer

Simulation of the system's behavior

Question 31

What do the poles of a transfer function represent?

Accepted Answer

Frequencies where the system becomes unstable

Answer

Frequencies where the system's output is zero

Answer

Frequencies where the system's response is critically damped

Answer

Frequencies where the system's response is overdamped

Question 32

What do the zeros of a transfer function represent?

Accepted Answer

Frequencies where the system's output is zero

Answer

Frequencies where the system becomes unstable

Answer

Frequencies where the system's response is critically damped

Answer

Frequencies where the system's response is overdamped

Question 33

Which of the following characterizes a transient response?

Accepted Answer

A and B only

Answer

It is the system's response to an initial condition.

Answer

It decays to zero over time.

Answer

It is caused by the input signal.

Question 34

A system is stable if:

Accepted Answer

All its poles lie in the left half of the s-plane.

Answer

All its poles lie in the right half of the s-plane.

Answer

It has at least one pole at the origin.

Answer

Its damping ratio is non-zero.

Question 35

The root locus of a system plots:

Accepted Answer

Poles and zeros as a function of a system parameter

Answer

Gain and phase margin as a function of frequency

Answer

Transient and steady-state responses as a function of time

Answer

Bode plot as a function of gain

Question 36

The transfer function of a system is a mathematical representation of its:

Accepted Answer

Input-output relationship

Answer

State-space representation

Answer

Root locus

Answer

Bode plot

Question 37

A block diagram of a control system is a graphical representation of its:

Accepted Answer

Structure and signal flow

Answer

Transfer function

Answer

Root locus

Answer

Bode plot

Question 38

How does negative feedback affect the stability of a control system?

Accepted Answer

Negative feedback improves system stability.

Answer

Positive feedback increases system stability.

Answer

Feedback does not impact system stability.

Question 39

What is the characteristic equation of a control system with a transfer function G(s) = 5/(s^3 + 4s^2 + 3s + 2)?

Accepted Answer

s^3 + 4s^2 + 3s + 5 = 0

Answer

s^3 + 3s^2 + 4s + 5 = 0

Answer

5s^3 + 4s^2 + 3s + 1 = 0

Answer

5s^3 + 3s^2 + 4s + 1 = 0

Question 40

The time constant of a first-order system with a transfer function G(s) = 1/(2s + 1) is:

Accepted Answer

0.5 seconds

Answer

1 second

Answer

2 seconds

Answer

4 seconds

Question 41

The frequency at which the phase of the Bode plot crosses the -180 degree line is known as the:

Accepted Answer

Phase crossover frequency

Answer

Resonant frequency

Answer

Natural frequency

Answer

Cutoff frequency

Question 42

Consider a control system with the transfer function G(s) = 10/(s(s+5)). Determine the settling time (to within 2%) of the system.

Accepted Answer

4.6 seconds

Answer

10 seconds

Answer

2.3 seconds

Answer

5 seconds

Question 43

A second-order system exhibits an overshoot of 20% in its step response. Which of the following statements about the system's damping ratio is accurate?

Accepted Answer

The damping ratio (ζ) is between 0 and 1, indicating an underdamped system.

Answer

The damping ratio is 0, indicating a critically damped system.

Answer

The damping ratio is greater than 1, indicating an overdamped system.

Question 44

What is the significance of the time constant in a first-order system?

Accepted Answer

It represents the time required for the system's output to reach approximately 63.2% of its final value.

Answer

It determines the system's natural frequency.

Answer

It indicates the system's steady-state error.

Question 45

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

Accepted Answer

Sustained oscillations in the output

Answer

Settling to a steady-state value

Answer

A bounded output response

Answer

Responding to input changes without diverging

Question 46

Consider a system with a transfer function G(s) = 1/(s+1). What is the system's time constant (τ)?

Accepted Answer

1 second

Answer

2 seconds

Answer

Cannot be determined from the given transfer function.

Answer

0.5 seconds

Question 47

In a root locus analysis, which parameter is typically varied to observe the movement of the closed-loop poles?

Accepted Answer

Gain

Answer

Damping ratio

Answer

Time constant

Answer

Natural frequency

Question 48

A Bode plot is commonly used to represent a system's frequency response. What information can be obtained from the magnitude and phase plots of a Bode plot?

Accepted Answer

Magnitude plot: Gain at different frequencies; Phase plot: Phase shift at different frequencies.

Answer

Magnitude plot: Time constant; Phase plot: Damping ratio.

Answer

Magnitude plot: Stability margin; Phase plot: Steady-state error.

Question 49

A step response of a control system exhibits significant overshoot and prolonged oscillations. What can be inferred about the system's stability based on these observations?

Accepted Answer

The system is potentially unstable due to underdamping.

Answer

The system is likely critically damped and stable.

Answer

The system is likely overdamped and stable.

Question 50

In a closed-loop control system, what is the primary purpose of feedback?

Accepted Answer

To enhance system stability and accuracy by reducing errors.

Answer

To amplify the input signal.

Answer

To increase the system's bandwidth.