Time-Domain Analysis of Control Systems Quizzes - Master Your Control Engineering Skills

Question 1

A first-order system with a time constant of 2 seconds has an initial condition of 5 units. If a unit step input is applied at t = 0, what is the system's response at t = 4 seconds?

Accepted Answer

2.5 units

Answer

1 unit

Answer

4 units

Answer

5 units

Question 2

Which of the following system responses is characterized by an overshoot and settling time?

Accepted Answer

Step response

Answer

Impulse response

Answer

Ramp response

Answer

Parabolic response

Question 3

A unity feedback system has the following open-loop transfer function: G(s) = 10/(s(s+2)). What is the system's type?

Accepted Answer

1

Answer

0

Answer

2

Answer

3

Question 4

A linear time-invariant system has a state-space representation of: ẋ = Ax + Bu, y = Cx. What is the system's transfer function?

Accepted Answer

G(s) = C(sI - A)^-1B

Answer

G(s) = (sI - A)^-1B

Answer

G(s) = C(sI + A)^-1B

Answer

G(s) = (sI + A)^-1B

Question 5

A system has a transfer function of G(s) = K/(s(s+1)). What is the value of K that results in a system with a damping ratio of 0.5?

Accepted Answer

1

Answer

0.5

Answer

2

Answer

4

Question 6

Which property does NOT describe a first-order system?

Accepted Answer

Time constant dependent on input type

Answer

Single energy storage element

Answer

Exponential transient response

Answer

Zero steady-state error to step inputs

Question 7

To determine the stability of a system with a continuous-time transfer function, which stability criterion is employed?

Accepted Answer

Routh-Hurwitz criterion

Answer

Nyquist criterion

Answer

Bode stability criterion

Answer

Root locus method

Question 8

The system's response to a unit impulse input is known as its:

Accepted Answer

Impulse response

Answer

Step response

Answer

Frequency response

Answer

Bode plot

Question 9

In a second-order system, which time constant determines the decay rate of the transient response?

Accepted Answer

Natural time constant

Answer

Settling time

Answer

Transient time constant

Answer

Steady-state time constant

Question 10

Which technique is commonly used to enhance the transient response of a control system?

Accepted Answer

Adding a lead compensator

Answer

Adding a lag compensator

Answer

Increasing the gain

Answer

Decreasing the time constant

Question 11

What is the term for the time required for the system output to reach 95% of its final value?

Accepted Answer

Settling time

Answer

Rise time

Answer

Peak time

Answer

Delay time

Question 12

A second-order system with a damping ratio of 0.5 exhibits which type of response?

Accepted Answer

Underdamped

Answer

Unstable

Answer

Overdamped

Answer

Critically Damped

Question 13

What does the time constant (τ) of a first-order system represent?

Accepted Answer

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

Answer

The time it takes for the system to reach steady-state.

Answer

The inverse of the system's natural frequency.

Question 14

A system with a pole located in the right half of the s-plane is considered:

Accepted Answer

Unstable

Answer

Critically Damped

Answer

Stable

Answer

Marginally Stable

Question 15

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

Accepted Answer

Oscillations with increasing amplitude.

Answer

Finite settling time.

Answer

Bounded output for bounded input.

Answer

Exponential decay of transients.

Question 16

A unity feedback system has an open-loop transfer function G(s) = 1/(s(s+2)). What is the system's type?

Accepted Answer

Type 1

Answer

Type 3

Answer

Type 0

Answer

Type 2

Question 17

The settling time of a second-order system is primarily determined by:

Accepted Answer

The damping ratio and natural frequency.

Answer

The system's time constant.

Answer

The system's gain.

Answer

The input signal's amplitude.

Question 18

What is the significance of the dominant poles in a system's transfer function?

Accepted Answer

They primarily shape the system's transient response.

Answer

They determine the system's steady-state error.

Answer

They represent the system's natural frequency.

Question 19

Which method is commonly used to analyze the stability of a closed-loop system using its open-loop transfer function?

Accepted Answer

Routh-Hurwitz Criterion

Answer

Root Locus Method

Answer

Bode Plot Analysis

Answer

Nyquist Stability Criterion