Control Systems: Master the Fundamentals for Electrical Engineers

Question 1

Determine the order and type of the system with the transfer function G(s) = s / (s^2 + 2s + 1).

Accepted Answer

Order: 2, Type: 1

Answer

Order: 1, Type: 0

Answer

Order: 1, Type: 1

Answer

Order: 2, Type: 0

Question 2

Which of the following is not a type of stability in control systems?

Accepted Answer

Input-Output stability

Answer

Bounded-Input, Bounded-Output (BIBO) stability

Answer

Asymptotic stability

Answer

Lyapunov stability

Question 3

In the domain of Control Systems, which of the following is not a recognized classification of control systems?

Accepted Answer

Intelligent control

Answer

Open-loop control

Answer

Closed-loop control

Answer

Adaptive control

Question 4

What is the defining characteristic of a negative feedback control system?

Accepted Answer

Maintains the system's output within a desired range

Answer

Amplifies the system's output using positive feedback

Answer

Increases the system's sensitivity to input changes

Answer

Operates without an external input signal

Question 5

Which of the following is NOT a type of control system commonly used in engineering applications?

Accepted Answer

Management information system

Answer

Open-loop control system

Answer

Closed-loop control system

Answer

Adaptive control system

Question 6

In root locus analysis, system stability is determined by examining the:

Accepted Answer

Location of poles and zeros on the complex plane

Answer

Gain and phase margins

Answer

Frequency response of the system

Answer

Magnitude and phase of the transfer function

Question 7

In a negative feedback closed-loop control system, what is the transfer function from the reference input to the system output?

Accepted Answer

G/(1-GH)

Answer

1/G

Answer

(G+H)/G

Answer

H/(1-G)

Question 8

What is a defining trait of a feedback control system?

Accepted Answer

It measures and compares actual outputs with desired references, adjusting errors accordingly.

Answer

It generates outputs solely based on inputs, unaffected by external factors.

Answer

It maintains a constant output despite input variations.

Answer

It relies solely on external power sources.

Question 9

Calculate the damping ratio of a unity-feedback closed-loop control system with the transfer function:

```
G(s) = (s + 1)/(s^2 + 2s + 1)
```

Accepted Answer

0.5

Answer

0.25

Answer

1

Answer

2

Question 10

For a system to be controllable, which condition must be met?

Accepted Answer

The system matrix is of full rank.

Answer

All state variables are measurable.

Answer

The state variables are observable.

Answer

The system has at least two inputs.

Question 11

What is a key characteristic of a closed-loop control system?

Accepted Answer

It continuously adjusts its output based on feedback

Answer

It is always linear and time-invariant

Answer

It does not require any external input

Answer

It is always stable and free from oscillations

Question 12

For a control system to be controllable, which condition must be met?

Accepted Answer

The control input matrix has full rank.

Answer

The number of inputs is less than or equal to the number of states.

Answer

The system is stable.

Answer

The system is observable.

Question 13

Which characteristic is NOT unique to negative feedback control systems?

Accepted Answer

Employs an external signal to define the desired output.

Answer

Mitigates the impact of disturbances on the system's output.

Answer

Enhances system stability and minimizes oscillations.

Answer

Utilizes sensors to monitor the system's actual output.

Question 14

Which of the following is NOT a graphical method used for stability analysis in control systems?

Accepted Answer

Time-domain simulation

Answer

Root locus analysis

Answer

Bode plot

Answer

Nyquist plot

Question 15

For a linear time-invariant system to be controllable, which condition must be met?

Accepted Answer

The controllability matrix has full rank.

Answer

The system is square.

Answer

The system is stable.

Answer

The system is observable.

Question 16

What characteristic is exclusive to positive feedback control systems?

Accepted Answer

Error signal amplification

Answer

Error reduction over time

Answer

System stability maintenance

Answer

Sensor usage for output measurement

Question 17

In control system design, stability analysis primarily aims to determine:

Accepted Answer

The system's behavior under disturbances and its ability to return to equilibrium

Answer

The system's sensitivity to changes in its parameters

Answer

The time it takes for the system to respond to control inputs

Answer

The system's ability to minimize the impact of external noise

Question 18

In a control system's root locus plot, which curve shows how the closed-loop poles move as the system's gain changes?

Accepted Answer

Root locus

Answer

Nyquist curve

Answer

Bode plot

Answer

Gain margin plot

Question 19

In a feedback control system, what is the primary purpose of using a derivative controller?

Accepted Answer

Enhance stability and reduce overshoot

Answer

Reduce steady-state error

Answer

Increase system rise time

Answer

Improve system gain margin

Question 20

Which type of system can be analyzed for stability using the Nyquist stability criterion?

Accepted Answer

Linear, time-invariant systems

Answer

Linear, time-varying systems

Answer

Nonlinear, time-varying systems

Answer

Nonlinear, time-invariant systems

Question 21

Which type of control system is specifically designed to follow and track varying reference input signals?

Accepted Answer

Tracking control system

Answer

Set-point control system

Answer

Adaptive control system

Question 22

Which of the following is a disadvantage of using closed-loop control systems?

Accepted Answer

Increased system complexity and cost

Answer

Improved accuracy and precision

Answer

Increased system stability

Answer

Reduced sensitivity to parameter variations

Question 23

A control system with transfer function G(s) = K / (s^2 + 2ζs + ωn^2) is considered overdamped when:

Accepted Answer

ζ is greater than 1

Answer

ζ is less than 1

Answer

ζ is equal to 1

Answer

ωn is greater than ζ

Question 24

In frequency-domain analysis, which method is specifically used to assess the stability of a control system?

Accepted Answer

Nyquist plot

Answer

Bode plot

Answer

Root locus plot

Answer

Laplace transform

Question 25

What does a root locus plot show in a control system?

Accepted Answer

The path of closed-loop poles as gain varies

Answer

The frequency response of the system

Answer

The location of open-loop poles and zeros

Answer

The stability margins of the system

Question 26

In a root locus plot, the closed-loop poles trace out different regions as the system's gain changes. Where are the closed-loop poles located when the system is unstable?

Accepted Answer

Right-half plane

Answer

Left-half plane

Answer

Imaginary axis

Answer

Origin

Question 27

In a closed-loop control system, what is the fundamental role of the control law?

Accepted Answer

To regulate system output by systematically adjusting system input based on real-time error measurements.

Answer

To monitor system performance and raise alerts in the event of system anomalies.

Answer

To develop a sophisticated mathematical model of the system for simulation and analysis purposes.

Answer

To convert sensor measurements into digital signals for processing by the controller.

Question 28

What is the primary advantage of using an integral controller in systems facing constant disturbances?

Accepted Answer

Eliminates steady-state error due to the disturbance.

Answer

Enhances stability by increasing gain margin.

Answer

Reduces overshoot by introducing damping.

Answer

Expands system bandwidth by decreasing phase lag.

Question 29

In the context of Bode plots, what is the significance of the phase margin in determining the stability and performance of a control system?

Accepted Answer

It indicates the system's stability, with a larger phase margin indicating greater stability.

Answer

It is related to the system's bandwidth, with a larger phase margin indicating a wider bandwidth and faster response.

Answer

It is irrelevant in assessing the stability and performance of a control system.

Answer

It is primarily used to determine the system's gain margin.

Question 30

Identify the transfer function that represents a first-order system:

Accepted Answer

K / (s+p)

Answer

K

Answer

K / (s^2+2ps+p^2)

Answer

K(s+p) / (s^2+2ps+p^2)

Question 31

Which statement best describes the output voltage of a derivative controller?

Accepted Answer

It is proportional to the rate of change of the input voltage.

Answer

It is directly proportional to the current input voltage.

Answer

It is the integral of the input voltage over time.

Question 32

In a PID controller, what is the main function of the derivative term?

Accepted Answer

Reducing overshoot and settling time in the system's response to a step input

Answer

Eliminating steady-state error in the system's response to a step input

Answer

Increasing the controller's gain and improving the system's bandwidth

Question 33

Which of the following is NOT a systematic method for designing a controller for a control system?

Accepted Answer

Trial and error method

Answer

Root locus method

Answer

Bode plot method

Question 34

For a control system to be stable, which condition must be met?

Accepted Answer

All poles are located in the left half of the s-plane

Answer

Output remains within limits for any input

Answer

No error in steady-state for a step input

Question 35

Determine the stability of a unity feedback control system with the plant transfer function G(s) = 1 / (s(s+2)) using the Routh-Hurwitz criterion.

Accepted Answer

Stable: All coefficients of the characteristic equation are positive.

Answer

Unstable: One root of the characteristic equation lies in the right-half of the s-plane.

Answer

Marginally stable: The characteristic equation has a root at the origin.

Answer

Indeterminate: The Routh-Hurwitz criterion cannot determine stability.

Question 36

In a feedback control system, which component is responsible for measuring the output and generating an error signal?

Accepted Answer

Sensor

Answer

Controller

Answer

Plant

Answer

Load

Question 37

The Laplace transform of the unit step function u(t) is given by:

Accepted Answer

1/s

Answer

s

Answer

1/(s^2 + 1)

Answer

s/(s^2 + 1)

Question 38

Which of the following equations represents the characteristic equation of a second-order system?

Accepted Answer

s^2 + 2ζωns + ωn^2 = 0

Answer

(s + a)(s + b) = 0

Answer

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

Answer

s^4 + 4s^3 + 6s^2 + 4s + 1 = 0

Question 39

The Nyquist criterion is a graphical technique used to determine:

Accepted Answer

The stability of a closed-loop system

Answer

The time response of a system

Answer

The frequency response of a system

Answer

The poles and zeros of a system

Question 40

The primary purpose of a Kalman filter is to:

Accepted Answer

Estimate the state of a system from noisy measurements

Answer

Control a system based on feedback

Answer

Design a controller for a system

Answer

Analyze the stability of a system

Question 41

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

Accepted Answer

Unstable equilibrium point

Answer

Bounded output

Answer

Negative phase margin

Answer

Positive damping factor

Question 42

The fundamental difference between a closed-loop and an open-loop control system is:

Accepted Answer

Closed-loop systems use feedback, while open-loop systems do not

Answer

Open-loop systems use feedback, while closed-loop systems do not

Answer

Closed-loop systems are always stable, while open-loop systems are always unstable

Answer

Open-loop systems are always unstable, while closed-loop systems are always stable

Question 43

A unity feedback control system has an open-loop transfer function of G(s) = K / (s^2 + 2ζs + ωn^2).  For what range of K values will the closed-loop system exhibit underdamped behavior?

Accepted Answer

0 < K < 4ζωn

Answer

K > 0

Answer

K > 4ζωn

Question 44

Which of the following is the primary purpose of a feedback loop in a control system?

Accepted Answer

To reduce the error between the desired and actual outputs

Answer

To increase the gain of the system

Answer

To eliminate the need for a controller

Answer

To stabilize the system

Question 45

The Laplace transform of the first-order derivative of a function f(t) is:

Accepted Answer

sF(s) - f(0)

Answer

sF(s) + f(0)

Answer

F(s)/s

Answer

F(s)*s

Question 46

In the state-space representation ẋ(t) = Ax(t) + Bu(t), what does the dimension of the state vector x(t) represent?

Accepted Answer

Number of states in the system

Answer

Number of inputs to the system

Answer

Number of outputs from the system

Answer

Sum of the number of states and the number of inputs

Question 47

Identify the characteristic equation of a second-order system.

Accepted Answer

s^2 + 2ζωns + ωn^2 = 0

Answer

s^3 + 2ζωns^2 + ωn^2s + k = 0

Answer

s^4 + 2ζωns^3 + ωn^2s^2 + k = 0

Answer

s^5 + 2ζωns^4 + ωn^2s^3 + k = 0

Question 48

What is the name given to the response of a control system to a unit step input?

Accepted Answer

Step response

Answer

Impulse response

Answer

Frequency response

Answer

Bode plot

Question 49

Which characteristic is NOT generally desirable in a control system?

Accepted Answer

Excessive gain

Answer

High accuracy

Answer

Fast response

Answer

Stability

Question 50

Which control system design method involves adjusting controller gains to achieve desired performance?

Accepted Answer

Proportional-integral-derivative (PID) control

Answer

Pole placement

Answer

LQG control

Answer

State feedback control

Question 51

In a Proportional-Integral-Derivative (PID) controller, the derivative term contributes primarily to:

Accepted Answer

Shortening settling time

Answer

Reducing overshoot

Answer

Rejecting disturbances

Answer

Improving stability

Question 52

Which of the following is NOT an application area of control systems?

Accepted Answer

Painting

Answer

Robotics

Answer

Automotive engineering

Answer

Medical devices

Question 53

A key benefit of utilizing state feedback control is:

Accepted Answer

Enhanced performance

Answer

Reduced design complexity

Answer

Lower cost

Answer

Reduced system stability

Question 54

Is the following linear, time-invariant system controllable? 
 x(k+1) = [1 0; 1 1] x(k) + [1; 0] u(k)

Accepted Answer

Controllable

Answer

Uncontrollable

Answer

Cannot be determined

Question 55

When implementing a control system design on a microcontroller or embedded computer, which of the following factors must be taken into account?

Accepted Answer

Accuracy of numerical computations

Accepted Answer

Sampling rate of sensors

Accepted Answer

Power consumption of the device

Answer

Dimensions and weight of the microcontroller

Question 56

The transfer function of a control system typically takes the form of:

Accepted Answer

A Laplace transform

Answer

A differential equation

Answer

A block diagram

Answer

A state-space model

Question 57

The PID controller is a type of feedback controller that utilizes:

Accepted Answer

Proportional, integral, and derivative actions

Answer

Proportional and integral actions

Answer

Integral and derivative actions

Answer

Proportional and derivative actions

Question 58

The term 'controllability' in control systems refers to:

Accepted Answer

The ability to drive the system from any initial state to any desired final state

Answer

The ability to maintain a desired system state in the presence of disturbances

Answer

The ability to observe the system's internal states

Answer

The ability to stabilize an unstable system

Question 59

The primary objective of feedback control is to:

Accepted Answer

Reduce the error between a desired output and the actual output

Answer

Increase the system's gain

Answer

Eliminate noise in the system

Answer

Make the system independent of external disturbances

Question 60

Which of the following is a key advantage of using a model predictive controller (MPC) over traditional control methods?

Accepted Answer

Faster response time

Answer

Lower cost

Answer

Improved stability

Answer

Reduced complexity

Question 61

In a closed-loop control system, the feedback loop primarily serves which purpose?

Accepted Answer

To minimize disturbances and enhance system performance.

Answer

To extend the system's bandwidth.

Answer

To amplify the overall system gain.

Question 62

The Nyquist stability criterion is applicable for determining the stability of a feedback control system based on which factor?

Accepted Answer

The frequency response of its open-loop transfer function.

Answer

The locations of poles in the characteristic equation.

Answer

The time-domain response of the closed-loop system.

Question 63

The steady-state error of a closed-loop control system refers to the difference between the desired output and actual output when the system reaches:

Accepted Answer

Steady State

Answer

Transient State

Answer

Overdamped State

Question 64

Which type of stability analysis evaluates the system's response to small input variations?

Accepted Answer

Small Signal Stability

Answer

Asymptotic Stability

Answer

Global Stability

Answer

Lyapunov Stability