Q.1 What is the primary purpose of a control system?
To store data permanently
To regulate the behavior of a physical system
To transmit signals over long distances
To convert AC to DC
Explanation - Control systems are designed to manage, command, direct, or regulate the behavior of other devices or systems.
Correct answer is: To regulate the behavior of a physical system
Q.2 Which of the following represents a simple closed‑loop control system?
A thermostat regulating room temperature
A clock displaying the time
A flashlight that turns on when pressed
A bicycle pedal without brakes
Explanation - A thermostat measures temperature and feeds back the error to control heating, forming a closed‑loop.
Correct answer is: A thermostat regulating room temperature
Q.3 What is a block diagram in control theory?
A diagram that shows electrical power lines
A schematic for building a PCB
A graphical representation of system components and signal flow
A chart of temperature gradients
Explanation - Block diagrams illustrate how signals move through blocks that represent system elements.
Correct answer is: A graphical representation of system components and signal flow
Q.4 Which transform is most commonly used to analyze linear time‑invariant (LTI) systems?
Fourier Transform
Laplace Transform
Z-Transform
Wavelet Transform
Explanation - The Laplace transform converts differential equations into algebraic equations, simplifying LTI system analysis.
Correct answer is: Laplace Transform
Q.5 In a first‑order system, the transfer function is G(s) = 1/(τs + 1). What does τ represent?
Gain
Time constant
Bandwidth
Resonant frequency
Explanation - τ (tau) is the time constant, indicating how quickly the system responds to changes.
Correct answer is: Time constant
Q.6 Which of the following is NOT a type of feedback?
Negative feedback
Positive feedback
Derivative feedback
No feedback
Explanation - Feedback is typically negative or positive; derivative feedback is a control action, not a type of feedback loop.
Correct answer is: Derivative feedback
Q.7 A system is considered stable if all poles of its transfer function lie:
In the right half of the s‑plane
On the imaginary axis
In the left half of the s‑plane
At the origin
Explanation - For continuous‑time systems, left‑half plane poles ensure bounded response to bounded input.
Correct answer is: In the left half of the s‑plane
Q.8 What does a Bode plot represent?
Time‑domain step response
Frequency response magnitude and phase
Pole‑zero map
State‑space realization
Explanation - Bode plots display gain and phase versus frequency on logarithmic scales.
Correct answer is: Frequency response magnitude and phase
Q.9 A Proportional‑Integral‑Derivative (PID) controller has which of the following terms?
Only proportional and integral
Only proportional
Proportional, integral, and derivative
Only integral and derivative
Explanation - A PID controller combines P, I, and D terms to produce the control signal.
Correct answer is: Proportional, integral, and derivative
Q.10 Which of the following is a common application of a PID controller?
Temperature control in an oven
Human speech synthesis
Data encryption
Solar panel orientation
Explanation - PID controllers are widely used for temperature, speed, and position control in many industrial systems.
Correct answer is: Temperature control in an oven
Q.11 What does the 's' variable represent in Laplace transform?
A spatial coordinate
Complex frequency
Sampling period
Signal amplitude
Explanation - In Laplace transform, s = σ + jω is the complex frequency variable.
Correct answer is: Complex frequency
Q.12 In a feedback system, the transfer function of the forward path is G(s) and that of the feedback path is H(s). What is the closed‑loop transfer function?
G(s) + H(s)
G(s) - H(s)
G(s) / (1 + G(s)H(s))
G(s) * H(s)
Explanation - The standard closed‑loop transfer function is G/(1+GH) for unity negative feedback.
Correct answer is: G(s) / (1 + G(s)H(s))
Q.13 Which of the following best describes a first‑order system?
A system whose transfer function has at most one pole
A system with no zeros
A system with only a single state variable
All of the above
Explanation - First‑order systems have one pole, no zeros, and one state variable.
Correct answer is: All of the above
Q.14 A system with a transfer function G(s) = (s+2)/(s^2+3s+2) has how many poles?
1
2
3
0
Explanation - The denominator has two roots, so the system has two poles.
Correct answer is: 2
Q.15 Which of these is a discrete‑time equivalent of a continuous‑time integrator?
Summation
Differentiation
Sampling
Zero‑order hold
Explanation - Discrete integration is implemented by accumulating (summing) sample values.
Correct answer is: Summation
Q.16 In a root‑locus plot, increasing the proportional gain of a controller typically moves the closed‑loop poles:
Toward the origin
Toward the right half‑plane
Toward the left half‑plane
Unchanged
Explanation - Higher proportional gain generally improves stability by moving poles leftwards.
Correct answer is: Toward the left half‑plane
Q.17 What is the purpose of a sensor in a control system?
To act as an actuator
To generate the control signal
To measure system output for feedback
To supply power
Explanation - Sensors provide measurements that the controller uses to compute the error.
Correct answer is: To measure system output for feedback
Q.18 Which of the following is NOT a typical actuator type?
Electric motor
Hydraulic cylinder
Thermocouple
Servo valve
Explanation - A thermocouple measures temperature; it is not an actuator.
Correct answer is: Thermocouple
Q.19 A unit step input to a first‑order system with time constant τ yields a steady‑state value of:
0
τ
1
∞
Explanation - For G(s)=1/(τs+1), the step response tends to 1 as t→∞.
Correct answer is: 1
Q.20 In feedback control, the term 'error' refers to:
The difference between setpoint and measured output
The sum of all signals
The derivative of the input
The integral of the output
Explanation - Error is the deviation from the desired reference.
Correct answer is: The difference between setpoint and measured output
Q.21 Which of the following best describes an over‑damped second‑order system?
Poles are complex conjugates with positive real parts
Poles are real and distinct with negative real parts
Poles are repeated at the origin
Poles are at the imaginary axis
Explanation - Over‑damped systems have two distinct real negative poles.
Correct answer is: Poles are real and distinct with negative real parts
Q.22 In a control system, the term 'bandwidth' refers to:
The maximum input frequency
The range of frequencies where the gain is within 3 dB of the low‑frequency gain
The time constant of the system
The frequency of oscillation at resonance
Explanation - Bandwidth is defined as the frequency where the magnitude drops 3 dB from the DC gain.
Correct answer is: The range of frequencies where the gain is within 3 dB of the low‑frequency gain
Q.23 What does the 'zero' of a transfer function represent?
A frequency at which the magnitude is zero
A pole with zero magnitude
A root of the numerator polynomial
A point of maximum output
Explanation - Zeros are the values of s that make the numerator zero, causing attenuation at that frequency.
Correct answer is: A root of the numerator polynomial
Q.24 Which of the following is an example of a linear time‑invariant (LTI) system?
A thermostat with a temperature‑dependent heater
A pendulum with friction proportional to velocity
A digital filter with constant coefficients
A camera with automatic exposure that changes over time
Explanation - LTI systems have constant parameters and obey superposition, as in linear digital filters.
Correct answer is: A digital filter with constant coefficients
Q.25 The Laplace transform of a unit impulse δ(t) is:
0
1
s
e^s
Explanation - ∫δ(t)e^{-st}dt = 1 for all s.
Correct answer is: 1
Q.26 Which of the following is a typical role of a controller in a feedback loop?
Measure the output
Generate the reference input
Calculate the control action based on error
Apply the control action to the plant
Explanation - The controller processes the error to produce a control signal.
Correct answer is: Calculate the control action based on error
Q.27 In a standard feedback configuration, if the forward path has a gain of G and the feedback path has a gain of H, the loop gain is:
G + H
G * H
G - H
H / G
Explanation - Loop gain is the product of the forward and feedback gains.
Correct answer is: G * H
Q.28 A second‑order under‑damped system has a damping ratio ζ such that:
0 < ζ < 1
ζ = 1
ζ > 1
ζ = 0
Explanation - Underdamped systems have a damping ratio between 0 and 1, leading to oscillatory response.
Correct answer is: 0 < ζ < 1
Q.29 Which of the following is NOT an advantage of using negative feedback?
Improved system stability
Reduced sensitivity to parameter variations
Increased system gain
Enhanced bandwidth
Explanation - Negative feedback generally reduces the closed‑loop gain relative to the open‑loop gain.
Correct answer is: Increased system gain
Q.30 In state‑space representation, the matrix A is called the:
Output matrix
Input matrix
State matrix
Feed‑forward matrix
Explanation - A defines the system dynamics in the state equation \.x˙ = A\.x + B\.u.
Correct answer is: State matrix
Q.31 The Laplace transform of the unit step function u(t) is:
s
1/s
e^{-s}
0
Explanation - ∫₀^∞ e^{-st} dt = 1/s for Re(s) > 0.
Correct answer is: 1/s
Q.32 Which of the following is a common method to assess the stability of a system without computing poles?
Bode plot phase margin
Root locus
Time‑domain step test
All of the above
Explanation - Phase margin, root locus, and step response can all provide stability information.
Correct answer is: All of the above
Q.33 The transfer function of a pure integrator is:
1/s
s
1/s^2
s^2
Explanation - An integrator divides by s in the Laplace domain.
Correct answer is: 1/s
Q.34 Which of the following is a measure of how fast a system responds to a change?
Gain
Phase shift
Time constant
Bandwidth
Explanation - The time constant τ defines the time it takes the response to reach 63% of its final value.
Correct answer is: Time constant
Q.35 In a feedback system, the 'loop gain' refers to:
The gain from input to output only
The product of forward and feedback gains
The ratio of output to input
The sum of the forward path and feedback path
Explanation - Loop gain is the combined effect of the forward and feedback paths.
Correct answer is: The product of forward and feedback gains
Q.36 Which of the following best describes a dead‑zone in a control system?
A region where the controller output is zero even though the error is non‑zero
A region where the output is always zero
A region where the error is zero
A region where the sensor has no output
Explanation - Dead‑zone nonlinearity causes the controller to ignore small errors.
Correct answer is: A region where the controller output is zero even though the error is non‑zero
Q.37 Which of the following is a common type of sampling in digital signal processing?
Uniform sampling
Random sampling
Adaptive sampling
All of the above
Explanation - Uniform sampling at a fixed rate is the standard approach in digital control.
Correct answer is: Uniform sampling
Q.38 A system with a transfer function G(s) = 5/(s+5) has a static gain of:
5
1
0.5
10
Explanation - Static gain is G(0) = 5/5 = 1.
Correct answer is: 1
Q.39 In a root‑locus plot, the asymptotes of the poles and zeros are determined by:
The frequency range
The number of poles and zeros
The time constant
The sampling period
Explanation - Asymptotes are calculated from the difference between pole and zero counts.
Correct answer is: The number of poles and zeros
Q.40 Which of the following is NOT a typical function of a sensor in a control system?
Detect the system state
Provide reference signal
Feed back information to the controller
Convert physical quantity to electrical signal
Explanation - The reference signal is usually set externally, not generated by the sensor.
Correct answer is: Provide reference signal
Q.41 Which of the following is a typical method to design a PID controller?
Ziegler–Nichols tuning
Fourier analysis
State‑space decomposition
Wavelet transform
Explanation - Ziegler–Nichols is a classic empirical tuning rule for PID parameters.
Correct answer is: Ziegler–Nichols tuning
Q.42 In the context of control systems, 'bandwidth' is most directly related to:
The maximum time constant
The frequency response
The steady‑state error
The sampling period
Explanation - Bandwidth refers to the range of frequencies where the system response remains effective.
Correct answer is: The frequency response
Q.43 What is the Laplace transform of t·u(t)?
1/s^2
1/s
s
0
Explanation - ∫₀^∞ t e^{-st} dt = 1/s².
Correct answer is: 1/s^2
Q.44 A system that has all its poles in the left half of the s‑plane is said to be:
Unstable
Marginally stable
Stable
Over‑damped
Explanation - Left‑half plane poles guarantee bounded output for bounded input.
Correct answer is: Stable
Q.45 Which of the following represents an example of an actuator?
Temperature sensor
Hydraulic pump
Accelerometer
Pressure gauge
Explanation - An actuator changes the system state, like a pump or motor.
Correct answer is: Hydraulic pump
Q.46 Which of the following is a typical property of a linear system?
Time variance
Memoryless
Non‑superposition
Non‑causal
Explanation - Linear systems obey superposition and often have no memory of past inputs.
Correct answer is: Memoryless
Q.47 What is the steady‑state error of a type‑0 system for a unit step input?
0
1
Infinity
0.5
Explanation - For a type‑0 system, the steady‑state error to a step is 1/(1+Kp), where Kp is finite.
Correct answer is: 0.5
Q.48 Which of the following best describes the 'time constant' of a second‑order system?
The inverse of the natural frequency
The damping ratio
The reciprocal of the dominant pole
The period of oscillation
Explanation - The dominant pole's real part determines the exponential decay rate.
Correct answer is: The reciprocal of the dominant pole
Q.49 Which of the following is an example of a continuous‑time system?
A digital thermostat
A microcontroller program
A DC motor with analog controller
An analog audio amplifier
Explanation - Analog amplifiers operate continuously over time, unlike digital systems.
Correct answer is: An analog audio amplifier
Q.50 In a closed‑loop system, increasing the feedback gain generally:
Reduces the error
Increases the error
Has no effect on the error
Increases the noise level
Explanation - Higher feedback gain improves tracking by reducing the error signal.
Correct answer is: Reduces the error
Q.51 What does the term 'sampling period' refer to?
The interval between consecutive samples in a digital system
The time it takes for an integrator to settle
The period of oscillation in a system
The time between two successive poles
Explanation - Sampling period T = 1/Fs determines the digital representation frequency.
Correct answer is: The interval between consecutive samples in a digital system
Q.52 A zero at s = -3 in a transfer function G(s) will cause:
A phase lag of 90° at all frequencies
An attenuation of the output at low frequencies
A phase lead at frequencies below 3 rad/s
No effect on the magnitude
Explanation - A zero introduces phase lead at frequencies below its value.
Correct answer is: A phase lead at frequencies below 3 rad/s
Q.53 Which of the following is NOT a characteristic of a stable closed‑loop system?
All poles in the left half‑plane
No poles on the imaginary axis
No right‑half plane poles
Infinite steady‑state error to a step input
Explanation - A stable closed‑loop system can have finite steady‑state error.
Correct answer is: Infinite steady‑state error to a step input
Q.54 In a PID controller, the integral term primarily helps to eliminate:
Transient oscillations
Steady‑state error
Noise amplification
High‑frequency disturbances
Explanation - Integral action accumulates error, driving steady‑state error to zero.
Correct answer is: Steady‑state error
Q.55 The transfer function of an ideal differentiator is:
1/s
s
s^2
1
Explanation - Differentiation corresponds to multiplication by s in the Laplace domain.
Correct answer is: s
Q.56 Which of the following statements is true about a unit‑gain feedback loop?
The loop gain equals the system gain
The closed‑loop transfer function is G/(1+G)
The closed‑loop transfer function is G/(1−G)
The closed‑loop transfer function is 1/(1+G)
Explanation - With H=1, the standard formula gives G/(1+G).
Correct answer is: The closed‑loop transfer function is G/(1+G)
Q.57 The term 'dead time' refers to:
The time lag between input and output
The time it takes for the system to reach half of its final value
The time constant of a first‑order system
The time between successive samples
Explanation - Dead time is an inherent delay where the output does not respond immediately.
Correct answer is: The time lag between input and output
Q.58 Which of the following is a typical measure of a system’s ability to reject disturbances?
Phase margin
Sensitivity function
Time constant
Bandwidth
Explanation - The sensitivity function quantifies disturbance rejection capability.
Correct answer is: Sensitivity function
Q.59 In a Bode plot, the magnitude plot is typically expressed in:
Radians per second
Decibels
Volts
Seconds
Explanation - The magnitude is plotted in dB to show relative gain over frequency.
Correct answer is: Decibels
Q.60 A second‑order system with a damping ratio ζ = 0.707 is known as a:
Over‑damped system
Critically damped system
Underdamped system with optimal settling time
Underdamped system with maximum oscillation
Explanation - ζ = 0.707 provides the fastest rise time without excessive overshoot.
Correct answer is: Underdamped system with optimal settling time
Q.61 Which of the following best describes a digital controller?
A controller that uses continuous‑time equations
A controller implemented in software that operates on sampled data
A controller that only uses analog hardware
A controller that has infinite bandwidth
Explanation - Digital controllers process discrete samples via algorithms.
Correct answer is: A controller implemented in software that operates on sampled data
Q.62 What is the unit of the Laplace variable s?
Seconds
Radians per second
Hertz
Dimensionless
Explanation - s has units of 1/s, which corresponds to radians per second.
Correct answer is: Radians per second
Q.63 Which of the following is a common approach to handle dead time in a control loop?
Increase proportional gain
Add a lag compensator
Use a Smith predictor
Decrease the sampling period
Explanation - A Smith predictor compensates for known dead time in feedback loops.
Correct answer is: Use a Smith predictor
Q.64 The sum of the orders of the numerator and denominator polynomials in a transfer function is called the:
System order
Transfer order
Degree
Rank
Explanation - The overall order equals the highest power of s in the denominator.
Correct answer is: System order
Q.65 In the context of control systems, 'phase margin' is a measure of:
Stability buffer against gain variations
Stability buffer against phase variations
Sensitivity to sensor noise
Bandwidth of the system
Explanation - Phase margin quantifies how much additional phase lag the system can tolerate.
Correct answer is: Stability buffer against phase variations
Q.66 Which of the following is a typical form of a transfer function for a second‑order system?
K/(τs + 1)
K/(s^2 + 2ζω_ns + ω_n^2)
K/(s + 1)
K/(s^3 + s^2 + s + 1)
Explanation - The standard second‑order form includes damping ratio ζ and natural frequency ω_n.
Correct answer is: K/(s^2 + 2ζω_ns + ω_n^2)
Q.67 The presence of which of the following in a transfer function indicates a system’s ability to reject high‑frequency disturbances?
Poles at the origin
Zeros at the origin
High‑frequency poles
High‑frequency zeros
Explanation - Zeros at high frequencies create a high‑frequency roll‑off, improving disturbance rejection.
Correct answer is: High‑frequency zeros
Q.68 A transfer function G(s) = K/(τs + 1) has a corner frequency of:
1/τ
τ
K
0
Explanation - The corner (break) frequency ω_c = 1/τ for a first‑order system.
Correct answer is: 1/τ
Q.69 Which of the following is a typical characteristic of a lag compensator?
Improves transient response
Provides high‑frequency attenuation
Adds a leading phase
Reduces steady‑state error
Explanation - A lag compensator increases low‑frequency gain to improve steady‑state accuracy.
Correct answer is: Reduces steady‑state error
Q.70 The time delay in a system that can be modeled by a factor e^{-sT_d} is known as:
Phase shift
Group delay
Dead time
Damping ratio
Explanation - e^{-sT_d} represents a pure time delay of T_d seconds.
Correct answer is: Dead time
Q.71 In a discrete‑time system, the z‑transform of a unit step is:
1/(1-z^{-1})
1/(1+z^{-1})
z/(z-1)
z/(z+1)
Explanation - The sum of a geometric series yields 1/(1-z^{-1}) for |z|>1.
Correct answer is: 1/(1-z^{-1})
Q.72 Which of the following best describes the Nyquist stability criterion?
A method to compute the poles of a transfer function
A graphical test for stability based on frequency response
A technique to design PID controllers
A rule to determine the system order
Explanation - Nyquist plots examine encirclements of the critical point to assess stability.
Correct answer is: A graphical test for stability based on frequency response
Q.73 The 'steady‑state gain' of a system is also known as its:
Bandwidth
DC gain
Gain margin
Phase margin
Explanation - Steady‑state gain is the system’s gain at zero frequency (DC).
Correct answer is: DC gain
Q.74 What is the effect of increasing the proportional gain on the closed‑loop natural frequency?
It decreases the natural frequency
It increases the natural frequency
It has no effect
It causes the natural frequency to become zero
Explanation - Higher proportional gain generally raises the system’s natural frequency.
Correct answer is: It increases the natural frequency
Q.75 Which of the following represents a stable first‑order system with a pole at s = -2?
G(s) = 1/(s + 2)
G(s) = 1/(s - 2)
G(s) = 1/(s^2 + 4)
G(s) = 1/(s^2 - 4)
Explanation - A pole at -2 lies in the left half‑plane, ensuring stability.
Correct answer is: G(s) = 1/(s + 2)
Q.76 In the context of control, which of the following is a measure of how fast an error signal decays?
Time constant
Damping ratio
Settling time
Rise time
Explanation - The time constant quantifies the exponential decay rate of the error.
Correct answer is: Time constant
Q.77 Which of the following is NOT a typical feature of a PID controller implemented in software?
Integral wind‑up protection
Finite‑precision arithmetic
Continuous‑time dynamics
Digital filtering of the derivative term
Explanation - Software controllers are discrete and cannot implement continuous‑time dynamics directly.
Correct answer is: Continuous‑time dynamics
Q.78 The term 'steady‑state error' is defined as the difference between:
Desired output and actual output as t → ∞
Desired input and actual input as t → 0
Actual output and zero
Desired output and zero
Explanation - Steady‑state error measures the asymptotic tracking error.
Correct answer is: Desired output and actual output as t → ∞
Q.79 In state‑space representation, the matrix B is called the:
State matrix
Input matrix
Output matrix
Feed‑forward matrix
Explanation - B maps the input vector u into the state derivative equation.
Correct answer is: Input matrix
Q.80 Which of the following is a typical disadvantage of using a high integral gain?
Increased overshoot
Longer settling time
Reduced steady‑state error
Improved noise rejection
Explanation - High integral gain can cause slow convergence and potential oscillations.
Correct answer is: Longer settling time
Q.81 A system that is not memoryless has:
No dependence on past inputs
Dependence on past inputs
Only present inputs
Only future inputs
Explanation - Systems with memory require past input history to compute the output.
Correct answer is: Dependence on past inputs
Q.82 What is the purpose of a disturbance observer in a control system?
To estimate external disturbances affecting the plant
To measure sensor noise
To generate the setpoint
To provide actuation signals
Explanation - Disturbance observers estimate and cancel the effect of unknown inputs.
Correct answer is: To estimate external disturbances affecting the plant
Q.83 Which of the following represents a typical form of a transfer function for a lag compensator?
K(1 + sT_d)/(1 + sT_d)
K(1 + sT)/(1 + sT/α)
K(s + 1/T)/(s + 1/αT)
K/(1 + sT)
Explanation - A lag compensator has a pole at the origin slightly shifted, giving a low‑frequency gain boost.
Correct answer is: K(1 + sT)/(1 + sT/α)
Q.84 Which of the following statements best describes the phase margin of a system?
The phase lag at the frequency where the magnitude equals 0 dB
The amount of gain increase before instability
The steady‑state error to a step input
The bandwidth of the system
Explanation - Phase margin is the additional phase lag required to reach instability at the -3 dB point.
Correct answer is: The phase lag at the frequency where the magnitude equals 0 dB
Q.85 In a Bode plot, the slope of the magnitude curve for a pole at s = -1 is:
-20 dB/decade
-6 dB/octave
0 dB/decade
-40 dB/decade
Explanation - A single pole contributes a -20 dB/decade slope beyond its corner frequency.
Correct answer is: -20 dB/decade
Q.86 Which of the following is a common effect of sensor noise on a control system?
Reduced steady‑state error
Increased bandwidth
Higher measurement uncertainty
Lower phase margin
Explanation - Noise degrades the precision of the sensor reading.
Correct answer is: Higher measurement uncertainty
Q.87 Which of the following is a typical application of a lead compensator?
Increase steady‑state error
Improve transient response by adding phase lead
Add a lag at high frequencies
Reduce sensor noise
Explanation - Lead compensators increase phase margin, speeding up the response.
Correct answer is: Improve transient response by adding phase lead
Q.88 In the Laplace domain, the transfer function of a pure delay T_d is given by:
e^{-sT_d}
1/(s + T_d)
sT_d
T_d/s
Explanation - A pure time delay is represented by the exponential term in the Laplace domain.
Correct answer is: e^{-sT_d}
Q.89 The stability of a discrete system can be determined by examining:
Poles in the right half‑plane
Poles inside the unit circle
Zeros on the imaginary axis
Zeros on the real axis
Explanation - Discrete stability requires all poles to lie inside the unit circle in the z‑plane.
Correct answer is: Poles inside the unit circle
Q.90 The term 'gain margin' refers to:
The amount of gain increase before instability
The amount of phase increase before instability
The steady‑state error to a step input
The bandwidth of the system
Explanation - Gain margin is the factor by which the loop gain can be increased before the system becomes unstable.
Correct answer is: The amount of gain increase before instability
Q.91 Which of the following is an example of a non‑linear element in a control system?
Proportional gain
Integral controller
Saturation block
Differentiator
Explanation - Saturation introduces non‑linearity by limiting the output amplitude.
Correct answer is: Saturation block
Q.92 Which of the following best describes the purpose of a sensor’s transfer function?
To model the sensor’s frequency response
To describe the sensor’s output as a function of time
To compute the sensor’s gain
All of the above
Explanation - A sensor’s transfer function captures its dynamic behavior and frequency response.
Correct answer is: All of the above
Q.93 Which of the following statements about a zero at the origin is true?
It introduces a phase lead of 90° at all frequencies
It reduces the steady‑state error to a step input
It has no effect on the magnitude
It is equivalent to an integrator
Explanation - A zero at the origin (s=0) adds a differentiator effect that can improve tracking.
Correct answer is: It reduces the steady‑state error to a step input
Q.94 Which of the following is a typical step response characteristic of an under‑damped second‑order system?
No overshoot
Overshoot followed by oscillation
Immediate settling
Exponential decay without oscillation
Explanation - Under‑damped responses exhibit overshoot and damped oscillations.
Correct answer is: Overshoot followed by oscillation
Q.95 The term 'static error constant' refers to:
The error for a sinusoidal input at steady state
The error for a step input at steady state
The error for a ramp input at steady state
All of the above
Explanation - Static error constants (Kp, Kv, Ka) correspond to step, ramp, and parabolic inputs respectively.
Correct answer is: All of the above
Q.96 Which of the following best describes the role of an actuator in a control loop?
To measure the system output
To apply the control signal to the plant
To compute the control law
To filter sensor noise
Explanation - Actuators physically influence the plant based on the controller’s output.
Correct answer is: To apply the control signal to the plant
Q.97 What is the Laplace transform of a unit ramp function r(t) = t·u(t)?
1/s^2
1/s^3
t/s
s
Explanation - The Laplace of t·u(t) is 1/s².
Correct answer is: 1/s^2
Q.98 Which of the following is a typical characteristic of a well‑designed control system?
High sensitivity to parameter variations
Low bandwidth
Fast transient response with minimal overshoot
High steady‑state error
Explanation - Good design balances speed, accuracy, and stability.
Correct answer is: Fast transient response with minimal overshoot
Q.99 Which of the following best defines the term 'system bandwidth' in a control system?
The maximum frequency at which the system can operate
The frequency at which the closed‑loop gain falls 3 dB below its DC value
The difference between the highest and lowest resonant frequencies
The bandwidth of the sensor alone
Explanation - Bandwidth is defined by the -3 dB point on the magnitude plot.
Correct answer is: The frequency at which the closed‑loop gain falls 3 dB below its DC value
Q.100 Which of the following statements is correct about the sensitivity function S(s) = 1/(1+GH)?
It measures how disturbances at the output affect the error
It measures how changes in plant parameters affect the output
It is identical to the complementary sensitivity function
It has poles at the same locations as the plant
Explanation - S(s) describes the system’s response to disturbances and parameter variations.
Correct answer is: It measures how disturbances at the output affect the error
Q.101 Which of the following best describes a lead‑lag compensator?
A combination of lead and lag elements to shape the frequency response
A single pole at the origin
A pure integrator
An uncompensated system
Explanation - Lead‑lag compensators adjust phase and gain to meet performance specs.
Correct answer is: A combination of lead and lag elements to shape the frequency response
Q.102 The Laplace transform of the derivative of a function f(t) is:
F(s)
sF(s)
F(s)/s
sF(s) + f(0)
Explanation - Differentiation in time domain adds a term sF(s) plus the initial value f(0).
Correct answer is: sF(s) + f(0)
Q.103 In the context of control systems, the term 'bandwidth' is directly related to:
The location of the dominant pole
The value of the proportional gain
The time delay of the system
The steady‑state error constant
Explanation - Bandwidth is influenced by the dominant pole’s distance from the origin.
Correct answer is: The location of the dominant pole
Q.104 Which of the following is NOT a characteristic of an ideal sensor?
No noise
Infinite bandwidth
Zero offset
Perfect linearity
Explanation - An ideal sensor would have no offset, but in practice, offsets are common.
Correct answer is: Zero offset
Q.105 The transfer function of a first‑order lag element with time constant τ and gain K is:
K/(s + 1/τ)
K/(τs + 1)
K(τs + 1)
Kτ/(s + 1)
Explanation - A lag element behaves like a first‑order system with gain K.
Correct answer is: K/(τs + 1)
Q.106 Which of the following is a typical effect of increasing the derivative gain in a PID controller?
Reduced steady‑state error
Increased overshoot
Reduced phase lag
Decreased noise sensitivity
Explanation - High derivative gain can amplify high‑frequency noise and cause overshoot.
Correct answer is: Increased overshoot
Q.107 The term 'dead time' in a control system is often modeled by:
1/(s + 1/τ)
e^{-sT_d}
sT_d
T_d/s
Explanation - Dead time corresponds to a pure time delay represented by an exponential.
Correct answer is: e^{-sT_d}
Q.108 Which of the following is a common approach to compensate for dead time in a feedback loop?
Use a high‑gain proportional controller
Add a lag compensator
Employ a Smith predictor
Decrease the sampling rate
Explanation - Smith predictors anticipate the delay and improve performance.
Correct answer is: Employ a Smith predictor
Q.109 In a digital controller, the zero‑order hold (ZOH) is used to:
Convert a continuous‑time input to a discrete signal
Sample the output of a system
Hold the input constant between samples
Filter the noise in the measurement
Explanation - The ZOH keeps the control signal constant over each sampling interval.
Correct answer is: Hold the input constant between samples
Q.110 Which of the following best describes the steady‑state error for a type‑1 system subject to a ramp input?
Zero
Finite but nonzero
Infinite
Dependent on the integral gain
Explanation - A type‑1 system has zero steady‑state error to a ramp input due to integral action.
Correct answer is: Zero
Q.111 A state‑space model of a system includes which of the following matrices?
A, B, C, and D
G, H, K, and L
M, N, O, and P
Only A and B
Explanation - The state‑space representation uses four matrices: system, input, output, and feed‑forward.
Correct answer is: A, B, C, and D
Q.112 The concept of 'phase margin' is primarily associated with:
Gain margin
Transient response
Stability robustness
Steady‑state error
Explanation - Phase margin indicates how close the system is to instability due to phase lag.
Correct answer is: Stability robustness
Q.113 Which of the following is a typical characteristic of a system with a pole at the origin?
Zero steady‑state error to a step input
Infinite steady‑state error to a step input
Zero steady‑state error to a ramp input
High natural frequency
Explanation - A pole at the origin corresponds to an integrator, eliminating steady‑state error to a step.
Correct answer is: Zero steady‑state error to a step input
Q.114 In a Bode plot, a pole at s = -10 rad/s will begin to affect the magnitude plot at:
Below 1 rad/s
Around 10 rad/s
Above 100 rad/s
At all frequencies
Explanation - The corner frequency occurs near the pole location, where the slope changes.
Correct answer is: Around 10 rad/s
Q.115 Which of the following is a typical use of a Smith predictor?
To cancel sensor noise
To compensate for actuator dead time
To increase the bandwidth of a system
To reduce steady‑state error
Explanation - Smith predictors are employed to counteract known delays in the feedback path.
Correct answer is: To compensate for actuator dead time
Q.116 The term 'steady‑state gain' refers to:
The gain of a system at infinite frequency
The gain of a system at zero frequency
The maximum gain achievable by the controller
The gain at the resonant frequency
Explanation - Steady‑state gain is the DC gain of the transfer function.
Correct answer is: The gain of a system at zero frequency
Q.117 Which of the following best describes the effect of a lag compensator on the phase margin?
It increases phase margin
It decreases phase margin
It has no effect
It eliminates phase lag
Explanation - Lag compensators add phase lag, reducing the phase margin.
Correct answer is: It decreases phase margin
Q.118 The Laplace transform of a unit step function u(t) is:
s
1/s
e^{-s}
0
Explanation - The integral of e^{-st} from 0 to ∞ yields 1/s.
Correct answer is: 1/s
Q.119 In a closed‑loop system, a high gain margin indicates:
The system is close to instability
The system is robust to parameter variations
The system has a high bandwidth
The system has low steady‑state error
Explanation - A large gain margin means the system can tolerate larger gain changes before instability.
Correct answer is: The system is robust to parameter variations
Q.120 A controller that includes proportional, integral, and derivative actions is commonly referred to as a:
PI controller
PD controller
PID controller
ILC controller
Explanation - PID stands for Proportional‑Integral‑Derivative.
Correct answer is: PID controller
Q.121 Which of the following is a typical method to reduce steady‑state error in a control system?
Increase proportional gain only
Add an integrator term
Add a differentiator term
Decrease the system bandwidth
Explanation - Integral action accumulates error, driving steady‑state error to zero.
Correct answer is: Add an integrator term
Q.122 In a root‑locus plot, the number of asymptotes is equal to:
The number of zeros minus the number of poles
The number of poles minus the number of zeros
The total number of poles and zeros
The number of poles
Explanation - Each asymptote corresponds to an extra pole not matched by a zero.
Correct answer is: The number of poles minus the number of zeros
Q.123 A sensor that measures temperature and outputs a voltage proportional to temperature is an example of:
A sensor with a transfer function
A sensor with no transfer function
A sensor without linearity
A sensor without bandwidth
Explanation - The voltage output relates linearly to temperature, representing a transfer function.
Correct answer is: A sensor with a transfer function
Q.124 Which of the following describes the main advantage of state‑space representation over transfer functions?
It is limited to SISO systems
It can handle MIMO systems
It is easier to design PID controllers
It does not require a Laplace transform
Explanation - State‑space methods naturally extend to multi‑input/multi‑output (MIMO) systems.
Correct answer is: It can handle MIMO systems
Q.125 Which of the following is a typical feature of a lead‑lag compensator?
It always increases bandwidth
It introduces a single pole and zero
It adds a pure integrator
It eliminates steady‑state error to a step input
Explanation - Lead‑lag compensators have a pole and zero placed to shape the frequency response.
Correct answer is: It introduces a single pole and zero
Q.126 The Bode plot of a system with a pole at -5 rad/s and a zero at -1 rad/s will show:
A 20 dB/decade slope starting at 1 rad/s
A 20 dB/decade slope starting at 5 rad/s
A 0 dB slope throughout
A -20 dB/decade slope starting at 1 rad/s
Explanation - The zero adds a +20 dB/decade slope from 1 rad/s, while the pole adds a -20 dB/decade after 5 rad/s.
Correct answer is: A 20 dB/decade slope starting at 1 rad/s
Q.127 In control theory, the term 'complementary sensitivity function' refers to:
T(s) = GH/(1+GH)
S(s) = 1/(1+GH)
C(s) = G/(1+GH)
K(s) = 1/(1+GH)
Explanation - The complementary sensitivity function describes the closed‑loop response to reference signals.
Correct answer is: T(s) = GH/(1+GH)
Q.128 The Laplace transform of a second‑order step response with natural frequency ω_n and damping ratio ζ is:
1/(s(s+ω_n))
(2ζω_n)/(s^2 + 2ζω_ns + ω_n^2)
ω_n^2/(s^2 + 2ζω_ns + ω_n^2)
s/(s^2 + 2ζω_ns + ω_n^2)
Explanation - This is the standard Laplace form of a second‑order step response.
Correct answer is: (2ζω_n)/(s^2 + 2ζω_ns + ω_n^2)
Q.129 Which of the following best describes the effect of increasing the proportional gain on the steady‑state error to a step input?
It increases the error
It decreases the error
It has no effect
It makes the error oscillatory
Explanation - Higher proportional gain reduces the steady‑state error for a given plant.
Correct answer is: It decreases the error
Q.130 A discrete‑time system that is stable if all its poles lie inside the unit circle is a:
Continuous‑time system
Digital filter
Analog filter
Time‑invariant system
Explanation - Digital filters are discrete‑time systems whose stability is determined by the unit circle.
Correct answer is: Digital filter
Q.131 Which of the following is an advantage of using a state‑space approach?
It is limited to scalar systems
It is easier to model time delays
It allows systematic observer design
It eliminates the need for Laplace transforms
Explanation - State‑space methods facilitate the design of observers for state estimation.
Correct answer is: It allows systematic observer design
Q.132 The transfer function of an ideal differentiator is represented as:
s
1/s
s^2
0
Explanation - Differentiation in time corresponds to multiplication by s in the Laplace domain.
Correct answer is: s
Q.133 The concept of 'steady‑state error' is most relevant for:
Transient response analysis
Frequency response analysis
Steady‑state error analysis
Noise analysis
Explanation - Steady‑state error deals with the difference between desired and actual output as t → ∞.
Correct answer is: Steady‑state error analysis
Q.134 Which of the following describes a system that has a zero at the origin?
It has a differentiator action
It has an integrator action
It has no effect on steady‑state error
It reduces phase lag
Explanation - A zero at s=0 adds a zero to the transfer function, akin to differentiation.
Correct answer is: It has a differentiator action
Q.135 The Nyquist stability criterion checks for:
Number of poles in the right half‑plane
Encirclements of the -1 point in the complex plane
Poles on the imaginary axis
Zeros in the right half‑plane
Explanation - The criterion examines the Nyquist plot for encirclements of the critical point.
Correct answer is: Encirclements of the -1 point in the complex plane
Q.136 The Bode plot of a system with a pole at -1 rad/s will exhibit a slope change of:
+20 dB/decade
-20 dB/decade
+6 dB/octave
-6 dB/octave
Explanation - A single pole produces a -20 dB/decade slope beyond its corner frequency.
Correct answer is: -20 dB/decade
Q.137 A sensor’s accuracy is defined by:
Its linearity range
Its noise level
Its bias error
All of the above
Explanation - Accuracy encompasses linearity, noise, bias, and other error sources.
Correct answer is: All of the above
Q.138 In a feedback loop, the transfer function of the controller is C(s). The overall open‑loop transfer function is:
C(s)G(s)H(s)
G(s)H(s)C(s)
C(s) + G(s)H(s)
G(s)/(1+H(s))
Explanation - Open‑loop transfer is the product of controller, plant, and feedback elements.
Correct answer is: C(s)G(s)H(s)
Q.139 Which of the following best explains the concept of 'pole‑zero cancellation'?
When a pole and zero occur at the same frequency, the system becomes unstable
When a pole and zero occur at the same frequency, they cancel each other in the frequency response
It refers to adding more poles and zeros to a system
It is the same as adding a lag compensator
Explanation - Pole‑zero cancellation reduces the order of the transfer function but may affect stability in practice.
Correct answer is: When a pole and zero occur at the same frequency, they cancel each other in the frequency response
Q.140 The steady‑state error for a type‑2 system subjected to a quadratic input is:
Zero
Finite but nonzero
Infinite
Dependent on the proportional gain
Explanation - A type‑2 system has two integrators, eliminating steady‑state error to quadratic inputs.
Correct answer is: Zero
Q.141 In a control system, a 'plant' refers to:
The controller
The sensor
The process or device being controlled
The feedback path
Explanation - The plant is the physical system that the controller acts upon.
Correct answer is: The process or device being controlled
Q.142 The term 'unity feedback' means:
The feedback transfer function is 1
The system has a gain of 1
The controller has unity gain
The sensor output is normalized
Explanation - Unity feedback means the feedback path has a transfer function of 1.
Correct answer is: The feedback transfer function is 1
Q.143 Which of the following is a typical feature of a well‑designed control system?
High sensitivity to parameter changes
Fast response with minimal overshoot
Large steady‑state error
Limited bandwidth
Explanation - Good control design seeks a fast, accurate, and stable response.
Correct answer is: Fast response with minimal overshoot
Q.144 The transfer function G(s) = 1/(s+1) has a time constant of:
1 s
0.5 s
2 s
1 rad/s
Explanation - The time constant τ equals the reciprocal of the pole location (1).
Correct answer is: 1 s
Q.145 In the Laplace domain, the transfer function of a pure delay of T_d seconds is e^{-sT_d}. This introduces:
A pure phase shift
A magnitude change
Both magnitude and phase changes
No effect on the frequency response
Explanation - A delay adds a linear phase shift that increases with frequency.
Correct answer is: A pure phase shift
Q.146 Which of the following is a benefit of using a digital controller over an analog controller?
Infinite precision
Unlimited bandwidth
Ease of implementing complex algorithms
No need for sampling
Explanation - Digital controllers can run sophisticated control laws more readily.
Correct answer is: Ease of implementing complex algorithms
Q.147 The steady‑state error for a type‑0 system to a ramp input is:
Zero
Finite but nonzero
Infinite
Dependent on the integral gain
Explanation - A type‑0 system (no integrator) has a finite steady‑state error to a ramp input.
Correct answer is: Finite but nonzero
Q.148 The Nyquist plot is commonly used to:
Design state‑space observers
Assess transient response
Evaluate closed‑loop stability
Determine the steady‑state error
Explanation - The Nyquist plot checks for encirclements that indicate instability.
Correct answer is: Evaluate closed‑loop stability
Q.149 Which of the following best describes a 'dead‑time compensator'?
A filter that removes sensor noise
A lead compensator to counteract dead time
A lag compensator to improve steady‑state error
A zero‑order hold element
Explanation - Lead compensation can compensate for the phase lag caused by dead time.
Correct answer is: A lead compensator to counteract dead time
Q.150 Which of the following statements about a first‑order lag compensator is correct?
It adds a pole at the origin
It increases low‑frequency gain
It improves the high‑frequency roll‑off
It adds a zero at the origin
Explanation - Lag compensators provide a boost at low frequencies, improving steady‑state error.
Correct answer is: It increases low‑frequency gain
Q.151 The transfer function of a second‑order system with a natural frequency ω_n and damping ratio ζ is:
K/(s^2 + 2ζω_ns + ω_n^2)
K/(s + ω_n)
K(1 + s/ω_n)
K/(s^2 + ω_n^2)
Explanation - This is the standard form for a second‑order denominator.
Correct answer is: K/(s^2 + 2ζω_ns + ω_n^2)
Q.152 In a state‑space model, the matrix D represents:
Direct transmission from input to output
The state transition matrix
The output matrix
The input matrix
Explanation - D captures any direct feed‑forward path between input and output.
Correct answer is: Direct transmission from input to output
Q.153 The Bode magnitude plot of a system with a zero at -5 rad/s will show:
A +20 dB/decade slope starting at 5 rad/s
A -20 dB/decade slope starting at 5 rad/s
No change in slope at 5 rad/s
A 0 dB slope throughout
Explanation - A zero adds +20 dB/decade beyond its corner frequency.
Correct answer is: A +20 dB/decade slope starting at 5 rad/s
Q.154 The term 'phase margin' is measured in degrees and refers to:
The angle at which the magnitude is zero
The angle difference between the open‑loop transfer and -180° at the unity‑gain frequency
The angle at which the system becomes unstable
The difference between the actual phase and the desired phase
Explanation - Phase margin quantifies how far the system is from the stability boundary.
Correct answer is: The angle difference between the open‑loop transfer and -180° at the unity‑gain frequency
Q.155 Which of the following is a key difference between a PID controller and a PI controller?
The PID controller has a derivative term
The PI controller has no proportional action
The PID controller has no integral action
The PI controller has an extra zero
Explanation - A PID adds a derivative term to a PI controller.
Correct answer is: The PID controller has a derivative term
Q.156 In a discrete system, the z‑transform of a unit delay is z^{-1}. This delay introduces:
A phase lead
A phase lag
A magnitude gain
No effect on phase
Explanation - A unit delay in discrete time adds a phase lag of -ωT at frequency ω.
Correct answer is: A phase lag