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Control Systems MCQs

Practice Control Systems MCQs from fundamental concepts through intermediate, advanced and application-oriented questions. Each page contains up to 100 questions with answers and explanations where available.

Question 1
Control SystemsStability

For a stable continuous-time linear system, poles of the closed-loop transfer function should generally lie in which region of the s-plane?

  • ARight half-plane
  • BLeft half-plane
  • COnly on the imaginary axis
  • DAt the origin only
Report an error
Correct Answer: B. Left half-plane
Explanation: For an asymptotically stable continuous-time LTI closed-loop system, its poles lie in the left half of the s-plane.
Reference: Classical control-system stability criterion
Question 4
Control SystemsTransfer Functions

The transfer function of a linear time-invariant system is defined, with zero initial conditions, as?

  • ALaplace transform of output divided by Laplace transform of input
  • BInput divided by output
  • COutput plus input
  • DDerivative of output only
Report an error
Correct Answer: A. Laplace transform of output divided by Laplace transform of input
Explanation: The transfer function is G(s)=C(s)/R(s) under zero initial conditions.
Reference: Standard control systems: transfer functions
Question 5
Control SystemsTransfer Functions

The poles of a transfer function are the values of s that make its?

  • ANumerator zero
  • BDenominator zero
  • CGain always unity
  • DInput zero
Report an error
Correct Answer: B. Denominator zero
Explanation: Poles are the roots of the denominator polynomial after pole-zero cancellations are accounted for.
Reference: Standard control systems: transfer functions
Question 6
Control SystemsTransfer Functions

For G(s)=10/(s+5), the pole is located at?

  • As=+5
  • Bs=-5
  • Cs=0
  • Ds=-10
Report an error
Correct Answer: B. s=-5
Explanation: The denominator is zero when s+5=0, giving the pole s=-5.
Reference: Standard control systems: transfer functions
Question 12
Control SystemsControl Fundamentals

A control system that uses feedback from the output is generally called?

  • AOpen-loop system
  • BClosed-loop system
  • CUncontrolled system
  • DIsolated system
Report an error
Correct Answer: B. Closed-loop system
Explanation: A closed-loop system compares output-related feedback with the reference and uses the resulting error in control action.
Reference: Standard control systems: control fundamentals
Question 13
Control SystemsFeedback

Which is a common advantage of negative feedback in a control system?

  • AReduced sensitivity to parameter variations
  • BInfinite output for every input
  • CElimination of all components
  • DGuaranteed zero error for every system
Report an error
Correct Answer: A. Reduced sensitivity to parameter variations
Explanation: Negative feedback generally reduces sensitivity to plant parameter variations and can improve accuracy and robustness when properly designed.
Reference: Standard control systems: feedback
Question 14
Control SystemsFeedback

In a standard negative-feedback system, the error signal is commonly?

  • AReference minus feedback signal
  • BReference plus feedback signal always
  • COutput multiplied by input
  • DFeedback divided by reference
Report an error
Correct Answer: A. Reference minus feedback signal
Explanation: At the summing junction of a standard negative-feedback loop, e(t)=r(t)-b(t).
Reference: Standard control systems: feedback
Question 16
Control SystemsSecond-Order Systems

For s²+6s+25=0, the damping ratio ζ is?

  • A0.3
  • B0.6
  • C1.0
  • D1.2
Report an error
Correct Answer: B. 0.6
Explanation: 2ζωn=6 and ωn=5, hence ζ=6/(2×5)=0.6.
Reference: Standard control systems: second-order systems
Question 20
Control SystemsSecond-Order Systems

In a standard second-order system, ζ denotes the?

  • ADamping ratio
  • BNatural frequency
  • CStatic gain
  • DTime delay
Report an error
Correct Answer: A. Damping ratio
Explanation: The symbol ζ (zeta) denotes damping ratio.
Reference: Standard control systems: second-order systems
Question 21
Control SystemsSecond-Order Systems

In a standard second-order system, ωn denotes the?

  • AUndamped natural frequency
  • BDamping ratio
  • CDC error
  • DFeedback factor
Report an error
Correct Answer: A. Undamped natural frequency
Explanation: ωn is the undamped natural frequency, usually expressed in rad/s.
Reference: Standard control systems: second-order systems
Question 22
Control SystemsSecond-Order Systems

A second-order system with 0<ζ<1 is classified as?

  • AUnderdamped
  • BCritically damped
  • COverdamped
  • DUndamped only
Report an error
Correct Answer: A. Underdamped
Explanation: A damping ratio between zero and one gives an underdamped response.
Reference: Standard control systems: second-order systems
Question 23
Control SystemsSecond-Order Systems

A second-order system with ζ=1 is?

  • AUnderdamped
  • BCritically damped
  • COverdamped
  • DUnstable necessarily
Report an error
Correct Answer: B. Critically damped
Explanation: ζ=1 corresponds to critical damping.
Reference: Standard control systems: second-order systems
Question 24
Control SystemsSecond-Order Systems

A second-order system with ζ>1 is?

  • AUnderdamped
  • BUndamped
  • COverdamped
  • DCritically damped
Report an error
Correct Answer: C. Overdamped
Explanation: A damping ratio greater than one gives an overdamped response.
Reference: Standard control systems: second-order systems
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Question 26
Control SystemsRouth-Hurwitz

The Routh-Hurwitz criterion is primarily used to determine?

  • AAbsolute stability without explicitly calculating all roots
  • BOnly steady-state gain
  • COnly system bandwidth
  • DInput signal amplitude
Report an error
Correct Answer: A. Absolute stability without explicitly calculating all roots
Explanation: The Routh-Hurwitz criterion determines how many characteristic roots lie in the right half-plane and hence assesses absolute stability.
Reference: Standard control systems: routh-hurwitz
Question 27
Control SystemsRouth-Hurwitz

For a polynomial with all positive coefficients, positivity of coefficients alone is?

  • AAlways sufficient for stability
  • BNecessary but not generally sufficient for Hurwitz stability
  • CNever relevant
  • DSufficient only for every fourth-order system
Report an error
Correct Answer: B. Necessary but not generally sufficient for Hurwitz stability
Explanation: For a Hurwitz polynomial, coefficients must satisfy necessary sign conditions, but positive coefficients alone do not guarantee all roots lie in the left half-plane.
Reference: Standard control systems: routh-hurwitz
Question 28
Control SystemsSystem Type & Error Constants

The type of a unity-feedback control system is determined by the number of?

  • AZeros at the origin
  • BOpen-loop poles at the origin
  • CClosed-loop poles in the right half-plane
  • DFinite zeros only
Report an error
Correct Answer: B. Open-loop poles at the origin
Explanation: System type equals the number of pure integrators, or poles at s=0, in the open-loop transfer function G(s)H(s).
Reference: Standard control systems: system type & error constants
Question 43
Control SystemsRouth-Hurwitz

At K=6 for s³+2s²+3s+K, the system is at the?

  • AStability boundary
  • BAlways strictly stable
  • CAlways overdamped
  • DOrigin with three repeated poles
Report an error
Correct Answer: A. Stability boundary
Explanation: At K=6, a Routh first-column element becomes zero and a conjugate pair lies on the imaginary axis, marking the stability boundary.
Reference: Standard control systems: routh-hurwitz
Question 45
Control SystemsRoot Locus

Root-locus branches start, for K=0, at the?

  • AOpen-loop poles
  • BOpen-loop zeros
  • CClosed-loop zeros only
  • DImaginary-axis crossings
Report an error
Correct Answer: A. Open-loop poles
Explanation: At zero gain, closed-loop poles coincide with the open-loop poles.
Reference: Standard control systems: root locus
Question 46
Control SystemsRoot Locus

As K approaches infinity, root-locus branches terminate at?

  • AOpen-loop zeros, including zeros at infinity
  • BOpen-loop poles only
  • CThe origin only
  • DThe positive real axis only
Report an error
Correct Answer: A. Open-loop zeros, including zeros at infinity
Explanation: Branches end at finite open-loop zeros; if there are more poles than finite zeros, the remaining branches terminate at zeros at infinity.
Reference: Standard control systems: root locus
Question 47
Control SystemsRoot Locus

The number of root-locus branches equals the number of?

  • AOpen-loop poles
  • BOpen-loop finite zeros only
  • CClosed-loop zeros
  • DBreakaway points
Report an error
Correct Answer: A. Open-loop poles
Explanation: Each open-loop pole is the starting point of one root-locus branch.
Reference: Standard control systems: root locus
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Question 60
Control SystemsRoot Locus

The centroid of root-locus asymptotes is located at?

  • A(sum of poles - sum of zeros)/(n-m)
  • B(sum of poles + sum of zeros)/(n+m)
  • CProduct of poles divided by product of zeros
  • DOrigin in every system
Report an error
Correct Answer: A. (sum of poles - sum of zeros)/(n-m)
Explanation: For n>m, the asymptote centroid is σa=(Σpoles-Σzeros)/(n-m).
Reference: Standard control systems: root locus
Question 64
Control SystemsNyquist Stability

If an open-loop transfer function has no right-half-plane poles, closed-loop stability under the standard Nyquist criterion requires the Nyquist plot to have?

  • ANo encirclement of -1+j0
  • BOne clockwise encirclement of -1+j0
  • COne counterclockwise encirclement always
  • DAn encirclement of the origin
Report an error
Correct Answer: A. No encirclement of -1+j0
Explanation: When P=0, closed-loop stability requires Z=0; under the standard convention this means no net encirclement of the -1 point.
Reference: Standard control systems: nyquist stability
Question 65
Control SystemsNyquist Stability

The Nyquist plot is a mapping of a contour from the?

  • As-plane through the loop transfer function
  • BTime domain directly into the z-plane only
  • COutput plane into the input plane
  • DRoot locus into the Routh array
Report an error
Correct Answer: A. s-plane through the loop transfer function
Explanation: Nyquist analysis maps the Nyquist contour in the s-plane through the loop transfer function L(s)=G(s)H(s).
Reference: Standard control systems: nyquist stability
Question 66
Control SystemsFrequency Response

For a minimum-phase stable loop, larger positive phase margin generally indicates?

  • AGreater relative stability and damping tendency
  • BGuaranteed instability
  • CZero bandwidth
  • DInfinite steady-state error
Report an error
Correct Answer: A. Greater relative stability and damping tendency
Explanation: Within ordinary design tradeoffs, a larger positive phase margin generally corresponds to greater relative stability and a more damped closed-loop response.
Reference: Standard control systems: frequency response
Question 72
Control SystemsStability Margins

Phase margin is measured at the?

  • AGain crossover frequency
  • BPhase crossover frequency only
  • CNatural frequency always
  • DDC frequency only
Report an error
Correct Answer: A. Gain crossover frequency
Explanation: Phase margin is the additional phase lag needed to reach -180° at the gain crossover frequency.
Reference: Standard control systems: stability margins
Question 73
Control SystemsStability Margins

Gain margin is evaluated at the?

  • AGain crossover frequency
  • BPhase crossover frequency
  • CResonant frequency only
  • DSampling frequency
Report an error
Correct Answer: B. Phase crossover frequency
Explanation: Gain margin is determined from the loop magnitude at the phase crossover frequency.
Reference: Standard control systems: stability margins
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Question 76
Control SystemsControllers

The transfer function of an ideal PID controller is?

  • AKp+Ki/s+Kd s
  • BKp s+Ki+Kd/s²
  • CKp/(s+1) only
  • DKi s only
Report an error
Correct Answer: A. Kp+Ki/s+Kd s
Explanation: An ideal PID controller combines proportional, integral and derivative actions: Gc(s)=Kp+Ki/s+Kd s.
Reference: Standard control systems: controllers
Question 78
Control SystemsCompensators

A phase-lead compensator is commonly used to improve?

  • APhase margin and transient response
  • BSteady-state error only with no transient effect
  • CSensor noise generation
  • DSystem type by two automatically
Report an error
Correct Answer: A. Phase margin and transient response
Explanation: Lead compensation adds positive phase over a frequency range and is commonly used to improve phase margin, bandwidth and transient response.
Reference: Standard control systems: compensators
Question 79
Control SystemsCompensators

A phase-lag compensator is commonly used mainly to improve?

  • ASteady-state accuracy by increasing low-frequency gain
  • BHigh-frequency noise amplification
  • CNatural frequency to infinity
  • DPhase lead at all frequencies
Report an error
Correct Answer: A. Steady-state accuracy by increasing low-frequency gain
Explanation: Lag compensation can raise effective low-frequency loop gain relative to high-frequency gain, improving steady-state accuracy with modest transient impact.
Reference: Standard control systems: compensators
Question 80
Control SystemsCompensators

A lead compensator typically has its zero located?

  • ACloser to the origin than its pole on the negative real axis
  • BFarther from the origin than its pole
  • CAt exactly the same location as its pole
  • DIn the right half-plane necessarily
Report an error
Correct Answer: A. Closer to the origin than its pole on the negative real axis
Explanation: A standard lead network has a zero at a lower break frequency than its pole, so the zero lies closer to the origin on the negative real axis.
Reference: Standard control systems: compensators
Question 89
Control SystemsControllers

A proportional controller primarily has control law?

  • Au(t)=Kp e(t)
  • Bu(t)=Ki∫e(t)dt only
  • Cu(t)=Kd de(t)/dt only
  • Du(t)=0
Report an error
Correct Answer: A. u(t)=Kp e(t)
Explanation: A P controller produces control effort proportional to the instantaneous error.
Reference: Standard control systems: controllers
Question 90
Control SystemsControllers

Integral control is particularly useful for reducing or eliminating?

  • ASteady-state error for suitable stable systems
  • BAll measurement noise
  • CPlant order
  • DEvery transient oscillation
Report an error
Correct Answer: A. Steady-state error for suitable stable systems
Explanation: Integral action accumulates error and increases low-frequency loop gain, often eliminating steady-state error to constant inputs when the resulting closed loop is stable.
Reference: Standard control systems: controllers
Question 91
Control SystemsControllers

Derivative control responds to?

  • AThe rate of change of error
  • BOnly accumulated error
  • COnly constant error magnitude
  • DThe reference amplitude squared
Report an error
Correct Answer: A. The rate of change of error
Explanation: Derivative action is proportional to de(t)/dt and anticipates changes in error.
Reference: Standard control systems: controllers
Question 93
Control SystemsState Space

The eigenvalues of the state matrix A correspond to the system’s?

  • APoles for a minimal state-space realization
  • BZeros only
  • CInput frequencies only
  • DStatic error constants
Report an error
Correct Answer: A. Poles for a minimal state-space realization
Explanation: For a minimal realization, eigenvalues of A are the system poles.
Reference: Standard control systems: state space
Question 94
Control SystemsState Space

A continuous-time state-space system x_dot=Ax is asymptotically stable if all eigenvalues of A have?

  • AStrictly negative real parts
  • BStrictly positive real parts
  • CZero real parts only
  • DMagnitude greater than one
Report an error
Correct Answer: A. Strictly negative real parts
Explanation: For a finite-dimensional continuous-time LTI system, asymptotic stability requires all eigenvalues of A to lie strictly in the left half-plane.
Reference: Standard control systems: state space
Question 97
Control SystemsState Space

The observability matrix for an n-state system begins as?

  • A[C; CA; CA²; ...; CA^(n-1)]
  • B[B; AB; A²B; ...]
  • C[A; B; C]
  • D[D; CD] only
Report an error
Correct Answer: A. [C; CA; CA²; ...; CA^(n-1)]
Explanation: The standard observability matrix is formed by stacking C, CA, CA², ..., CA^(n-1).
Reference: Standard control systems: state space
Question 99
Control SystemsState Space

For the state matrix A=diag(-2,-5), the system poles are?

  • A2 and 5
  • B-2 and -5
  • C-7 and 10
  • D0 and -10
Report an error
Correct Answer: B. -2 and -5
Explanation: The eigenvalues of a diagonal matrix are its diagonal entries, so the poles are -2 and -5.
Reference: Standard control systems: state space
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