71. The characteristic equation of a closed-loop control system is given by:
A)
B)
C)
D)
✅ Answer: A)
Explanation:
Closed-loop poles are obtained from , representing the characteristic equation.
Q72. In a unity feedback system, the sensitivity of the system to disturbances decreases with:
A) Increased loop gain
B) Reduced gain
C) No change in gain
D) Decreased feedback
✅ Answer: A) Increased loop gain
Explanation:
Higher loop gain improves disturbance rejection, reducing system sensitivity.
Q73. The open-loop transfer function of a stable system can be unstable when:
A) Feedback is negative
B) Feedback is positive
C) Gain is zero
D) Poles are real
✅ Answer: B) Feedback is positive
Explanation:
Positive feedback drives instability by increasing the effective loop gain.
Q74. The polar plot of a first-order system lies entirely in:
A) First quadrant
B) Second quadrant
C) Third quadrant
D) Fourth quadrant
✅ Answer: D) Fourth quadrant
Explanation:
For , phase lag between 0° and -90° → 4th quadrant.
Q75. A root locus passing through the imaginary axis indicates:
A) Stable system
B) Unstable system
C) Marginally stable system
D) Non-causal system
✅ Answer: C) Marginally stable system
Explanation:
Imaginary-axis poles correspond to sustained oscillations → marginal stability.
Q76. The damping ratio (ζ) of 0 means:
A) Overdamped
B) Underdamped
C) Critically damped
D) Undamped
✅ Answer: D) Undamped
Explanation:
ζ = 0 → purely oscillatory system with no damping.
Q77. If ζ = 1, the system is:
A) Underdamped
B) Overdamped
C) Critically damped
D) Unstable
✅ Answer: C) Critically damped
Explanation:
ζ = 1 → system returns to equilibrium fastest without oscillation.
Q78. The natural frequency affects:
A) Speed of response
B) Overshoot only
C) Steady-state error
D) Damping ratio
✅ Answer: A) Speed of response
Explanation:
Higher → faster oscillations → quicker response.
Q79. For stable feedback, the open-loop transfer function must have:
A) Even number of poles in RHP
B) No poles in RHP
C) Odd number of zeros in RHP
D) Zeros on imaginary axis
✅ Answer: B) No poles in RHP
Explanation:
Open-loop stability is a precondition for predictable closed-loop behavior.
Q80. The gain margin is positive when the Nyquist plot crosses the real axis:
A) To the right of (-1, 0)
B) To the left of (-1, 0)
C) At origin
D) Below x-axis
✅ Answer: A) To the right of (-1, 0)
Explanation:
Right of (-1,0) → system has gain margin > 0 → stable.
Q81. The Nyquist plot for a stable open-loop system encircles (-1, 0) point:
A) Clockwise
B) Counter-clockwise
C) Not at all (for stable closed-loop)
D) Twice clockwise
✅ Answer: C) Not at all (for stable closed-loop)
Explanation:
No encirclements of (-1,0) means closed-loop stability.
Q82. A system with phase margin of 60° is considered:
A) Highly stable
B) Marginally stable
C) Unstable
D) Oscillatory
✅ Answer: A) Highly stable
Explanation:
Phase margin > 45° indicates good stability and damping.
Q83. In a feedback system, increasing derivative gain (K_D):
A) Increases overshoot
B) Reduces overshoot and oscillation
C) Increases steady-state error
D) Decreases damping
✅ Answer: B) Reduces overshoot and oscillation
Explanation:
Derivative term adds damping → smoother response.
Q84. The rise time of an underdamped second-order system:
A) Increases with damping ratio
B) Decreases with damping ratio
C) Independent of damping
D) Inversely proportional to ζ²
✅ Answer: A) Increases with damping ratio
Explanation:
More damping → slower rise to the final value.
Q85. The unit impulse response of a system is:
A) Its transfer function
B) Its inverse
C) Derivative of step response
D) Integral of step response
✅ Answer: C) Derivative of step response
Explanation:
Impulse response = derivative of step response in time domain.
Q86. The controllability matrix is:
A) [B AB A²B ... Aⁿ⁻¹B]
B) [A B C D]
C) [C CB CAB ... CAⁿ⁻¹B]
D) [AB BA ...]
✅ Answer: A) [B AB A²B ... Aⁿ⁻¹B]
Explanation:
System controllable if rank(controllability matrix) = n.
Q87. The observability matrix is:
A) [B AB A²B ...]
B) [C; CA; CA²; ...; CAⁿ⁻¹]
C) [A B C D]
D) [C CB CAB ...]
✅ Answer: B) [C; CA; CA²; ...; CAⁿ⁻¹]
Explanation:
System observable if rank(observability matrix) = n.
Q88. A diagonalizable system matrix A indicates:
A) Complex eigenvalues
B) Distinct eigenvalues
C) Singular matrix
D) Uncontrollable
✅ Answer: B) Distinct eigenvalues
Explanation:
Distinct eigenvalues → matrix can be diagonalized (independent modes).
Q89. The eigenvalues of the system matrix A are equivalent to:
A) System zeros
B) Poles of the system
C) Gain constants
D) State variables
✅ Answer: B) Poles of the system
Explanation:
System poles = eigenvalues of A in state-space representation.
Q90. Sampling theorem states that the sampling frequency must be:
A) Less than signal frequency
B) Equal to signal frequency
C) At least twice the maximum signal frequency
D) Four times signal frequency
✅ Answer: C) At least twice the maximum signal frequency
Explanation:
Nyquist rate = 2 × highest signal frequency to avoid aliasing.
Q91. The z-transform is used in:
A) Continuous-time systems
B) Discrete-time systems
C) Mechanical systems only
D) Frequency domain only
✅ Answer: B) Discrete-time systems
Explanation:
Z-transform converts discrete signals to algebraic equations.
Q92. The relation between Laplace and z-transform is:
A)
B)
C)
D)
✅ Answer: A)
Explanation:
Laplace (continuous) and z-transform (discrete) domains are related via .
Q93. A discrete system is stable if all poles of its transfer function lie:
A) Inside the unit circle
B) Outside the unit circle
C) On imaginary axis
D) On real axis
✅ Answer: A) Inside the unit circle
Explanation:
|z| < 1 → bounded-input, bounded-output stability in z-plane.
Q94. The root locus angle condition is:
A) ∠GH = 0°
B) ∠GH = ±180°
C) ∠GH = 90°
D) ∠GH = 45°
✅ Answer: B) ∠GH = ±180°
Explanation:
For a point to be on root locus, ∠G(s)H(s) = (2k+1)180°.
Q95. The number of asymptotes in root locus equals:
A) P + Z
B) P − Z
C) P × Z
D) Z − P
✅ Answer: B) P − Z
Explanation:
When number of poles > zeros, asymptotes = P − Z.
Q96. The frequency response of a first-order system has a phase shift of:
A) 0°
B) −45°
C) −90°
D) Depends on frequency
✅ Answer: D) Depends on frequency
Explanation:
Phase shift varies from 0° (low freq) to −90° (high freq).
Q97. The steady-state error of a Type-1 system for a unit ramp input is:
A) Zero
B) 1/Kv
C) Infinite
D) 1/Kp
✅ Answer: B) 1/Kv
Explanation:
Ramp error constant .
Q98. In frequency response analysis, resonant frequency is the frequency where:
A) Gain is maximum
B) Phase = −180°
C) Output is minimum
D) Gain = 0 dB
✅ Answer: A) Gain is maximum
Explanation:
Resonant frequency corresponds to maximum magnitude in frequency response.
Q99. The Nyquist path includes:
A) Only imaginary axis
B) Entire s-plane
C) Right half of s-plane
D) Imaginary axis + semicircle at infinity
✅ Answer: D) Imaginary axis + semicircle at infinity
Explanation:
Nyquist contour covers right-half s-plane to map stability.
Q100. For an all-pass system, the magnitude response is:
A) Constant
B) Varying with frequency
C) Zero
D) Infinity
✅ Answer: A) Constant
Explanation:
All-pass filters have unity magnitude for all frequencies; only phase varies.
Q101. Which of the following is not a basic control action?
A) Proportional
B) Integral
C) Derivative
D) Modulating
✅ Answer: D) Modulating
Explanation:
Basic control actions: P, I, D.
Q102. The transient response of a system is mainly affected by:
A) Location of zeros
B) Location of poles
C) System gain only
D) Feedback path
✅ Answer: B) Location of poles
Explanation:
Poles determine the exponential terms of transient response.
Q103. Stability of a system can be improved by:
A) Increasing gain only
B) Using negative feedback
C) Using positive feedback
D) Reducing damping
✅ Answer: B) Using negative feedback
Explanation:
Negative feedback stabilizes the system and reduces errors.
Q104. The steady-state error for a Type-0 system with a step input is:
A) Zero
B) Finite
C) Infinite
D) Depends on K
✅ Answer: B) Finite
Explanation:
Type-0 system has constant error for step input.
Q105. The principal of superposition applies only to:
A) Nonlinear systems
B) Linear systems
C) Time-varying systems
D) Random systems
✅ Answer: B) Linear systems
Explanation:
Superposition holds only for linear systems due to linear differential equations.
Q106. The transient response of a system depends on:
A) Poles only
B) Zeros only
C) Both poles and zeros
D) Gain only
✅ Answer: C) Both poles and zeros
Explanation:
Poles affect decay rate; zeros influence overshoot and shape.
Q107. The signal flow graph is based on:
A) Block diagram reduction
B) Mason’s gain formula
C) Routh array
D) Root locus
✅ Answer: B) Mason’s gain formula
Explanation:
Signal flow graphs simplify system representation using Mason’s rule.
Q108. In Mason’s gain formula, the determinant Δ represents:
A) Total loop gain
B) Path gain
C) System characteristic equation
D) Overall feedback
✅ Answer: C) System characteristic equation
Explanation:
Δ = 1 − (sum of loop gains) + (sum of product of non-touching loops) − …
Q109. The advantage of signal flow graph over block diagram is:
A) Simpler feedback handling
B) Works only for digital systems
C) Harder for large systems
D) No path representation
✅ Answer: A) Simpler feedback handling
Explanation:
SFG handles complex feedback loops easily.
Q110. The main disadvantage of derivative control is:
A) Slow response
B) Amplifies noise
C) Reduces damping
D) Increases steady-state error
✅ Answer: B) Amplifies noise
Explanation:
Derivative action amplifies high-frequency measurement noise.
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