State-space model represents the system in

 

ng ratio ζ > 1, the system is:
A) Underdamped
B) Overdamped
C) Critically damped
D) Oscillatory

✅ Answer: B) Overdamped
Explanation:
ζ > 1 → non-oscillatory, slow response with real, distinct poles.

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Q51. State-space model represents the system in:
A) Frequency domain
B) Time domain
C) Hybrid domain
D) None

✅ Answer: B) Time domain
Explanation:
State-space form uses first-order differential equations in time domain.

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Q52. The state-space equation is:
A) $x' = Ax + Bu, \ y = Cx + Du$
B) $x = Au + By$
C) $y = Ax + Bu$
D) $x' = Bx + Au$

✅ Answer: A) $x' = Ax + Bu, \ y = Cx + Du$
Explanation:
Standard state-space form defining dynamics and output.

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Q53. Controllability of a system ensures:
A) Stability
B) Output tracking
C) State variables can be driven to any value
D) Zero steady-state error

✅ Answer: C) State variables can be driven to any value
Explanation:
Controllable if rank of controllability matrix = n (order of system).

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Q54. Observability ensures:
A) States can be observed from outputs
B) Inputs can be changed
C) System is stable
D) Poles are real

✅ Answer: A) States can be observed from outputs
Explanation:
Observable if internal states can be deduced from output measurements.

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Q55. The advantage of state-space over transfer function is:
A) Only for linear systems
B) Time-domain and multi-input handling
C) Simpler for SISO
D) No matrix form

✅ Answer: B) Time-domain and multi-input handling
Explanation:
State-space handles MIMO systems, non-linearities, and time-domain design.

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Q56. A unity feedback system has $G(s) = \frac{K}{s(s+3)(s+5)}$. For stability, K must be:
A) > 0
B) < 0
C) Within a finite range
D) Infinite

✅ Answer: C) Within a finite range
Explanation:
K affects closed-loop pole positions; too high → instability.

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Q57. A tachogenerator provides feedback proportional to:
A) Displacement
B) Velocity
C) Acceleration
D) Current

✅ Answer: B) Velocity
Explanation:
Tachogenerator output voltage ∝ angular velocity → velocity feedback.

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Q58. Nyquist stability depends on:
A) Number of encirclements of (-1,0)
B) Poles of closed-loop
C) Gain only
D) Root locus

✅ Answer: A) Number of encirclements of (-1,0)
Explanation:
Encirclements determine system stability by Nyquist criterion.

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Q59. The gain crossover frequency is the frequency at which:
A) Phase = -180°
B) Magnitude = 1 (0 dB)
C) Both magnitude and phase are zero
D) Gain margin = 0

✅ Answer: B) Magnitude = 1 (0 dB)
Explanation:
Gain crossover frequency is where |G(jω)H(jω)| = 1.

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Q60. If the open-loop transfer function has one pole in the right half-plane, it is:
A) Stable
B) Conditionally stable
C) Unstable
D) Marginally stable

✅ Answer: C) Unstable
Explanation:
Any pole in RHP → open-loop unstable.

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Q61. The advantage of PID control is:
A) Fast response only
B) Eliminates steady-state error and improves stability
C) Increases steady-state error
D) Causes oscillations

✅ Answer: B) Eliminates steady-state error and improves stability
Explanation:
PID combines proportional, integral, and derivative effects for optimum control.

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Q62. In a PD controller, derivative action:
A) Anticipates error change
B) Slows down response
C) Reduces steady-state error
D) Decreases stability

✅ Answer: A) Anticipates error change
Explanation:
Derivative term provides a predictive action → adds damping.

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Q63. In a PI controller, integral action:
A) Speeds up response
B) Reduces overshoot
C) Eliminates steady-state error
D) Adds phase lead

✅ Answer: C) Eliminates steady-state error
Explanation:
Integral accumulates error over time → drives steady-state error to zero.

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Q64. Which controller is not ideal for systems requiring fast response?
A) P
B) PI
C) PD
D) PID

✅ Answer: B) PI
Explanation:
Integral term slows response → not ideal for fast systems.

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Q65. Lead compensator adds:
A) Phase lag
B) Phase lead
C) No phase change
D) Damping only

✅ Answer: B) Phase lead
Explanation:
Lead compensator increases phase margin → faster, more stable system.

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Q66. Lag compensator is used when:
A) Faster response needed
B) Steady-state accuracy required
C) Oscillation desired
D) Bandwidth to be reduced

✅ Answer: B) Steady-state accuracy required
Explanation:
Lag compensator improves low-frequency gain → better accuracy.

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Q67. State variable feedback is used to:
A) Change eigenvalues (pole placement)
B) Improve steady-state error
C) Increase bandwidth
D) Reduce overshoot only

✅ Answer: A) Change eigenvalues (pole placement)
Explanation:
State feedback allows desired pole placement for performance tuning.

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Q68. If the phase margin is 0°, the system is:
A) Stable
B) Marginally stable
C) Unstable
D) Critically stable

✅ Answer: B) Marginally stable
Explanation:
Zero phase margin means system is on the verge of oscillation.

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Q69. If the real part of poles increases, the system becomes:
A) Slower
B) Faster
C) Oscillatory
D) Unstable

✅ Answer: B) Faster
Explanation:
Poles further left → faster decay → faster response.

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Q70. The frequency at which phase shift = -180° is called:
A) Gain crossover frequency
B) Phase crossover frequency
C) Nyquist frequency
D) Resonant frequency

✅ Answer: B) Phase crossover frequency
Explanation:
At phase crossover, phase = -180°; used for gain margin determination.