When a pole is moved farther left in s-plane, the response becomes

 Q271. The purpose of a lead compensator is to:

A) Increase steady-state accuracy
B) Improve phase margin and speed of response
C) Reduce damping ratio
D) Increase steady-state error

✅ Answer: B) Improve phase margin and speed of response
Explanation:
Lead compensator adds positive phase → faster and more stable system.

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Q272. A lag compensator is mainly used to:
A) Improve transient response
B) Improve steady-state accuracy
C) Reduce bandwidth
D) Reduce phase margin

✅ Answer: B) Improve steady-state accuracy
Explanation:
Lag increases low-frequency gain → reduces steady-state error.

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Q273. The transfer function of a PD controller is:
A) $K_p(1 + T_d s)$
B) $K_p(1 + \frac{1}{T_i s})$
C) $K_p(1 + \frac{T_d}{s})$
D) $\frac{K_p}{s}$

✅ Answer: A) $K_p(1 + T_d s)$
Explanation:
Derivative action → term $T_d s$ improves transient response.

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Q274. The integral term in a PID controller improves:
A) Damping
B) Steady-state accuracy
C) Speed
D) Overshoot

✅ Answer: B) Steady-state accuracy
Explanation:
Integral term eliminates constant steady-state error.

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Q275. Which one of the following can cause instability in a control system?
A) High gain
B) Feedback delay
C) Improper compensation
D) All of the above

✅ Answer: D) All of the above
Explanation:
All can move poles toward right-half plane → instability.

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Q276. A system having damping ratio $ζ = 0$ is:
A) Overdamped
B) Underdamped
C) Critically damped
D) Undamped

✅ Answer: D) Undamped
Explanation:
ζ = 0 → pure oscillation (no damping).

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Q277. For a stable discrete-time system, poles should lie:
A) On real axis
B) Inside unit circle
C) On unit circle
D) Outside unit circle

✅ Answer: B) Inside unit circle
Explanation:
In z-plane → |z| < 1 ensures bounded output.

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Q278. The z-transform of a unit step signal is:
A) $\frac{1}{1 - z^{-1}}$
B) $\frac{z}{z-1}$
C) $\frac{1}{z-1}$
D) Both A and B

✅ Answer: D) Both A and B
Explanation:
Equivalent forms of same z-transform.

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Q279. The sampling period (T) should be:
A) Too large
B) As small as possible
C) Equal to input signal period
D) Random

✅ Answer: B) As small as possible
Explanation:
Smaller T → better digital representation and control precision.

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Q280. Aliasing can be prevented by:
A) Oversampling
B) Using anti-aliasing filter
C) Increasing gain
D) Using derivative controller

✅ Answer: B) Using anti-aliasing filter
Explanation:
Low-pass filter removes high-frequency components before sampling.

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Q281. In Nyquist criterion, if N = 0 and P = 0, then the system is:
A) Unstable
B) Marginally stable
C) Stable
D) Oscillatory

✅ Answer: C) Stable
Explanation:
$Z = N + P = 0$ → no RHP poles → stable.

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Q282. A phase margin of 0° indicates:
A) Stable system
B) Unstable system
C) Marginal stability
D) Critically stable

✅ Answer: C) Marginal stability
Explanation:
At 0° phase margin → Nyquist touches -1 point.

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Q283. Increasing damping ratio (ζ) results in:
A) Increase in overshoot
B) Decrease in overshoot
C) Increase in settling time
D) None

✅ Answer: B) Decrease in overshoot
Explanation:
Higher ζ → less oscillation and smaller overshoot.

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Q284. The phase margin should ideally be:
A) 0°
B) 30° to 60°
C) 90°
D) > 100°

✅ Answer: B) 30° to 60°
Explanation:
Provides a good trade-off between speed and stability.

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Q285. The gain margin should be at least:
A) 0 dB
B) 3 dB
C) 6 dB or more
D) 10 dB

✅ Answer: C) 6 dB or more
Explanation:
Gain margin ≥ 6 dB ensures adequate robustness.

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Q286. The settling time of a second-order system is approximately:
A) $\frac{4}{ζω_n}$
B) $\frac{2}{ω_n}$
C) $\frac{1}{ζω_n}$
D) $\frac{1}{ω_n}$

✅ Answer: A) $\frac{4}{ζω_n}$
Explanation:
Standard second-order formula (for 2% criterion).

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Q287. The rise time decreases when:
A) Damping increases
B) Natural frequency increases
C) Gain decreases
D) None

✅ Answer: B) Natural frequency increases
Explanation:
Higher ωₙ → faster system → smaller rise time.

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Q288. For a unity feedback system, steady-state error for unit ramp input is $e_{ss} = \frac{1}{K_v}$. Here $K_v =$?
A) $\lim_{s→0} G(s)$
B) $\lim_{s→0} sG(s)$
C) $\lim_{s→0} s^2G(s)$
D) $\lim_{s→∞} G(s)$

✅ Answer: B) $\lim_{s→0} sG(s)$
Explanation:
Velocity error constant definition.

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Q289. For a second-order system, maximum overshoot $M_p$ depends on:
A) ωₙ only
B) ζ only
C) ωₙ and ζ
D) Gain

✅ Answer: B) ζ only
Explanation:
$M_p = e^{-\piζ/\sqrt{1-ζ^2}}$, depends only on damping ratio.

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Q290. In a unity feedback system, error signal =
A) Output
B) Reference − Output
C) Input + Output
D) None

✅ Answer: B) Reference − Output
Explanation:
Error = difference between reference input and feedback output.

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Q291. A system with all poles on the imaginary axis is:
A) Stable
B) Unstable
C) Marginally stable
D) Oscillatory

✅ Answer: C) Marginally stable
Explanation:
Purely imaginary poles → sustained oscillations.

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Q292. Nyquist plot moving clockwise around (-1,0) indicates:
A) Stable
B) Unstable
C) Phase lag
D) None

✅ Answer: B) Unstable
Explanation:
Clockwise encirclement corresponds to RHP poles.

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Q293. In Bode magnitude plot, slope changes by −20 dB/dec for:
A) Each zero
B) Each pole
C) Each integrator
D) Both B and C

✅ Answer: D) Both B and C
Explanation:
Poles and integrators contribute −20 dB/dec slope.

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Q294. A lag-lead compensator combines:
A) High and low frequency improvements
B) Both steady-state and transient improvements
C) Both A & B
D) None

✅ Answer: C) Both A & B
Explanation:
Lag improves accuracy; lead improves speed.

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Q295. The main advantage of feedback is:
A) Increases system gain
B) Reduces sensitivity
C) Makes system nonlinear
D) Adds instability

✅ Answer: B) Reduces sensitivity
Explanation:
Feedback reduces sensitivity to disturbances and parameter variations.

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Q296. Which of the following represents a non-minimum phase system?
A) Zeros in left half plane
B) Zeros in right half plane
C) All poles in left half plane
D) No zeros

✅ Answer: B) Zeros in right half plane
Explanation:
RHP zeros cause inverse or delayed response → non-minimum phase.

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Q297. For discrete-time systems, the bilinear transformation maps:
A) s-plane → jω-axis
B) s-plane → z-plane
C) z-plane → s-plane
D) None

✅ Answer: B) s-plane → z-plane
Explanation:
Used for continuous → discrete conversion: $z = \frac{1 + sT/2}{1 - sT/2}$.

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Q298. The damping ratio can be determined from frequency response using:
A) Resonant frequency
B) Resonant peak
C) Both A & B
D) None

✅ Answer: C) Both A & B
Explanation:
ζ relates to $M_r$ and $ω_r$ in second-order system frequency response.

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Q299. A first-order system has transfer function $\frac{K}{τs + 1}$. Its DC gain =
A) 0
B) 1
C) K
D) $\frac{1}{τ}$

✅ Answer: C) K
Explanation:
DC gain = $G(0) = K$.

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Q300. The phase of a pure differentiator is:
A) +45°
B) +90°
C) −90°
D) 0°

✅ Answer: B) +90°
Explanation:
Differentiator leads input by 90° phase.

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Q301. The phase of a pure integrator is:
A) −90°
B) +90°
C) 0°
D) −45°

✅ Answer: A) −90°
Explanation:
Integrator lags input by 90°.

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Q302. The system bandwidth is defined as the frequency range where:
A) Gain < 0 dB
B) Magnitude > −3 dB
C) Phase = 0°
D) None

✅ Answer: B) Magnitude > −3 dB
Explanation:
Bandwidth → frequency at which gain drops 3 dB from DC value.

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Q303. The open-loop transfer function $G(s)H(s)$ has poles at (−1, −2, −3). It is:
A) Stable
B) Marginally stable
C) Unstable
D) Oscillatory

✅ Answer: A) Stable
Explanation:
All poles in LHP → stable open-loop.

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Q304. The steady-state error for step input in Type 1 system is:
A) 0
B) Finite
C) Infinite
D) Undefined

✅ Answer: A) 0
Explanation:
Integrator in loop → eliminates steady-state error for step.

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Q305. The resonant peak $M_r$ increases when:
A) Damping increases
B) Damping decreases
C) ωₙ increases
D) Gain decreases

✅ Answer: B) Damping decreases
Explanation:
Less damping → more resonance → higher $M_r$.

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Q306. The frequency at which M_r occurs is:
A) ωₙ
B) $ωₙ\sqrt{1 - 2ζ^2}$
C) $ωₙ/ζ$
D) $ωₙζ$

✅ Answer: B) $ωₙ\sqrt{1 - 2ζ^2}$
Explanation:
For second-order systems, resonant frequency depends on ζ.

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Q307. The closed-loop transfer function has the form $\frac{G}{1 + GH}$. If $GH$ → ∞, output =
A) 0
B) Equal to input
C) Infinity
D) Undefined

✅ Answer: B) Equal to input
Explanation:
High loop gain → perfect tracking (zero steady-state error).

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Q308. In Nyquist stability, a clockwise encirclement of (−1,0) counts as:
A) +1
B) −1
C) 0
D) +2

✅ Answer: B) −1
Explanation:
Clockwise encirclement = negative count in Nyquist criterion.

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Q309. When a pole is moved farther left in s-plane, the response becomes:
A) Slower
B) Faster
C) Unstable
D) Oscillatory

✅ Answer: B) Faster
Explanation:
More negative real part → faster decay → faster response.

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Q310. A system with negative feedback always:
A) Increases sensitivity
B) Decreases bandwidth
C) Improves stability
D) Degrades transient

✅ Answer: C) Improves stability
Explanation:
Negative feedback reduces gain, increases damping → stability.