The steady-state error for a unit step input in a type 1 system is

 

201. The damping ratio (ζ) of 0.707 corresponds to:

a) Underdamped
b) Overdamped
c) Critically damped
d) Optimum damping
Answer: d) Optimum damping
Explanation: ζ = 0.707 provides minimal overshoot and fast settling — considered “optimum damping.”

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202. The transient response is affected by:

a) Poles only
b) Zeros only
c) Both poles and zeros
d) Input type only
Answer: c) Both poles and zeros
Explanation: Poles determine dynamics; zeros modify transient response.

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203. For a stable system, all poles must lie:

a) On imaginary axis
b) In right half-plane
c) In left half-plane
d) Anywhere on s-plane
Answer: c) In left half-plane
Explanation: Stability requires all poles to have negative real parts.

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204. The steady-state error for a unit step input in a type 1 system is:

a) 0
b) 1
c) ∞
d) Depends on K
Answer: a) 0
Explanation: Type 1 systems have one integrator → zero steady-state error for step input.

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205. A higher gain in closed-loop control generally:

a) Increases stability
b) Reduces steady-state error
c) Increases damping
d) None
Answer: b) Reduces steady-state error
Explanation: Increased gain reduces steady-state error but may affect stability.

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206. The number of branches in a root locus equals:

a) Number of poles
b) Number of zeros
c) Difference of poles and zeros
d) Product of poles and zeros
Answer: a) Number of poles
Explanation: Each pole corresponds to one locus branch.

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207. For a system $G(s) = \frac{K}{s(s+2)(s+5)}$, the number of asymptotes is:

a) 1
b) 2
c) 3
d) 0
Answer: b) 2
Explanation: $n-m = 3-1 = 2$ → two asymptotes (n = poles, m = zeros).

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208. A system with pure integrator has:

a) Type 0
b) Type 1
c) Type 2
d) Unstable nature
Answer: b) Type 1
Explanation: One pole at origin → one integrator → Type 1 system.

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209. The steady-state error for a ramp input in a Type 1 system is:

a) 0
b) 1/Kv
c) ∞
d) None
Answer: b) 1/Kv
Explanation: For ramp, error constant Kv determines steady-state error.

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210. Nyquist plot passes through (-1,0) indicates:

a) Stable
b) Marginally stable
c) Unstable
d) Oscillatory
Answer: b) Marginally stable
Explanation: Passing exactly through critical point indicates marginal stability.

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211. Lead compensator adds:

a) Negative phase
b) Positive phase
c) Zero phase
d) None
Answer: b) Positive phase
Explanation: Lead compensation adds phase lead, improving phase margin.

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212. Lag compensator is used to:

a) Improve steady-state accuracy
b) Improve phase margin
c) Reduce rise time
d) Increase overshoot
Answer: a) Improve steady-state accuracy
Explanation: Lag compensation adds low-frequency gain, reducing steady-state error.

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213. A system is Type 2 if it has:

a) Two zeros
b) Two poles at origin
c) Two feedback loops
d) None
Answer: b) Two poles at origin
Explanation: Each pole at origin represents an integrator → Type number = poles at origin.

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214. Root locus branches end at:

a) Poles
b) Zeros
c) Infinity
d) a & b
Answer: d) a & b
Explanation: Locus starts from poles and ends at zeros or infinity.

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215. The term “phase margin” refers to:

a) Gain difference
b) Phase difference from -180°
c) Bandwidth
d) Frequency ratio
Answer: b) Phase difference from -180°
Explanation: Phase margin = angle by which phase is above -180° at gain crossover.

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216. Gain margin is measured in:

a) Radians
b) Decibels (dB)
c) Hertz
d) Degrees
Answer: b) Decibels (dB)
Explanation: It indicates the gain increase required to reach instability (in dB).

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217. A system has poles at -2, -4, and zeros at -3. The centroid is:

$(\sum \text{poles} - \sum \text{zeros})/(n-m)$
= $((-2-4) - (-3))/(3-1)$ = ?
a) -1.5
b) -2.5
c) -3.5
d) -4.5
Answer: b) -2.5
Explanation: Centroid = (-6 + 3)/2 = -1.5? Wait — correction → (-6 - (-3)) / 2 = (-3)/2 = -1.5 actually → Answer: a)
Correction: a) -1.5

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218. A system with all real negative poles is:

a) Unstable
b) Stable
c) Marginally stable
d) Oscillatory
Answer: b) Stable
Explanation: All poles in left half-plane → stable.

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219. If transfer function numerator order > denominator order, system is:

a) Stable
b) Improper
c) Type 0
d) Causal
Answer: b) Improper
Explanation: Improper systems are physically unrealizable.

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220. The “bandwidth” of a system indicates:

a) Speed of response
b) Damping
c) Stability margin
d) Phase shift
Answer: a) Speed of response
Explanation: Higher bandwidth = faster response to input.

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221. The Laplace transform of $\frac{d^2y(t)}{dt^2}$ is:

a) sY(s)
b) s²Y(s) – s y(0) – y’(0)
c) s²Y(s)
d) None
Answer: b) s²Y(s) – s y(0) – y’(0)
Explanation: Standard Laplace derivative property.

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222. The steady-state error for a parabolic input in a Type 2 system is:

a) 0
b) 1/K
c) Infinite
d) None
Answer: a) 0
Explanation: Type 2 can follow parabolic input with zero steady-state error.

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223. The number of poles in a second-order system is:

a) 1
b) 2
c) 3
d) Depends on order
Answer: b) 2
Explanation: Order = number of poles.

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224. The breakaway point occurs where:

a) Two loci meet
b) Locus leaves real axis
c) Gain = ∞
d) Both a & b
Answer: d) Both a & b
Explanation: Breakaway occurs when two loci diverge from real axis.

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225. Frequency corresponding to maximum magnitude in closed-loop is called:

a) Resonant frequency
b) Crossover frequency
c) Cutoff frequency
d) Gain margin frequency
Answer: a) Resonant frequency
Explanation: Resonant frequency corresponds to the peak of magnitude response.