he transfer function can be obtained from state-space using

 136. A system with poles on the imaginary axis is said to be:

A) Stable
B) Unstable
C) Marginally stable
D) Conditionally stable

✅ Answer: C) Marginally stable
Explanation:
Poles on jω-axis produce sustained oscillations → marginal stability.

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Q137. If all poles are in the left half of s-plane, the system is:
A) Stable
B) Unstable
C) Oscillatory
D) Critically stable

✅ Answer: A) Stable
Explanation:
Left-half-plane poles → exponentially decaying → stable.

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Q138. In root locus, breakaway points occur where:
A) Two branches meet
B) Two branches diverge
C) dK/ds = 0
D) Both A & C

✅ Answer: D) Both A & C
Explanation:
Breakaway points occur where multiple roots of characteristic equation coalesce (dK/ds = 0).

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Q139. Nyquist plot passes through the point (-1, 0). The system is:
A) Stable
B) Marginally stable
C) Unstable
D) Conditionally stable

✅ Answer: B) Marginally stable
Explanation:
When Nyquist plot touches (-1,0), gain margin = 0 → marginally stable.

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Q140. The slope of magnitude curve in Bode plot for a double pole is:
A) -20 dB/decade
B) -40 dB/decade
C) -60 dB/decade
D) -80 dB/decade

✅ Answer: B) -40 dB/decade
Explanation:
Each pole contributes -20 dB/decade; two poles → -40 dB/decade.

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Q141. A derivative controller increases:
A) Rise time
B) Damping
C) Overshoot
D) Steady-state error

✅ Answer: B) Damping
Explanation:
Derivative term adds damping → reduces overshoot and oscillations.

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Q142. The main drawback of derivative control is:
A) Slow response
B) Noise amplification
C) Steady-state error
D) Instability

✅ Answer: B) Noise amplification
Explanation:
Derivative amplifies high-frequency noise → practical limitation.

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Q143. In a control system, the transfer function $\frac{C(s)}{R(s)} = \frac{G(s)}{1+G(s)H(s)}$ represents:
A) Open-loop system
B) Closed-loop system
C) Cascade system
D) Feedforward system

✅ Answer: B) Closed-loop system
Explanation:
Closed-loop transfer function = forward gain / (1 + open-loop gain).

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Q144. The system type is determined by:
A) Number of zeros at origin
B) Number of poles at origin
C) Highest power of s in numerator
D) Denominator order

✅ Answer: B) Number of poles at origin
Explanation:
System type = number of poles at origin (integrators).

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Q145. The error constant $K_v$ corresponds to:
A) Step input
B) Ramp input
C) Parabolic input
D) Impulse input

✅ Answer: B) Ramp input
Explanation:
$K_v = \lim_{s→0} sG(s)$ measures steady-state error for ramp input.

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Q146. For a Type 0 system, steady-state error for a ramp input is:
A) Zero
B) Finite
C) Infinite
D) Undefined

✅ Answer: C) Infinite
Explanation:
Type 0 → no integrators → infinite error to ramp input.

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Q147. A Type 1 system can track which input with zero error?
A) Step
B) Ramp
C) Parabolic
D) Impulse

✅ Answer: A) Step
Explanation:
Type 1 → one integrator → zero error for step input.

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Q148. The transient response of a system depends on:
A) Zeros only
B) Poles only
C) Both poles and zeros
D) Damping ratio only

✅ Answer: C) Both poles and zeros
Explanation:
Poles dominate response; zeros affect speed and shape.

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Q149. The steady-state response depends mainly on:
A) Poles near origin
B) Zeros
C) Gain
D) Damping

✅ Answer: A) Poles near origin
Explanation:
Poles near origin determine steady-state behavior (slow modes).

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Q150. Which method gives exact stability information?
A) Bode plot
B) Root locus
C) Nyquist plot
D) Routh-Hurwitz

✅ Answer: D) Routh-Hurwitz
Explanation:
Routh-Hurwitz provides analytical stability without plotting.

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Q151. A lead compensator phase angle contribution is maximum at:
A) ω = 1/√(τ₁τ₂)
B) ω = √(1/τ₁τ₂)
C) ω = 1/τ₁
D) ω = τ₁/τ₂

✅ Answer: A) ω = 1/√(τ₁τ₂)
Explanation:
Maximum phase occurs at geometric mean of corner frequencies.

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Q152. Which of the following is a non-linear element?
A) Resistor
B) Inductor
C) Saturating amplifier
D) Capacitor

✅ Answer: C) Saturating amplifier
Explanation:
Saturation introduces non-linearity in control system.

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Q153. Time constant of first-order system =
A) 1/pole value
B) Reciprocal of gain
C) Equal to damping ratio
D) Sum of pole and zero

✅ Answer: A) 1/pole value
Explanation:
If transfer function = 1/(τs+1), τ = time constant.

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Q154. A non-minimum phase system has:
A) Real negative zeros
B) Real positive zeros
C) Complex conjugate poles
D) Zeros at infinity

✅ Answer: B) Real positive zeros
Explanation:
Positive (RHP) zeros → non-minimum phase → inverse response.

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Q155. Root locus exists on real axis where:
A) ΣP - ΣZ = 0
B) Number of poles and zeros to the right is odd
C) Even
D) None

✅ Answer: B) Odd
Explanation:
Root locus exists on segments with odd number of poles/zeros to the right.

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Q156. A second-order system is critically damped when ζ =
A) 0
B) < 1
C) 1
D) > 1

✅ Answer: C) 1
Explanation:
ζ = 1 → fastest non-oscillatory response (critical damping).

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Q157. The bandwidth of a control system is directly proportional to:
A) Damping ratio
B) Natural frequency
C) Settling time
D) Overshoot

✅ Answer: B) Natural frequency
Explanation:
Higher ωₙ → wider bandwidth → faster response.

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Q158. The condition for sustained oscillations in Barkhausen criterion is:
A) |GH| < 1 and ∠GH = 0°
B) |GH| = 1 and ∠GH = 360°
C) |GH| > 1 and ∠GH = 90°
D) |GH| = 0 and ∠GH = 180°

✅ Answer: B) |GH| = 1 and ∠GH = 360°
Explanation:
For oscillation: loop gain = 1, phase shift = 360° (0° effective).

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Q159. For discrete-time control systems, the stability criterion is:
A) Poles in left-half s-plane
B) Poles outside unit circle
C) Poles inside unit circle
D) Zeros on imaginary axis

✅ Answer: C) Poles inside unit circle
Explanation:
Discrete systems stable if all poles lie within unit circle in z-plane.

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Q160. The z-transform of a sampled signal is used for:
A) Time-domain analysis
B) Frequency-domain analysis
C) Discrete-domain analysis
D) Continuous-domain analysis

✅ Answer: C) Discrete-domain analysis
Explanation:
z-transform converts difference equations → algebraic form in z-domain.

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Q161. A phase-lead network improves:
A) Speed of response
B) Steady-state error
C) Gain margin only
D) Damping ratio only

✅ Answer: A) Speed of response
Explanation:
Lead compensator increases phase → faster transient response.

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Q162. Lag compensator improves:
A) Phase margin
B) Speed
C) Steady-state accuracy
D) Overshoot

✅ Answer: C) Steady-state accuracy
Explanation:
Lag compensator boosts low-frequency gain → reduces steady-state error.

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Q163. The number of asymptotes on root locus =
A) P + Z
B) P − Z
C) P/Z
D) Z − P

✅ Answer: B) P − Z
Explanation:
Asymptotes = number of excess poles over zeros.

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Q164. Phase margin increases when:
A) Gain increases
B) Gain decreases
C) Poles move right
D) Damping decreases

✅ Answer: B) Gain decreases
Explanation:
Reducing gain shifts crossover → improves phase margin and stability.

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Q165. The system is more stable if:
A) Gain margin and phase margin are small
B) Both margins are large
C) Margins are negative
D) Gain is high

✅ Answer: B) Both margins are large
Explanation:
Larger margins → greater tolerance to variations → higher stability.

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Q166. The effect of feedback on system sensitivity is:
A) Increases
B) Decreases
C) No change
D) Unstable

✅ Answer: B) Decreases
Explanation:
Feedback reduces sensitivity to parameter variations.

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Q167. State feedback control requires:
A) All states measured
B) One state measured
C) No measurements
D) Only output

✅ Answer: A) All states measured
Explanation:
State feedback law uses all state variables for control input.

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Q168. The transfer function can be obtained from state-space using:
A) $G(s) = C(sI - A)^{-1}B + D$
B) $G(s) = (sI - A)B + CD$
C) $G(s) = AB + CD$
D) $G(s) = (A+B)(C+D)$

✅ Answer: A) $G(s) = C(sI - A)^{-1}B + D$
Explanation:
That’s the mathematical relation between state-space and transfer function.