Sunday, November 2, 2025

In Nyquist plot, clockwise encirclements correspond to

 0°

B) -90°
C) +180°
D) 0°

Answer: A) +90°
Explanation:
Differentiation (s) leads by +90° in phase.


Q174. The system is stable if all roots of the characteristic equation have:
A) Positive real parts
B) Negative real parts
C) Imaginary roots
D) Zero real parts

Answer: B) Negative real parts
Explanation:
Negative real parts → exponential decay → stable system.


Q175. The damping ratio of a system affects mainly:
A) Rise time
B) Peak overshoot
C) Steady-state error
D) Bandwidth

Answer: B) Peak overshoot
Explanation:
Overshoot is directly related to damping ratio Mp=e(πζ/(1ζ2))M_p = e^{(-πζ/√(1−ζ²))}.


Q176. If damping ratio ζ = 0, then the system response is:
A) Overdamped
B) Undamped
C) Critically damped
D) Oscillatory with decay

Answer: B) Undamped
Explanation:
ζ = 0 → sustained sinusoidal oscillations, no decay.


Q177. A stable system has all poles located in:
A) Left half-plane
B) Right half-plane
C) Imaginary axis
D) Origin

Answer: A) Left half-plane
Explanation:
Poles in left half-plane → negative exponentials → stable.


Q178. Root locus is symmetric with respect to:
A) Real axis
B) Imaginary axis
C) Origin
D) Axis of symmetry

Answer: A) Real axis
Explanation:
Because characteristic equations have real coefficients.


Q179. The centroid of asymptotes on root locus indicates:
A) Average pole location
B) Center of gravity of system
C) Intersection of asymptotes
D) Damping

Answer: C) Intersection of asymptotes
Explanation:
Centroid = (Σpoles − Σzeros)/(P−Z); intersection of asymptotes.


Q180. Root locus begins at:
A) Zeros of G(s)H(s)
B) Poles of G(s)H(s)
C) Origin
D) Infinity

Answer: B) Poles of G(s)H(s)
Explanation:
Root locus starts from open-loop poles and ends at open-loop zeros.


Q181. The slope of a Bode magnitude plot decreases by -20 dB/decade after each:
A) Zero
B) Pole
C) DC gain
D) Integrator

Answer: B) Pole
Explanation:
Each pole introduces -20 dB/decade slope.


Q182. The gain margin is measured in:
A) Degrees
B) dB
C) Radians/sec
D) Seconds

Answer: B) dB
Explanation:
Gain margin = difference in dB between 0 dB line and gain at phase = -180°.


Q183. Nyquist plot of stable open-loop system encloses (-1, 0) point once in clockwise direction. The closed-loop system is:
A) Stable
B) Unstable
C) Marginally stable
D) Oscillatory

Answer: B) Unstable
Explanation:
One clockwise encirclement → one unstable closed-loop pole.


Q184. In discrete control, sampling period Ts should be:
A) Very large
B) Very small
C) Equal to time constant
D) Infinite

Answer: B) Very small
Explanation:
Smaller Ts gives better approximation of continuous behavior.


Q185. The z-transform of a unit impulse δ[n] is:
A) 1
B) z
C) z⁻¹
D) 0

Answer: A) 1
Explanation:
Z{δ[n]} = 1 for all n ≥ 0.


Q186. The z-transform of a unit step u[n] is:
A) 1/(1−z⁻¹)
B) 1−z
C) z/(z−1)
D) z

Answer: C) z/(z−1)
Explanation:
Sum of infinite geometric series = z/(z−1).


Q187. In discrete systems, if a pole lies outside the unit circle, it implies:
A) Stable
B) Unstable
C) Marginally stable
D) Critically stable

Answer: B) Unstable
Explanation:
Poles outside unit circle → exponentially growing sequence.


Q188. Nyquist criterion relates:
A) Open-loop poles to closed-loop zeros
B) Open-loop poles to closed-loop poles
C) Zeros to gain margin
D) None

Answer: B) Open-loop poles to closed-loop poles
Explanation:
Encirclements in Nyquist plot relate number of open-loop poles in RHP to closed-loop stability.


Q189. The characteristic equation of a closed-loop system is:
A) 1 + G(s)H(s) = 0
B) 1 − G(s)H(s) = 0
C) G(s) = H(s)
D) G(s) + H(s) = 1

Answer: A) 1 + G(s)H(s) = 0
Explanation:
Closed-loop characteristic equation comes from denominator of transfer function.


Q190. A higher-order system can be approximated to second-order when:
A) Higher poles are dominant
B) Higher poles are far left
C) Zeros dominate
D) Poles are real

Answer: B) Higher poles are far left
Explanation:
Fast-decaying poles have negligible effect → can be ignored.


Q191. The root locus provides information about:
A) Transient response
B) Steady-state response
C) Frequency response
D) Noise response

Answer: A) Transient response
Explanation:
Movement of poles shows transient behavior variation with gain.


Q192. The breakaway point on root locus can be found from:
A) dK/ds = 0
B) dG/ds = 0
C) dH/ds = 0
D) K = 0

Answer: A) dK/ds = 0
Explanation:
Condition for multiple root points → slope of K vs s is zero.


Q193. A system with one zero and three poles will have how many asymptotes?
A) 1
B) 2
C) 3
D) 4

Answer: B) 2
Explanation:
Asymptotes = P − Z = 3 − 1 = 2.


Q194. Lead compensator improves:
A) Transient response
B) Steady-state error
C) Gain
D) Delay

Answer: A) Transient response
Explanation:
Lead increases phase margin → faster and better damping.


Q195. Lag compensator improves:
A) Transient response
B) Steady-state accuracy
C) Speed
D) Phase

Answer: B) Steady-state accuracy
Explanation:
Lag compensator improves low-frequency gain, reducing steady-state error.


Q196. Proportional control improves:
A) Rise time
B) Settling time
C) Overshoot
D) Steady-state error

Answer: A) Rise time
Explanation:
Increasing proportional gain reduces rise time.


Q197. Adding integral action in a controller will:
A) Decrease steady-state error
B) Increase overshoot
C) Reduce noise
D) Reduce damping

Answer: A) Decrease steady-state error
Explanation:
Integral action drives steady-state error to zero.


Q198. The phase lag introduced by a lag compensator is always:
A) Positive
B) Negative
C) Zero
D) 90°

Answer: B) Negative
Explanation:
Lag element delays the phase → negative shift.


Q199. The open-loop transfer function G(s) = K/s(s+3). Number of asymptotes = ?
A) 0
B) 1
C) 2
D) 3

Answer: C) 2
Explanation:
Two poles, zero at infinity → 2 asymptotes.


Q200. For a stable system, gain margin and phase margin must be:
A) Positive
B) Negative
C) Zero
D) Infinite

Answer: A) Positive
Explanation:
Positive margins → safe stability.


Q201. In Bode plot, corner frequency is the frequency at which:
A) Gain = 0
B) Phase = 0°
C) Magnitude changes slope
D) Poles cancel zeros

Answer: C) Magnitude changes slope
Explanation:
Slope changes by ±20 dB/decade at corner frequency.


Q202. The final value theorem applies only if:
A) System is stable
B) System unstable
C) System marginal
D) Nonlinear

Answer: A) System is stable
Explanation:
For FVT to hold, all poles must lie in left-half-plane.


Q203. Root locus moves toward infinity along:
A) Real axis
B) Asymptotes
C) Circle
D) Parabola

Answer: B) Asymptotes
Explanation:
Locus follows asymptotic directions as K → ∞.


Q204. The number of asymptote angles = P − Z. For three poles, one zero → angles are:
A) 60°, 180°, 300°
B) 0°, ±90°
C) 45°, 135°, 225°
D) 120°, 240°

Answer: D) 120°, 240°
Explanation:
Angles = (2k+1)180°/(P−Z) = 180°/2 = 90° intervals → here 120°, 240°.


Q205. The system with transfer function 1/s² is a:
A) Type 0
B) Type 1
C) Type 2
D) Type 3

Answer: C) Type 2
Explanation:
Two poles at origin → Type 2 system.


Q206. The steady-state error for unit ramp in a Type-1 system is:
A) 0
B) Finite
C) Infinite
D) Negative

Answer: B) Finite
Explanation:
Type-1 → finite constant velocity error.


Q207. The error constant Kv = 20 → steady-state error for unit ramp =
A) 0.05
B) 0.02
C) 0.2
D) 0.5

Answer: A) 0.05
Explanation:
Ess = 1/Kv = 1/20 = 0.05.


Q208. The open-loop transfer function has poles at -1, -2, -3. The centroid of asymptotes =
A) -1
B) -2
C) -3
D) 0

Answer: B) -2
Explanation:
Centroid = (Σpoles − Σzeros)/(P−Z) = (-6−0)/(3−0) = -2.


Q209. In Nyquist plot, clockwise encirclements correspond to:
A) RHP poles
B) LHP poles
C) Stable closed-loop
D) Phase margin

Answer: A) RHP poles
Explanation:
Clockwise encirclement of (-1,0) indicates RHP closed-loop pole.


Q210. For digital control, z = e^(sT). When s = jω, then z =
A) 1
B) e^(jωT)
C) jω
D) 0

Answer: B) e^(jωT)
Explanation:
Maps s-plane jω axis to unit circle in z-plane.

No comments:

Post a Comment