Electrical Engineering questions for GATE, PSU recruitment and SSC JE draw from network theory, electrical machines, power systems, control systems, measurements and instrumentation, analog and digital electronics, and electromagnetic fields. Numerical answers include the formula used and the unit at each stage, which is where marks are commonly lost even when the approach is correct.
In a Bode plot, what is the phase margin when the gain crossover frequency equals the phase crossover frequency?
Answer: A
At the gain crossover frequency, magnitude is 0 dB. When this equals phase crossover frequency, the phase is -180°, giving phase margin = -180° - (-180°) = 0°
Q.23Medium
For a second-order system with ζ = 0.5 and ωn = 4 rad/s, what is the peak overshoot?
What is the effect of adding a pole at the origin to a stable open-loop system?
Answer: C
Adding a pole at origin adds -90° phase shift at all frequencies, decreasing phase margin. It also reduces high-frequency gain, decreasing gain margin
Q.25Medium
A lead compensator Gc(s) = K(s+a)/(s+b) where b > a provides maximum phase lead at frequency:
Answer: A
For lead compensator, maximum phase lead occurs at ωm = 1/√(τ₁τ₂) where τ₁ = 1/a and τ₂ = 1/b, giving ωm = √(ab)
Q.26Medium
In state-space representation, if eigenvalues of A matrix are at s = -1, -2, -3, the system is:
Answer: B
Stability depends only on eigenvalue locations (all in LHP = stable). Controllability requires rank[B AB A²B] = n, which eigenvalues alone don't determine
Q.27Medium
For an underdamped second-order system, the relationship between settling time ts and damping ratio ζ is:
Answer: C
Settling time ts ≈ 4/(ζωn) for 2% criterion, thus ts ∝ 1/(ζωn)
Q.28Medium
Which compensator is preferred for improving steady-state error without significantly affecting transient response?
Answer: B
Lag compensator increases DC gain significantly, improving steady-state error, while its phase lag is restricted to lower frequencies, minimizing transient effects
Q.29Medium
A system has poles at -2±j3. The natural frequency and damping ratio are approximately:
Answer: A
ωn = √(4+9) = √13 ≈ 3.6 rad/s, ζ = 2/√13 ≈ 0.55
Q.30Medium
In a unity feedback system, increasing loop gain K generally:
Answer: B
Higher K reduces ess proportionally but shifts root locus rightward, potentially crossing into RHP, thus reducing stability margins
Q.31Medium
In a compensated system, if phase margin PM = 30° and gain margin GM = 8 dB, this indicates:
Answer: C
PM = 30° is acceptable (typically 30-60°), GM = 8 dB (>6 dB threshold) indicates good gain stability. Both margins suggest satisfactory performance
Q.32Medium
For a unity feedback control system with G(s) = 10/[s(s+5)], the static velocity error constant Kv is:
A system exhibits steady-state error of 0.2 for unit ramp input with loop gain K = 50. The static velocity error constant is:
Answer: A
For ramp input, ess = 1/Kv. Given ess = 0.2, therefore Kv = 01.2 = 5 sec⁻¹
Q.34Medium
The Nyquist stability criterion states that for stability, the Nyquist plot should not encircle:
Answer: B
The Nyquist criterion checks encirclements of the critical point (-1, 0) in the complex plane. No encirclement indicates stability for minimum phase systems.
Q.35Medium
A control system with gain margin of 6 dB means:
Answer: A
Gain margin in dB = 20log₁₀(GM). Therefore, 6 = 20log₁₀(GM), GM = 10^(206) ≈ 2
Q.36Medium
The settling time of a second-order underdamped system is approximately given by:
Answer: A
For 2% criteria, settling time ts ≈ 4/(ζωₙ). This is the standard formula for second-order systems.
Q.37Medium
In state-space representation, observability matrix rank should be equal to:
Answer: A
For a system to be completely observable, the observability matrix [C; CA; CA²; ...] must have rank equal to n (number of states).
Q.38Medium
A lead compensator with transfer function Gc(s) = (1 + aTs)/(1 + Ts) where a > 1 provides:
Answer: B
Lead compensator (a > 1) provides phase lead in mid-frequency range, improving transient response and system speed, hence used for transient improvement.
Q.39Medium
A system with transfer function H(s) = 100/(s² + 10s + 100) has natural frequency ωₙ and damping ratio ζ respectively as:
Answer: A
Standard form: ωₙ² = 100, so ωₙ = 10 rad/s. 2ζωₙ = 10, so ζ = 10/(2×10) = 0.5
Q.40Medium
Peak overshoot of underdamped second-order system depends on:
Answer: A
Peak overshoot Mp = e^(-πζ/√(1-ζ²)). It depends only on damping ratio ζ, not on ωₙ.
