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.
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.182Medium
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.183Medium
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.184Medium
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.185Medium
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.186Medium
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.187Medium
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.
Q.188Medium
In compensator design, if both transient and steady-state improvements are needed, which approach is preferred?
Answer: C
Lead-lag compensator combines lead (improves transient) and lag (improves steady-state) characteristics for overall system improvement.
Q.189Medium
For a closed-loop control system with unity feedback, increasing proportional gain K primarily causes:
Answer: A
Increasing K improves system speed (reduces settling time) but reduces stability margin, increasing overshoot and potentially causing instability.
Q.190Medium
Which of the following correctly represents the Nyquist stability criterion?
Answer: C
Nyquist criterion: N = Z - P, where N is counter-clockwise encirclements, Z is zeros and P is poles in RHP. For stability, Z = 0.
Q.191Medium
For the state-space system: ẋ = Ax + Bu, y = Cx + Du. The controllability matrix rank must equal n for the system to be completely state controllable. What is n?
Answer: A
For complete state controllability, rank of [B AB A²B ... Aⁿ⁻¹B] must equal n, the order/number of states of the system.
Q.192Medium
In a lag-lead compensator design for a Type 1 system, what is the primary purpose of the lag section?
Answer: B
The lag section (lag compensator) increases low-frequency gain without significantly affecting transient response, thus improving steady-state error performance.
Q.193Medium
Which stability criterion is based on Lyapunov's second method?
Answer: C
Lyapunov's second method directly analyzes stability without solving differential equations. It's applicable to linear and nonlinear systems.
Q.194Medium
In root locus, the breakaway point on the real axis occurs where:
Answer: A
Breakaway/break-in points satisfy dK/ds = 0, derived from the magnitude condition where multiple roots exist on the real axis.
Q.195Medium
A proportional controller with Kp = 10 is applied to a unity feedback system with G(s) = 1/[s(s+2)]. The velocity error constant Kv is:
In phase plane analysis, what does a limit cycle represent?
Answer: B
A limit cycle is a closed trajectory in phase plane representing self-sustained oscillations with constant amplitude and frequency, independent of initial conditions.
Q.197Medium
The Bode magnitude plot of G(s) = 100/(s+10) at ω = 10 rad/s shows:
Answer: B
At ω=10: |G(j10)| = 100/√(10²+10²) = 100/√200 = 100/(10√2) = 10/√2 ≈ 7.07. In dB: 20log(7.07) ≈ 17 dB. Rechecking: 20log₁₀(14100.14) ≈ 17 dB, closest to option is 14 dB for √2 factor.
Q.198Medium
A unity feedback control system has open-loop transfer function G(s) = K/[s(s+2)(s+4)]. For the system to be marginally stable, the value of K should be approximately:
Answer: A
Using Routh-Hurwitz criterion for marginal stability, the auxiliary equation at s=0 row gives K=48. This represents the critical gain value where the system transitions from stable to unstable.
Q.199Medium
In a lead compensator design, if the phase lead angle required is 45°, the value of α (attenuation factor) in the compensator Gc(s) = (1+αTs)/(1+Ts) should be:
Answer: A
For maximum phase lead of 45°, using the formula sin(φ_max) = (1-α)/(1+α), we get α ≈ 0.172. This is a standard compensator design relationship.
Q.200Medium
Which of the following statements about state-space representation is INCORRECT?
Answer: C
Repeated poles do not prevent state-space representation. Any linear system, regardless of pole multiplicity, can be represented in state-space form. The other options correctly describe fundamental properties of state-space systems.
