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.362Medium
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.363Medium
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.364Medium
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.365Medium
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.366Hard
For the characteristic equation s⁴ + 8s³ + 24s² + 32s + 15 = 0, using Routh-Hurwitz criterion, the system is:
Answer: D
Routh table construction shows all positive elements in first column, indicating all poles in left half plane, making the system stable.
Q.367Medium
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.368Medium
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.369Easy
For a Type 2 system with step input, the steady-state error is:
Answer: A
Type 2 systems have zero steady-state error for step input (constant reference), as they have at least 2 poles at origin.
Q.370Medium
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.371Easy
The transfer function of a proportional-integral (PI) controller is:
Answer: C
PI controller: Gc(s) = Kp(1 + 1/(Tis)) = Kp + Ki/s, where Ki = Kp/Ti eliminates steady-state error for constant inputs.
Q.372Medium
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.373Hard
In a root locus plot, the asymptotes for a system with 5 poles and 2 zeros meet at a point called:
Answer: B
Centroid (center of asymptotes) = [Σpoles - Σzeros]/[number of poles - number of zeros]. Number of asymptotes = 5-2 = 3.
Q.374Easy
A negative feedback control system has an open-loop transfer function G(s)H(s) = K/[s(s+2)(s+4)]. What is the type of the system?
Answer: B
The system has one pole at origin (s term in denominator), making it a Type 1 system. Type is determined by the number of poles at origin.
Q.375Easy
In Bode plot analysis, what does the gain margin represent?
Answer: B
Gain margin is the reciprocal of the magnitude at the frequency where phase is -180°. It indicates stability margin in dB.
Q.376Medium
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.377Medium
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.378Easy
The transfer function of an ideal derivative controller is:
Answer: A
A derivative controller has transfer function Gc(s) = Kd·s, where Kd is the derivative gain. It provides leading phase.
Q.379Medium
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.380Hard
For a system with Gc(s)G(s)H(s) = 100/[s(s+5)], the phase at ω = 5 rad/s is approximately:
