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 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.345Medium
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.346Medium
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.347Easy
The static error constant for a Type-1 system with G(s) = 20/(s(s+5)(s+10)) is:
For a system to be controllable using state feedback u = -Kx, which condition must be satisfied?
Answer: C
Controllability requires the controllability matrix to have full rank n. This ensures all states can be moved from origin to any desired state
Q.349Medium
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.350Medium
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.351Easy
The corner frequency of a transfer function H(s) = 1/(1 + s/10) occurs at:
Answer: B
Corner frequency = pole frequency. Rewriting: H(s) = 10/(s+10), so pole at -10, corner frequency = 10 rad/s
Q.352Hard
For improving transient response with minimal steady-state error impact, a lead compensator should be designed to add phase lead at:
Answer: B
Lead compensator adds phase lead at its designed center frequency ωm. For transient improvement, it should coincide with gain crossover frequency to increase phase margin
Q.353Easy
A system with characteristic equation s³ + 6s² + 11s + 6 = 0 has poles at:
Answer: A
Factoring: (s+1)(s+2)(s+3) = 0 gives poles at s = -1, -2, -3. All in LHP, so system is stable
Q.354Medium
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.355Easy
A control system has an open-loop transfer function G(s)H(s) = K/[s(s+2)(s+4)]. What is the type of this system?
Answer: B
The type of a system is determined by the number of poles at origin. Here, there is one pole at origin (s term), making it Type 1.
Q.356Easy
In a Bode plot, the magnitude plot slope in dB/decade for a pole at origin is:
Answer: A
Each pole contributes -20 dB/decade slope. A single pole at origin contributes -20 dB/decade.
Q.357Easy
A second-order system has damping ratio ζ = 0.5. This system is classified as:
Answer: B
For ζ < 1, the system is underdamped with oscillatory response. ζ = 0.5 falls in this category.
Q.358Easy
Which of the following is a characteristic of a lag compensator?
Answer: B
Lag compensator reduces steady-state error by increasing the DC gain without significantly affecting transient response or stability margins.
Q.359Medium
For a unity feedback control system with G(s) = 10/[s(s+5)], the static velocity error constant Kv is:
