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Electrical Engg (EEE)

Electrical machines, power systems, circuits

321 Q 7 Topics Take Mock Test
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Difficulty: All Easy Medium Hard 131–140 of 321
Topics in Electrical Engg (EEE)
Q.131 Medium Control Systems
In compensator design, if both transient and steady-state improvements are needed, which approach is preferred?
A Lead compensator only
B Lag compensator only
C Lead-lag compensator
D PID controller without compensation
Correct Answer:  C. Lead-lag compensator
EXPLANATION

Lead-lag compensator combines lead (improves transient) and lag (improves steady-state) characteristics for overall system improvement.

Test
Q.132 Medium Control Systems
Peak overshoot of underdamped second-order system depends on:
A Damping ratio only
B Natural frequency only
C Both damping ratio and natural frequency
D Loop gain only
Correct Answer:  A. Damping ratio only
EXPLANATION

Peak overshoot Mp = e^(-πζ/√(1-ζ²)). It depends only on damping ratio ζ, not on ωₙ.

Test
Q.133 Medium Control Systems
A system with transfer function H(s) = 100/(s² + 10s + 100) has natural frequency ωₙ and damping ratio ζ respectively as:
A ωₙ = 10 rad/s, ζ = 0.5
B ωₙ = 100 rad/s, ζ = 0.1
C ωₙ = 10 rad/s, ζ = 0.707
D ωₙ = 5 rad/s, ζ = 1
Correct Answer:  A. ωₙ = 10 rad/s, ζ = 0.5
EXPLANATION

Standard form: ωₙ² = 100, so ωₙ = 10 rad/s. 2ζωₙ = 10, so ζ = 10/(2×10) = 0.5

Test
Q.134 Medium Control Systems
A lead compensator with transfer function Gc(s) = (1 + aTs)/(1 + Ts) where a > 1 provides:
A Phase lag and reduced bandwidth
B Phase lead and improved transient response
C Reduced steady-state error only
D Increased settling time
Correct Answer:  B. Phase lead and improved transient response
EXPLANATION

Lead compensator (a > 1) provides phase lead in mid-frequency range, improving transient response and system speed, hence used for transient improvement.

Test
Q.135 Medium Control Systems
In state-space representation, observability matrix rank should be equal to:
A Number of states
B Number of inputs
C Number of outputs
D Number of poles
Correct Answer:  A. Number of states
EXPLANATION

For a system to be completely observable, the observability matrix [C; CA; CA²; ...] must have rank equal to n (number of states).

Test
Q.136 Medium Control Systems
The settling time of a second-order underdamped system is approximately given by:
A ts ≈ 4/(ζωₙ)
B ts ≈ 2/(ζωₙ)
C ts ≈ 1/(ζωₙ)
D ts ≈ π/(ωₙ)
Correct Answer:  A. ts ≈ 4/(ζωₙ)
EXPLANATION

For 2% criteria, settling time ts ≈ 4/(ζωₙ). This is the standard formula for second-order systems.

Test
Q.137 Medium Control Systems
A control system with gain margin of 6 dB means:
A Gain can be increased by factor of 2
B Gain can be increased by factor of 4
C Gain can be reduced by factor of 2
D Gain can be reduced by factor of 6
Correct Answer:  A. Gain can be increased by factor of 2
EXPLANATION

Gain margin in dB = 20log₁₀(GM). Therefore, 6 = 20log₁₀(GM), GM = 10^(6/20) ≈ 2

Test
Q.138 Medium Control Systems
The Nyquist stability criterion states that for stability, the Nyquist plot should not encircle:
A Origin (0,0)
B Point (-1, 0)
C Point (1, 0)
D Point (0, 1)
Correct Answer:  B. Point (-1, 0)
EXPLANATION

The Nyquist criterion checks encirclements of the critical point (-1, 0) in the complex plane. No encirclement indicates stability for minimum phase systems.

Test
Q.139 Medium Control Systems
A system exhibits steady-state error of 0.2 for unit ramp input with loop gain K = 50. The static velocity error constant is:
A 5 sec⁻¹
B 10 sec⁻¹
C 2.5 sec⁻¹
D 20 sec⁻¹
Correct Answer:  A. 5 sec⁻¹
EXPLANATION

For ramp input, ess = 1/Kv. Given ess = 0.2, therefore Kv = 1/0.2 = 5 sec⁻¹

Test
Q.140 Medium Control Systems
For a unity feedback control system with G(s) = 10/[s(s+5)], the static velocity error constant Kv is:
A 2 sec⁻¹
B 10 sec⁻¹
C 50 sec⁻¹
D 5 sec⁻¹
Correct Answer:  A. 2 sec⁻¹
EXPLANATION

Kv = lim(s→0) s·G(s) = lim(s→0) s·10/[s(s+5)] = 10/5 = 2 sec⁻¹

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