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
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Q.66Medium
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.67Medium
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.68Medium
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.69Medium
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.70Medium
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.71Hard
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.72Medium
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.73Medium
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.74Easy
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.75Medium
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.76Easy
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.77Medium
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.78Hard
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.79Easy
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.80Easy
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.
