What is the steady-state error for a unit step input to a Type 0 system?
Answer: C
For Type 0 system with unit step input, e_ss = 1/(1 + Kp) where Kp is the position error constant.
Q.2Medium
What does the Routh-Hurwitz criterion determine?
Answer: B
Routh-Hurwitz criterion is used to determine the stability of a system by examining the characteristic equation coefficients without calculating poles.
Q.3Medium
The gain margin of a system can be determined from the bode plot as:
Answer: C
Gain margin = 1/|G(jω)| at phase crossover frequency where phase = -180°. It indicates how much gain can be increased before instability.
Q.4Medium
For a second-order system with natural frequency ωn = 2 rad/s and damping ratio ζ = 0.5, the system is:
Answer: B
When ζ < 1 (0.5 < 1), the system is underdamped with oscillatory transient response.
Q.5Medium
The rise time of a second-order underdamped system decreases with:
Answer: A
Rise time tr ≈ (π - cos⁻¹(ζ))/(ωn√(1-ζ²)). It decreases with higher ωn and appropriate ζ value.
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Q.6Medium
Which compensation technique is used to improve steady-state accuracy?
Answer: B
Lag compensation increases the system type or gain at low frequencies, improving steady-state accuracy without affecting stability significantly.
Q.7Medium
The Nyquist plot is a mapping of:
Answer: B
Nyquist plot maps the frequency response G(jω)H(jω) in the complex plane by varying ω from 0 to ∞.
Q.8Medium
The overshoot of a second-order system is independent of:
Answer: C
Overshoot = e^(-πζ/√(1-ζ²)) depends only on damping ratio ζ, not on ωn or system gain K.
Q.9Medium
Which of the following is a state-space representation advantage over transfer function?
Answer: B
State-space representation naturally handles MIMO systems, non-linear systems, and time-varying systems better than transfer functions.
Q.10Medium
In a closed-loop control system, the feedback path gain is reduced from 1 to 0.5. How does this affect the system's steady-state error?
Answer: A
Reducing feedback gain reduces the effectiveness of feedback, leading to increased steady-state error for the same input command.
Q.11Medium
For a control system, the gain crossover frequency and phase crossover frequency are equal. What does this indicate about the system's stability margin?
Answer: C
When gain crossover frequency equals phase crossover frequency, the system is at the stability boundary (phase = -180°), indicating marginal stability.
Q.12Medium
A lead compensator has a transfer function Gc(s) = K(s+2)/(s+8). What is the effect of this compensator?
Answer: B
Lead compensator has zero at -2 and pole at -8 (pole further left). This increases bandwidth and adds phase lead, improving transient response.
Q.13Medium
For a system with transfer function G(s)H(s) = 10/(s²(s+2)), the number of asymptotes in the root locus is:
Answer: B
Number of asymptotes = |number of poles - number of zeros| = |3 - 0| = 3. However, for this specific configuration with two poles at origin, effective asymptotes for root locus are 2.
Q.14Medium
Which statement is correct regarding the Bode plot of a system?
Answer: B
For minimum phase systems, magnitude and phase are related through the Kramers-Kronig relations. Knowledge of magnitude plot uniquely determines phase plot.
Q.15Medium
A PID controller is used for a plant. If only the derivative gain Kd is increased while keeping Kp and Ki constant, what is the primary effect?
Answer: B
The derivative term acts as damping in the system. Increasing Kd increases damping, which reduces overshoot and oscillations without affecting steady-state error significantly.
Q.16Medium
In frequency response analysis, what does the gain margin represent?
Answer: B
Gain margin is the factor by which the system gain at phase crossover frequency can be increased before the system becomes unstable (phase reaching -180° at unity gain).
Q.17Medium
A lag compensator has the form Gc(s) = K(s+0.1)/(s+0.01). Which characteristic does it primarily improve?
Answer: B
Lag compensator (zero at -0.1, pole at -0.01, with pole closer to origin) adds gain at low frequencies without significantly affecting phase at crossover, improving steady-state accuracy.
Q.18Medium
The characteristic equation of a closed-loop system is s³ + 6s² + 11s + 6 = 0. What are the poles?
Answer: A
The polynomial factors as (s+1)(s+2)(s+3) = 0, giving poles at -1, -2, and -3. All poles are in the left half-plane, making the system stable.
Q.19Medium
For a unity feedback system, if the open-loop DC gain is 100, what is the closed-loop DC gain?
Answer: C
Closed-loop gain = G(s)/(1+G(s)). At DC, this becomes 100/(1+100) = 101100 ≈ 0.99, showing the effect of feedback on reducing overall gain.
Q.20Medium
In the Routh-Hurwitz stability criterion, if the first column has a sign change, what does it indicate?
Answer: C
The number of sign changes in the first column of the Routh array equals the number of poles in the right half-plane. A sign change indicates at least one pole in RHP, making the system unstable.
